From 125231ac1a3e5fe9e0165e17469944760a21b1c0 Mon Sep 17 00:00:00 2001 From: Morten Hjorth-Jensen Date: Mon, 11 Sep 2023 06:41:34 +0200 Subject: [PATCH] update notes --- doc/LectureNotes/DataFiles/cancer.dot | 8 +- doc/LectureNotes/DataFiles/cancer.png | Bin 247221 -> 249062 bytes .../Results/FigureFiles/EoSfitting.png | Bin 19248 -> 19175 bytes .../Results/FigureFiles/Masses2016.png | Bin 17356 -> 17747 bytes .../Results/FigureFiles/Masses2016OLS.png | Bin 17795 -> 17804 bytes .../Results/FigureFiles/Masses2016Trees.png | Bin 21697 -> 21975 bytes .../_build/.doctrees/chapter1.doctree | Bin 560523 -> 563392 bytes .../_build/.doctrees/chapter10.doctree | Bin 525404 -> 525351 bytes .../_build/.doctrees/chapter11.doctree | Bin 784515 -> 785342 bytes .../_build/.doctrees/chapter2.doctree | Bin 505420 -> 505419 bytes .../_build/.doctrees/chapter3.doctree | Bin 1637313 -> 1636128 bytes .../_build/.doctrees/chapter6.doctree | Bin 310124 -> 314870 bytes .../_build/.doctrees/chapter8.doctree | 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69f5a4045..398f41587 100644 --- a/doc/LectureNotes/DataFiles/cancer.dot +++ b/doc/LectureNotes/DataFiles/cancer.dot @@ -10,19 +10,19 @@ edge [fontname="helvetica"] ; 2 -> 3 ; 4 [label="gini = 0.0\nsamples = 239\nvalue = [[239, 0]\n[0, 239]]", fillcolor="#e58139"] ; 3 -> 4 ; -5 [label="mean radius <= 12.265\ngini = 0.444\nsamples = 3\nvalue = [[2, 1]\n[1, 2]]", fillcolor="#fdf6f0"] ; +5 [label="mean concavity <= 0.029\ngini = 0.444\nsamples = 3\nvalue = [[2, 1]\n[1, 2]]", fillcolor="#fdf6f0"] ; 3 -> 5 ; 6 [label="gini = 0.0\nsamples = 1\nvalue = [[0, 1]\n[1, 0]]", fillcolor="#e58139"] ; 5 -> 6 ; 7 [label="gini = 0.0\nsamples = 2\nvalue = [[2, 0]\n[0, 2]]", fillcolor="#e58139"] ; 5 -> 7 ; -8 [label="mean texture <= 20.84\ngini = 0.397\nsamples = 11\nvalue = [[8, 3]\n[3, 8]]", fillcolor="#fae9dd"] ; +8 [label="worst texture <= 29.455\ngini = 0.397\nsamples = 11\nvalue = [[8, 3]\n[3, 8]]", fillcolor="#fae9dd"] ; 2 -> 8 ; 9 [label="gini = 0.0\nsamples = 8\nvalue = [[8, 0]\n[0, 8]]", fillcolor="#e58139"] ; 8 -> 9 ; 10 [label="gini = 0.0\nsamples = 3\nvalue = [[0, 3]\n[3, 0]]", fillcolor="#e58139"] ; 8 -> 10 ; -11 [label="area error <= 13.475\ngini = 0.278\nsamples = 6\nvalue = [[1, 5]\n[5, 1]]", fillcolor="#f4caac"] ; +11 [label="worst texture <= 24.785\ngini = 0.278\nsamples = 6\nvalue = [[1, 5]\n[5, 1]]", fillcolor="#f4caac"] ; 1 -> 11 ; 12 [label="gini = 0.0\nsamples = 1\nvalue = [[1, 0]\n[0, 1]]", fillcolor="#e58139"] ; 11 -> 12 ; @@ -30,7 +30,7 @@ edge [fontname="helvetica"] ; 11 -> 13 ; 14 [label="worst texture <= 20.645\ngini = 0.202\nsamples = 167\nvalue = [[19, 148]\n[148, 19]]", fillcolor="#f0b68c"] ; 0 -> 14 [labeldistance=2.5, labelangle=-45, headlabel="False"] ; -15 [label="worst area <= 964.4\ngini = 0.375\nsamples = 16\nvalue = [[12, 4]\n[4, 12]]", fillcolor="#f9e3d4"] ; +15 [label="worst perimeter <= 116.8\ngini = 0.375\nsamples = 16\nvalue = [[12, 4]\n[4, 12]]", fillcolor="#f9e3d4"] ; 14 -> 15 ; 16 [label="gini = 0.0\nsamples = 11\nvalue = [[11, 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week 37\n", + "**September 11-15, 2023**\n", + "\n", + "Date: **Deadline is Sunday September 17 at midnight**" + ] + }, + { + "cell_type": "markdown", + "id": "f687d0b0", + "metadata": { + "editable": true + }, + "source": [ + "## Overarching aims of the exercises this week\n", + "\n", + "This exercise deals with various mean values and variances in linear regression method (here it may be useful to look up chapter 3, equation (3.8) of [Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer](https://www.springer.com/gp/book/9780387848570)). The exercise is also a part of project 1 and can be reused in the theory part of the project.\n", + "\n", + "For more discussions on Ridge regression and calculation of expectation values, [Wessel van Wieringen's](https://arxiv.org/abs/1509.09169) article is highly recommended.\n", + "\n", + "The assumption we have made is \n", + "that there exists a continuous function $f(\\boldsymbol{x})$ and a normal distributed error $\\boldsymbol{\\varepsilon}\\sim N(0, \\sigma^2)$\n", + "which describes our data" + ] + }, + { + "cell_type": "markdown", + "id": "b0b5ae03", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\boldsymbol{y} = f(\\boldsymbol{x})+\\boldsymbol{\\varepsilon}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "a5442d69", + "metadata": { + "editable": true + }, + "source": [ + "We then approximate this function $f(\\boldsymbol{x})$ with our model $\\boldsymbol{\\tilde{y}}$ from the solution of the linear regression equations (ordinary least squares OLS), that is our\n", + "function $f$ is approximated by $\\boldsymbol{\\tilde{y}}$ where we minimized $(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2$, with" + ] + }, + { + "cell_type": "markdown", + "id": "d9ac69f5", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\boldsymbol{\\tilde{y}} = \\boldsymbol{X}\\boldsymbol{\\beta}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "6f42da1d", + "metadata": { + "editable": true + }, + "source": [ + "The matrix $\\boldsymbol{X}$ is the so-called design or feature matrix." + ] + }, + { + "cell_type": "markdown", + "id": "5690cef0", + "metadata": { + "editable": true + }, + "source": [ + "## Exercise 1: Expectation values for ordinary least squares expressions\n", + "\n", + "Show that the expectation value of $\\boldsymbol{y}$ for a given element $i$" + ] + }, + { + "cell_type": "markdown", + "id": "3834fc47", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\mathbb{E}(y_i) =\\sum_{j}x_{ij} \\beta_j=\\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "bcfd68b4", + "metadata": { + "editable": true + }, + "source": [ + "and that\n", + "its variance is" + ] + }, + { + "cell_type": "markdown", + "id": "9551e381", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\mbox{Var}(y_i) = \\sigma^2.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "e470afef", + "metadata": { + "editable": true + }, + "source": [ + "Hence, $y_i \\sim N( \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta}, \\sigma^2)$, that is $\\boldsymbol{y}$ follows a normal distribution with \n", + "mean value $\\boldsymbol{X}\\boldsymbol{\\beta}$ and variance $\\sigma^2$.\n", + "\n", + "With the OLS expressions for the optimal parameters $\\boldsymbol{\\hat{\\beta}}$ show that" + ] + }, + { + "cell_type": "markdown", + "id": "6ece00ae", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\mathbb{E}(\\boldsymbol{\\hat{\\beta}}) = \\boldsymbol{\\beta}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "98bad716", + "metadata": { + "editable": true + }, + "source": [ + "Show finally that the variance of $\\boldsymbol{\\beta}$ is" + ] + }, + { + "cell_type": "markdown", + "id": "a8dad13c", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\mbox{Var}(\\boldsymbol{\\hat{\\beta}}) = \\sigma^2 \\, (\\mathbf{X}^{T} \\mathbf{X})^{-1}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "94cddcc3", + "metadata": { + "editable": true + }, + "source": [ + "We can use the last expression when we define a [so-called confidence interval](https://en.wikipedia.org/wiki/Confidence_interval) for the parameters $\\beta$. \n", + "A given parameter $\\beta_j$ is given by the diagonal matrix element of the above matrix." + ] + }, + { + "cell_type": "markdown", + "id": "8e5c2d66", + "metadata": { + "editable": true + }, + "source": [ + "## Exercise 2: Expectation values for Ridge regression\n", + "\n", + "Show that" + ] + }, + { + "cell_type": "markdown", + "id": "5d7e493e", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\mathbb{E} \\big[ \\boldsymbol{\\beta}^{\\mathrm{Ridge}} \\big]=(\\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I}_{pp})^{-1} (\\mathbf{X}^{\\top} \\mathbf{X})\\\n", + "\\boldsymbol{\\beta}^{\\mathrm{OLS}}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "44050008", + "metadata": { + "editable": true + }, + "source": [ + "We see clearly that\n", + "$\\mathbb{E} \\big[ \\boldsymbol{\\beta}^{\\mathrm{Ridge}} \\big] \\not= \\boldsymbol{\\beta}^{\\mathrm{OLS}}$ for any $\\lambda > 0$.\n", + "\n", + "Show also that the variance is" + ] + }, + { + "cell_type": "markdown", + "id": "c0bf3608", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\mbox{Var}[\\boldsymbol{\\beta}^{\\mathrm{Ridge}}]=\\sigma^2[ \\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1} \\mathbf{X}^{T} \\mathbf{X} \\{ [ \\m\\\n", + "athbf{X}^{\\top} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1}\\}^{T},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "371484f8", + "metadata": { + "editable": true + }, + "source": [ + "and it is easy to see that if the parameter $\\lambda$ goes to infinity then the variance of Ridge parameters $\\boldsymbol{\\beta}$ goes to zero." + ] + } + ], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/doc/LectureNotes/_build/html/_sources/week37.ipynb b/doc/LectureNotes/_build/html/_sources/week37.ipynb new file mode 100644 index 000000000..3d6a1c1b9 --- /dev/null +++ b/doc/LectureNotes/_build/html/_sources/week37.ipynb @@ -0,0 +1,2912 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "5d85a8ac", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "id": "82315184", + "metadata": { + "editable": true + }, + "source": [ + "# Week 37: Statitsitcal interpretations and Resampling Methods\n", + "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University\n", + "\n", + "Date: **Sep 11, 2023**\n", + "\n", + "Copyright 1999-2023, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n", + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "id": "7132df07", + "metadata": { + "editable": true + }, + "source": [ + "## Plans for week 37\n", + "\n", + "**Material for the active learning sessions on Tuesday and Wednesday.**\n", + "\n", + " * Lecture from last week on calculations of expectation values\n", + "\n", + " * Exercise for week 37\n", + "\n", + " * Work on project 1\n", + "\n", + " * See also additional note on scaling (jupyter-notebook) sent separately. This will be discussed during the first hour of each session.\n", + "\n", + " * For more discussions of Ridge regression and calculation of averages, [Wessel van Wieringen's](https://arxiv.org/abs/1509.09169) article is highly recommended.\n", + "\n", + " \n", + "**Material for the lecture on Thursday September 7.**\n", + "\n", + " * Statistical interpretation of Ridge and Lasso regression\n", + "\n", + " * Resampling techniques, Bootstrap and cross validation and bias-variance tradeoff\n", + "\n", + " * Reads and Videos:\n", + "\n", + " * Hastie et al Chapter 7, here we recommend 7.1-7.5 and 7.10 (cross-validation) and 7.11 (bootstrap). \n", + "\n", + " * [Video on cross validation](https://www.youtube.com/watch?v=fSytzGwwBVw)\n", + "\n", + " * [Video on bias-variance tradeoff](https://www.youtube.com/watch?v=EuBBz3bI-aA)" + ] + }, + { + "cell_type": "markdown", + "id": "0928fd34", + "metadata": { + "editable": true + }, + "source": [ + "## Material from last week and relevant for the weekly exercises" + ] + }, + { + "cell_type": "markdown", + "id": "9ee88de5", + "metadata": { + "editable": true + }, + "source": [ + "## Linking the regression analysis with a statistical interpretation\n", + "\n", + "We will now couple the discussions of ordinary least squares, Ridge\n", + "and Lasso regression with a statistical interpretation, that is we\n", + "move from a linear algebra analysis to a statistical analysis. In\n", + "particular, we will focus on what the regularization terms can result\n", + "in. We will amongst other things show that the regularization\n", + "parameter can reduce considerably the variance of the parameters\n", + "$\\beta$.\n", + "\n", + "The\n", + "advantage of doing linear regression is that we actually end up with\n", + "analytical expressions for several statistical quantities. \n", + "Standard least squares and Ridge regression allow us to\n", + "derive quantities like the variance and other expectation values in a\n", + "rather straightforward way.\n", + "\n", + "It is assumed that $\\varepsilon_i\n", + "\\sim \\mathcal{N}(0, \\sigma^2)$ and the $\\varepsilon_{i}$ are\n", + "independent, i.e.:" + ] + }, + { + "cell_type": "markdown", + "id": "fd2470fe", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\begin{align*} \n", + "\\mbox{Cov}(\\varepsilon_{i_1},\n", + "\\varepsilon_{i_2}) & = \\left\\{ \\begin{array}{lcc} \\sigma^2 & \\mbox{if}\n", + "& i_1 = i_2, \\\\ 0 & \\mbox{if} & i_1 \\not= i_2. \\end{array} \\right.\n", + "\\end{align*}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "8be57b04", + "metadata": { + "editable": true + }, + "source": [ + "The randomness of $\\varepsilon_i$ implies that\n", + "$\\mathbf{y}_i$ is also a random variable. In particular,\n", + "$\\mathbf{y}_i$ is normally distributed, because $\\varepsilon_i \\sim\n", + "\\mathcal{N}(0, \\sigma^2)$ and $\\mathbf{X}_{i,\\ast} \\, \\boldsymbol{\\beta}$ is a\n", + "non-random scalar. To specify the parameters of the distribution of\n", + "$\\mathbf{y}_i$ we need to calculate its first two moments. \n", + "\n", + "Recall that $\\boldsymbol{X}$ is a matrix of dimensionality $n\\times p$. The\n", + "notation above $\\mathbf{X}_{i,\\ast}$ means that we are looking at the\n", + "row number $i$ and perform a sum over all values $p$." + ] + }, + { + "cell_type": "markdown", + "id": "ee33fde6", + "metadata": { + "editable": true + }, + "source": [ + "## Assumptions made\n", + "\n", + "The assumption we have made here can be summarized as (and this is going to be useful when we discuss the bias-variance trade off)\n", + "that there exists a function $f(\\boldsymbol{x})$ and a normal distributed error $\\boldsymbol{\\varepsilon}\\sim \\mathcal{N}(0, \\sigma^2)$\n", + "which describe our data" + ] + }, + { + "cell_type": "markdown", + "id": "14124ae5", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\boldsymbol{y} = f(\\boldsymbol{x})+\\boldsymbol{\\varepsilon}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "02600bff", + "metadata": { + "editable": true + }, + "source": [ + "We approximate this function with our model from the solution of the linear regression equations, that is our\n", + "function $f$ is approximated by $\\boldsymbol{\\tilde{y}}$ where we want to minimize $(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2$, our MSE, with" + ] + }, + { + "cell_type": "markdown", + "id": "7df4b213", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\boldsymbol{\\tilde{y}} = \\boldsymbol{X}\\boldsymbol{\\beta}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "996d8e2d", + "metadata": { + "editable": true + }, + "source": [ + "## Expectation value and variance\n", + "\n", + "We can calculate the expectation value of $\\boldsymbol{y}$ for a given element $i$" + ] + }, + { + "cell_type": "markdown", + "id": "815b60ed", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\begin{align*} \n", + "\\mathbb{E}(y_i) & =\n", + "\\mathbb{E}(\\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta}) + \\mathbb{E}(\\varepsilon_i)\n", + "\\, \\, \\, = \\, \\, \\, \\mathbf{X}_{i, \\ast} \\, \\beta, \n", + "\\end{align*}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "a93b64c7", + "metadata": { + "editable": true + }, + "source": [ + "while\n", + "its variance is" + ] + }, + { + "cell_type": "markdown", + "id": "61c06c9b", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\begin{align*} \\mbox{Var}(y_i) & = \\mathbb{E} \\{ [y_i\n", + "- \\mathbb{E}(y_i)]^2 \\} \\, \\, \\, = \\, \\, \\, \\mathbb{E} ( y_i^2 ) -\n", + "[\\mathbb{E}(y_i)]^2 \\\\ & = \\mathbb{E} [ ( \\mathbf{X}_{i, \\ast} \\,\n", + "\\beta + \\varepsilon_i )^2] - ( \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta})^2 \\\\ &\n", + "= \\mathbb{E} [ ( \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta})^2 + 2 \\varepsilon_i\n", + "\\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta} + \\varepsilon_i^2 ] - ( \\mathbf{X}_{i,\n", + "\\ast} \\, \\beta)^2 \\\\ & = ( \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta})^2 + 2\n", + "\\mathbb{E}(\\varepsilon_i) \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta} +\n", + "\\mathbb{E}(\\varepsilon_i^2 ) - ( \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta})^2 \n", + "\\\\ & = \\mathbb{E}(\\varepsilon_i^2 ) \\, \\, \\, = \\, \\, \\,\n", + "\\mbox{Var}(\\varepsilon_i) \\, \\, \\, = \\, \\, \\, \\sigma^2. \n", + "\\end{align*}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "bb1eb3a5", + "metadata": { + "editable": true + }, + "source": [ + "Hence, $y_i \\sim \\mathcal{N}( \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta}, \\sigma^2)$, that is $\\boldsymbol{y}$ follows a normal distribution with \n", + "mean value $\\boldsymbol{X}\\boldsymbol{\\beta}$ and variance $\\sigma^2$ (not be confused with the singular values of the SVD)." + ] + }, + { + "cell_type": "markdown", + "id": "ea804d82", + "metadata": { + "editable": true + }, + "source": [ + "## Expectation value and variance for $\\boldsymbol{\\beta}$\n", + "\n", + "With the OLS expressions for the optimal parameters $\\boldsymbol{\\hat{\\beta}}$ we can evaluate the expectation value" + ] + }, + { + "cell_type": "markdown", + "id": "896c9968", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\mathbb{E}(\\boldsymbol{\\hat{\\beta}}) = \\mathbb{E}[ (\\mathbf{X}^{\\top} \\mathbf{X})^{-1}\\mathbf{X}^{T} \\mathbf{Y}]=(\\mathbf{X}^{T} \\mathbf{X})^{-1}\\mathbf{X}^{T} \\mathbb{E}[ \\mathbf{Y}]=(\\mathbf{X}^{T} \\mathbf{X})^{-1} \\mathbf{X}^{T}\\mathbf{X}\\boldsymbol{\\beta}=\\boldsymbol{\\beta}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "27adffa2", + "metadata": { + "editable": true + }, + "source": [ + "This means that the estimator of the regression parameters is unbiased.\n", + "\n", + "We can also calculate the variance\n", + "\n", + "The variance of the optimal value $\\boldsymbol{\\hat{\\beta}}$ is" + ] + }, + { + "cell_type": "markdown", + "id": "b3cb4e94", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\begin{eqnarray*}\n", + "\\mbox{Var}(\\boldsymbol{\\hat{\\beta}}) & = & \\mathbb{E} \\{ [\\boldsymbol{\\beta} - \\mathbb{E}(\\boldsymbol{\\beta})] [\\boldsymbol{\\beta} - \\mathbb{E}(\\boldsymbol{\\beta})]^{T} \\}\n", + "\\\\\n", + "& = & \\mathbb{E} \\{ [(\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\mathbf{Y} - \\boldsymbol{\\beta}] \\, [(\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\mathbf{Y} - \\boldsymbol{\\beta}]^{T} \\}\n", + "\\\\\n", + "% & = & \\mathbb{E} \\{ [(\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\mathbf{Y}] \\, [(\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\mathbf{Y}]^{T} \\} - \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T}\n", + "% \\\\\n", + "% & = & \\mathbb{E} \\{ (\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\mathbf{Y} \\, \\mathbf{Y}^{T} \\, \\mathbf{X} \\, (\\mathbf{X}^{T} \\mathbf{X})^{-1} \\} - \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T}\n", + "% \\\\\n", + "& = & (\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\, \\mathbb{E} \\{ \\mathbf{Y} \\, \\mathbf{Y}^{T} \\} \\, \\mathbf{X} \\, (\\mathbf{X}^{T} \\mathbf{X})^{-1} - \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T}\n", + "\\\\\n", + "& = & (\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\, \\{ \\mathbf{X} \\, \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T} \\, \\mathbf{X}^{T} + \\sigma^2 \\} \\, \\mathbf{X} \\, (\\mathbf{X}^{T} \\mathbf{X})^{-1} - \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T}\n", + "% \\\\\n", + "% & = & (\\mathbf{X}^T \\mathbf{X})^{-1} \\, \\mathbf{X}^T \\, \\mathbf{X} \\, \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^T \\, \\mathbf{X}^T \\, \\mathbf{X} \\, (\\mathbf{X}^T % \\mathbf{X})^{-1}\n", + "% \\\\\n", + "% & & + \\, \\, \\sigma^2 \\, (\\mathbf{X}^T \\mathbf{X})^{-1} \\, \\mathbf{X}^T \\, \\mathbf{X} \\, (\\mathbf{X}^T \\mathbf{X})^{-1} - \\boldsymbol{\\beta} \\boldsymbol{\\beta}^T\n", + "\\\\\n", + "& = & \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T} + \\sigma^2 \\, (\\mathbf{X}^{T} \\mathbf{X})^{-1} - \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T}\n", + "\\, \\, \\, = \\, \\, \\, \\sigma^2 \\, (\\mathbf{X}^{T} \\mathbf{X})^{-1},\n", + "\\end{eqnarray*}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "98964900", + "metadata": { + "editable": true + }, + "source": [ + "where we have used that $\\mathbb{E} (\\mathbf{Y} \\mathbf{Y}^{T}) =\n", + "\\mathbf{X} \\, \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T} \\, \\mathbf{X}^{T} +\n", + "\\sigma^2 \\, \\mathbf{I}_{nn}$. From $\\mbox{Var}(\\boldsymbol{\\beta}) = \\sigma^2\n", + "\\, (\\mathbf{X}^{T} \\mathbf{X})^{-1}$, one obtains an estimate of the\n", + "variance of the estimate of the $j$-th regression coefficient:\n", + "$\\boldsymbol{\\sigma}^2 (\\boldsymbol{\\beta}_j ) = \\boldsymbol{\\sigma}^2 [(\\mathbf{X}^{T} \\mathbf{X})^{-1}]_{jj} $. This may be used to\n", + "construct a confidence interval for the estimates.\n", + "\n", + "In a similar way, we can obtain analytical expressions for say the\n", + "expectation values of the parameters $\\boldsymbol{\\beta}$ and their variance\n", + "when we employ Ridge regression, allowing us again to define a confidence interval. \n", + "\n", + "It is rather straightforward to show that" + ] + }, + { + "cell_type": "markdown", + "id": "ae46385d", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\mathbb{E} \\big[ \\boldsymbol{\\beta}^{\\mathrm{Ridge}} \\big]=(\\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I}_{pp})^{-1} (\\mathbf{X}^{\\top} \\mathbf{X})\\boldsymbol{\\beta}^{\\mathrm{OLS}}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "862ec8d1", + "metadata": { + "editable": true + }, + "source": [ + "We see clearly that \n", + "$\\mathbb{E} \\big[ \\boldsymbol{\\beta}^{\\mathrm{Ridge}} \\big] \\not= \\boldsymbol{\\beta}^{\\mathrm{OLS}}$ for any $\\lambda > 0$.\n", + "\n", + "We can also compute the variance as" + ] + }, + { + "cell_type": "markdown", + "id": "1c05ca70", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\mbox{Var}[\\boldsymbol{\\beta}^{\\mathrm{Ridge}}]=\\sigma^2[ \\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1} \\mathbf{X}^{T} \\mathbf{X} \\{ [ \\mathbf{X}^{\\top} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1}\\}^{T},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "a714192d", + "metadata": { + "editable": true + }, + "source": [ + "and it is easy to see that if the parameter $\\lambda$ goes to infinity then the variance of Ridge parameters $\\boldsymbol{\\beta}$ goes to zero. \n", + "\n", + "With this, we can compute the difference" + ] + }, + { + "cell_type": "markdown", + "id": "bd80e6ae", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\mbox{Var}[\\boldsymbol{\\beta}^{\\mathrm{OLS}}]-\\mbox{Var}(\\boldsymbol{\\beta}^{\\mathrm{Ridge}})=\\sigma^2 [ \\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1}[ 2\\lambda\\mathbf{I} + \\lambda^2 (\\mathbf{X}^{T} \\mathbf{X})^{-1} ] \\{ [ \\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1}\\}^{T}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "272d7c5c", + "metadata": { + "editable": true + }, + "source": [ + "The difference is non-negative definite since each component of the\n", + "matrix product is non-negative definite. \n", + "This means the variance we obtain with the standard OLS will always for $\\lambda > 0$ be larger than the variance of $\\boldsymbol{\\beta}$ obtained with the Ridge estimator. This has interesting consequences when we discuss the so-called bias-variance trade-off below. \n", + "\n", + "For more discussions of Ridge regression and calculation of averages, [Wessel van Wieringen's](https://arxiv.org/abs/1509.09169) article is highly recommended." + ] + }, + { + "cell_type": "markdown", + "id": "c87b5aa5", + "metadata": { + "editable": true + }, + "source": [ + "## Material for lecture Thursday September 14" + ] + }, + { + "cell_type": "markdown", + "id": "c946f771", + "metadata": { + "editable": true + }, + "source": [ + "## Deriving OLS from a probability distribution\n", + "\n", + "Our basic assumption when we derived the OLS equations was to assume\n", + "that our output is determined by a given continuous function\n", + "$f(\\boldsymbol{x})$ and a random noise $\\boldsymbol{\\epsilon}$ given by the normal\n", + "distribution with zero mean value and an undetermined variance\n", + "$\\sigma^2$.\n", + "\n", + "We found above that the outputs $\\boldsymbol{y}$ have a mean value given by\n", + "$\\boldsymbol{X}\\hat{\\boldsymbol{\\beta}}$ and variance $\\sigma^2$. Since the entries to\n", + "the design matrix are not stochastic variables, we can assume that the\n", + "probability distribution of our targets is also a normal distribution\n", + "but now with mean value $\\boldsymbol{X}\\hat{\\boldsymbol{\\beta}}$. This means that a\n", + "single output $y_i$ is given by the Gaussian distribution" + ] + }, + { + "cell_type": "markdown", + "id": "e6b4e7dd", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "y_i\\sim \\mathcal{N}(\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta}, \\sigma^2)=\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta})^2}{2\\sigma^2}\\right]}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "8169d91a", + "metadata": { + "editable": true + }, + "source": [ + "## Independent and Identically Distrubuted (iid)\n", + "\n", + "We assume now that the various $y_i$ values are stochastically distributed according to the above Gaussian distribution. \n", + "We define this distribution as" + ] + }, + { + "cell_type": "markdown", + "id": "99e90d11", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "p(y_i, \\boldsymbol{X}\\vert\\boldsymbol{\\beta})=\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta})^2}{2\\sigma^2}\\right]},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "0b4adc26", + "metadata": { + "editable": true + }, + "source": [ + "which reads as finding the likelihood of an event $y_i$ with the input variables $\\boldsymbol{X}$ given the parameters (to be determined) $\\boldsymbol{\\beta}$.\n", + "\n", + "Since these events are assumed to be independent and identicall distributed we can build the probability distribution function (PDF) for all possible event $\\boldsymbol{y}$ as the product of the single events, that is we have" + ] + }, + { + "cell_type": "markdown", + "id": "9ca9e238", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "p(\\boldsymbol{y},\\boldsymbol{X}\\vert\\boldsymbol{\\beta})=\\prod_{i=0}^{n-1}\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta})^2}{2\\sigma^2}\\right]}=\\prod_{i=0}^{n-1}p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\beta}).\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "23dcb3a5", + "metadata": { + "editable": true + }, + "source": [ + "We will write this in a more compact form reserving $\\boldsymbol{D}$ for the domain of events, including the ouputs (targets) and the inputs. That is\n", + "in case we have a simple one-dimensional input and output case" + ] + }, + { + "cell_type": "markdown", + "id": "67cb2d01", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\boldsymbol{D}=[(x_0,y_0), (x_1,y_1),\\dots, (x_{n-1},y_{n-1})].\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "80d807da", + "metadata": { + "editable": true + }, + "source": [ + "In the more general case the various inputs should be replaced by the possible features represented by the input data set $\\boldsymbol{X}$. \n", + "We can now rewrite the above probability as" + ] + }, + { + "cell_type": "markdown", + "id": "14b1cbfd", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "p(\\boldsymbol{D}\\vert\\boldsymbol{\\beta})=\\prod_{i=0}^{n-1}\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta})^2}{2\\sigma^2}\\right]}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "cf86395e", + "metadata": { + "editable": true + }, + "source": [ + "It is a conditional probability (see below) and reads as the likelihood of a domain of events $\\boldsymbol{D}$ given a set of parameters $\\boldsymbol{\\beta}$." + ] + }, + { + "cell_type": "markdown", + "id": "4eee417a", + "metadata": { + "editable": true + }, + "source": [ + "## Maximum Likelihood Estimation (MLE)\n", + "\n", + "In statistics, maximum likelihood estimation (MLE) is a method of\n", + "estimating the parameters of an assumed probability distribution,\n", + "given some observed data. This is achieved by maximizing a likelihood\n", + "function so that, under the assumed statistical model, the observed\n", + "data is the most probable. \n", + "\n", + "We will assume here that our events are given by the above Gaussian\n", + "distribution and we will determine the optimal parameters $\\beta$ by\n", + "maximizing the above PDF. However, computing the derivatives of a\n", + "product function is cumbersome and can easily lead to overflow and/or\n", + "underflowproblems, with potentials for loss of numerical precision.\n", + "\n", + "In practice, it is more convenient to maximize the logarithm of the\n", + "PDF because it is a monotonically increasing function of the argument.\n", + "Alternatively, and this will be our option, we will minimize the\n", + "negative of the logarithm since this is a monotonically decreasing\n", + "function.\n", + "\n", + "Note also that maximization/minimization of the logarithm of the PDF\n", + "is equivalent to the maximization/minimization of the function itself." + ] + }, + { + "cell_type": "markdown", + "id": "02893846", + "metadata": { + "editable": true + }, + "source": [ + "## A new Cost Function\n", + "\n", + "We could now define a new cost function to minimize, namely the negative logarithm of the above PDF" + ] + }, + { + "cell_type": "markdown", + "id": "098674aa", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "C(\\boldsymbol{\\beta}=-\\log{\\prod_{i=0}^{n-1}p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\beta})}=-\\sum_{i=0}^{n-1}\\log{p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\beta})},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "76b18e95", + "metadata": { + "editable": true + }, + "source": [ + "which becomes" + ] + }, + { + "cell_type": "markdown", + "id": "52c82f5e", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "C(\\boldsymbol{\\beta}=\\frac{n}{2}\\log{2\\pi\\sigma^2}+\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})\\vert\\vert_2^2}{2\\sigma^2}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "46e101f5", + "metadata": { + "editable": true + }, + "source": [ + "Taking the derivative of the *new* cost function with respect to the parameters $\\beta$ we recognize our familiar OLS equation, namely" + ] + }, + { + "cell_type": "markdown", + "id": "e8527450", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\boldsymbol{X}^T\\left(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right) =0,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "a421d3d5", + "metadata": { + "editable": true + }, + "source": [ + "which leads to the well-known OLS equation for the optimal paramters $\\beta$" + ] + }, + { + "cell_type": "markdown", + "id": "22137f8a", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\hat{\\boldsymbol{\\beta}}^{\\mathrm{OLS}}=\\left(\\boldsymbol{X}^T\\boldsymbol{X}\\right)^{-1}\\boldsymbol{X}^T\\boldsymbol{y}!\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "4eb8b2fa", + "metadata": { + "editable": true + }, + "source": [ + "Before we make a similar analysis for Ridge and Lasso regression, we need a short reminder on statistics." + ] + }, + { + "cell_type": "markdown", + "id": "8752defc", + "metadata": { + "editable": true + }, + "source": [ + "## More basic Statistics and Bayes' theorem\n", + "\n", + "A central theorem in statistics is Bayes' theorem. This theorem plays a similar role as the good old Pythagoras' theorem in geometry.\n", + "Bayes' theorem is extremely simple to derive. But to do so we need some basic axioms from statistics.\n", + "\n", + "Assume we have two domains of events $X=[x_0,x_1,\\dots,x_{n-1}]$ and $Y=[y_0,y_1,\\dots,y_{n-1}]$.\n", + "\n", + "We define also the likelihood for $X$ and $Y$ as $p(X)$ and $p(Y)$ respectively.\n", + "The likelihood of a specific event $x_i$ (or $y_i$) is then written as $p(X=x_i)$ or just $p(x_i)=p_i$. \n", + "\n", + "**Union of events is given by.**" + ] + }, + { + "cell_type": "markdown", + "id": "4befff39", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "p(X \\cup Y)= p(X)+p(Y)-p(X \\cap Y).\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "d18ce941", + "metadata": { + "editable": true + }, + "source": [ + "**The product rule (aka joint probability) is given by.**" + ] + }, + { + "cell_type": "markdown", + "id": "0a4fd449", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "p(X \\cup Y)= p(X,Y)= p(X\\vert Y)p(Y)=p(Y\\vert X)p(X),\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "ec27160e", + "metadata": { + "editable": true + }, + "source": [ + "where we read $p(X\\vert Y)$ as the likelihood of obtaining $X$ given $Y$.\n", + "\n", + "If we have independent events then $p(X,Y)=p(X)p(Y)$." + ] + }, + { + "cell_type": "markdown", + "id": "cd11746f", + "metadata": { + "editable": true + }, + "source": [ + "## Marginal Probability\n", + "\n", + "The marginal probability is defined in terms of only one of the set of variables $X,Y$. For a discrete probability we have" + ] + }, + { + "cell_type": "markdown", + "id": "b966cbbf", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "p(X)=\\sum_{i=0}^{n-1}p(X,Y=y_i)=\\sum_{i=0}^{n-1}p(X\\vert Y=y_i)p(Y=y_i)=\\sum_{i=0}^{n-1}p(X\\vert y_i)p(y_i).\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "bccd1443", + "metadata": { + "editable": true + }, + "source": [ + "## Conditional Probability\n", + "\n", + "The conditional probability, if $p(Y) > 0$, is" + ] + }, + { + "cell_type": "markdown", + "id": "7b6361b1", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "p(X\\vert Y)= \\frac{p(X,Y)}{p(Y)}=\\frac{p(X,Y)}{\\sum_{i=0}^{n-1}p(Y\\vert X=x_i)p(x_i)}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "f1ff2fe1", + "metadata": { + "editable": true + }, + "source": [ + "## Bayes' Theorem\n", + "\n", + "If we combine the conditional probability with the marginal probability and the standard product rule, we have" + ] + }, + { + "cell_type": "markdown", + "id": "ccc6b096", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "p(X\\vert Y)= \\frac{p(X,Y)}{p(Y)},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "86507503", + "metadata": { + "editable": true + }, + "source": [ + "which we can rewrite as" + ] + }, + { + "cell_type": "markdown", + "id": "bee1fbb6", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "p(X\\vert Y)= \\frac{p(X,Y)}{\\sum_{i=0}^{n-1}p(Y\\vert X=x_i)p(x_i)}=\\frac{p(Y\\vert X)p(X)}{\\sum_{i=0}^{n-1}p(Y\\vert X=x_i)p(x_i)},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "ae2e7deb", + "metadata": { + "editable": true + }, + "source": [ + "which is Bayes' theorem. It allows us to evaluate the uncertainty in in $X$ after we have observed $Y$. We can easily interchange $X$ with $Y$." + ] + }, + { + "cell_type": "markdown", + "id": "8e262661", + "metadata": { + "editable": true + }, + "source": [ + "## Interpretations of Bayes' Theorem\n", + "\n", + "The quantity $p(Y\\vert X)$ on the right-hand side of the theorem is\n", + "evaluated for the observed data $Y$ and can be viewed as a function of\n", + "the parameter space represented by $X$. This function is not\n", + "necesseraly normalized and is normally called the likelihood function.\n", + "\n", + "The function $p(X)$ on the right hand side is called the prior while the function on the left hand side is the called the posterior probability. The denominator on the right hand side serves as a normalization factor for the posterior distribution.\n", + "\n", + "Let us try to illustrate Bayes' theorem through an example." + ] + }, + { + "cell_type": "markdown", + "id": "5de65e5b", + "metadata": { + "editable": true + }, + "source": [ + "## Example of Usage of Bayes' theorem\n", + "\n", + "Let us suppose that you are undergoing a series of mammography scans in\n", + "order to rule out possible breast cancer cases. We define the\n", + "sensitivity for a positive event by the variable $X$. It takes binary\n", + "values with $X=1$ representing a positive event and $X=0$ being a\n", + "negative event. We reserve $Y$ as a classification parameter for\n", + "either a negative or a positive breast cancer confirmation. (Short note on wordings: positive here means having breast cancer, although none of us would consider this being a positive thing).\n", + "\n", + "We let $Y=1$ represent the the case of having breast cancer and $Y=0$ as not.\n", + "\n", + "Let us assume that if you have breast cancer, the test will be positive with a probability of $0.8$, that is we have" + ] + }, + { + "cell_type": "markdown", + "id": "6f1ba40c", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "p(X=1\\vert Y=1) =0.8.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "0e4cdf38", + "metadata": { + "editable": true + }, + "source": [ + "This obviously sounds scary since many would conclude that if the test is positive, there is a likelihood of $80\\%$ for having cancer.\n", + "It is however not correct, as the following Bayesian analysis shows." + ] + }, + { + "cell_type": "markdown", + "id": "76584b5c", + "metadata": { + "editable": true + }, + "source": [ + "## Doing it correctly\n", + "\n", + "If we look at various national surveys on breast cancer, the general likelihood of developing breast cancer is a very small number.\n", + "Let us assume that the prior probability in the population as a whole is" + ] + }, + { + "cell_type": "markdown", + "id": "a879a6bd", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "p(Y=1) =0.004.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "dd0274e0", + "metadata": { + "editable": true + }, + "source": [ + "We need also to account for the fact that the test may produce a false positive result (false alarm). Let us here assume that we have" + ] + }, + { + "cell_type": "markdown", + "id": "684fbc25", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "p(X=1\\vert Y=0) =0.1.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "54cd9a76", + "metadata": { + "editable": true + }, + "source": [ + "Using Bayes' theorem we can then find the posterior probability that the person has breast cancer in case of a positive test, that is we can compute" + ] + }, + { + "cell_type": "markdown", + "id": "051338d6", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "p(Y=1\\vert X=1)=\\frac{p(X=1\\vert Y=1)p(Y=1)}{p(X=1\\vert Y=1)p(Y=1)+p(X=1\\vert Y=0)p(Y=0)}=\\frac{0.8\\times 0.004}{0.8\\times 0.004+0.1\\times 0.996}=0.031.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "e5f3d505", + "metadata": { + "editable": true + }, + "source": [ + "That is, in case of a positive test, there is only a $3\\%$ chance of having breast cancer!" + ] + }, + { + "cell_type": "markdown", + "id": "ef60f6e2", + "metadata": { + "editable": true + }, + "source": [ + "## Bayes' Theorem and Ridge and Lasso Regression\n", + "\n", + "Using Bayes' theorem we can gain a better intuition about Ridge and Lasso regression. \n", + "\n", + "For ordinary least squares we postulated that the maximum likelihood for the doamin of events $\\boldsymbol{D}$ (one-dimensional case)" + ] + }, + { + "cell_type": "markdown", + "id": "dde5ce68", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\boldsymbol{D}=[(x_0,y_0), (x_1,y_1),\\dots, (x_{n-1},y_{n-1})],\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "428b7cfc", + "metadata": { + "editable": true + }, + "source": [ + "is given by" + ] + }, + { + "cell_type": "markdown", + "id": "95ad5eba", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "p(\\boldsymbol{D}\\vert\\boldsymbol{\\beta})=\\prod_{i=0}^{n-1}\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta})^2}{2\\sigma^2}\\right]}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "6e6b706c", + "metadata": { + "editable": true + }, + "source": [ + "In Bayes' theorem this function plays the role of the so-called likelihood. We could now ask the question what is the posterior probability of a parameter set $\\boldsymbol{\\beta}$ given a domain of events $\\boldsymbol{D}$? That is, how can we define the posterior probability" + ] + }, + { + "cell_type": "markdown", + "id": "6e6a60cb", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "p(\\boldsymbol{\\beta}\\vert\\boldsymbol{D}).\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "c7127db8", + "metadata": { + "editable": true + }, + "source": [ + "Bayes' theorem comes to our rescue here since (omitting the normalization constant)" + ] + }, + { + "cell_type": "markdown", + "id": "60288e6d", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "p(\\boldsymbol{\\beta}\\vert\\boldsymbol{D})\\propto p(\\boldsymbol{D}\\vert\\boldsymbol{\\beta})p(\\boldsymbol{\\beta}).\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "0e8d9dfd", + "metadata": { + "editable": true + }, + "source": [ + "We have a model for $p(\\boldsymbol{D}\\vert\\boldsymbol{\\beta})$ but need one for the **prior** $p(\\boldsymbol{\\beta}$!" + ] + }, + { + "cell_type": "markdown", + "id": "c0450362", + "metadata": { + "editable": true + }, + "source": [ + "## Ridge and Bayes\n", + "\n", + "With the posterior probability defined by a likelihood which we have\n", + "already modeled and an unknown prior, we are now ready to make\n", + "additional models for the prior.\n", + "\n", + "We can, based on our discussions of the variance of $\\boldsymbol{\\beta}$ and the mean value, assume that the prior for the values $\\boldsymbol{\\beta}$ is given by a Gaussian with mean value zero and variance $\\tau^2$, that is" + ] + }, + { + "cell_type": "markdown", + "id": "5911b76d", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "p(\\boldsymbol{\\beta})=\\prod_{j=0}^{p-1}\\exp{\\left(-\\frac{\\beta_j^2}{2\\tau^2}\\right)}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "6029916b", + "metadata": { + "editable": true + }, + "source": [ + "Our posterior probability becomes then (omitting the normalization factor which is just a constant)" + ] + }, + { + "cell_type": "markdown", + "id": "b704a6fd", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "p(\\boldsymbol{\\beta\\vert\\boldsymbol{D})}=\\prod_{i=0}^{n-1}\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta})^2}{2\\sigma^2}\\right]}\\prod_{j=0}^{p-1}\\exp{\\left(-\\frac{\\beta_j^2}{2\\tau^2}\\right)}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "60c7948c", + "metadata": { + "editable": true + }, + "source": [ + "We can now optimize this quantity with respect to $\\boldsymbol{\\beta}$. As we\n", + "did for OLS, this is most conveniently done by taking the negative\n", + "logarithm of the posterior probability. Doing so and leaving out the\n", + "constants terms that do not depend on $\\beta$, we have" + ] + }, + { + "cell_type": "markdown", + "id": "51dcd9c3", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "C(\\boldsymbol{\\beta})=\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})\\vert\\vert_2^2}{2\\sigma^2}+\\frac{1}{2\\tau^2}\\vert\\vert\\boldsymbol{\\beta}\\vert\\vert_2^2,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "c6512c09", + "metadata": { + "editable": true + }, + "source": [ + "and replacing $1/2\\tau^2$ with $\\lambda$ we have" + ] + }, + { + "cell_type": "markdown", + "id": "2c5ca7b5", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "C(\\boldsymbol{\\beta})=\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})\\vert\\vert_2^2}{2\\sigma^2}+\\lambda\\vert\\vert\\boldsymbol{\\beta}\\vert\\vert_2^2,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "1c530682", + "metadata": { + "editable": true + }, + "source": [ + "which is our Ridge cost function! Nice, isn't it?" + ] + }, + { + "cell_type": "markdown", + "id": "81771a49", + "metadata": { + "editable": true + }, + "source": [ + "## Lasso and Bayes\n", + "\n", + "To derive the Lasso cost function, we simply replace the Gaussian prior with an exponential distribution ([Laplace in this case](https://en.wikipedia.org/wiki/Laplace_distribution)) with zero mean value, that is" + ] + }, + { + "cell_type": "markdown", + "id": "c2aac5ba", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "p(\\boldsymbol{\\beta})=\\prod_{j=0}^{p-1}\\exp{\\left(-\\frac{\\vert\\beta_j\\vert}{\\tau}\\right)}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "d2e548d7", + "metadata": { + "editable": true + }, + "source": [ + "Our posterior probability becomes then (omitting the normalization factor which is just a constant)" + ] + }, + { + "cell_type": "markdown", + "id": "2901f9c7", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "p(\\boldsymbol{\\beta}\\vert\\boldsymbol{D})=\\prod_{i=0}^{n-1}\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta})^2}{2\\sigma^2}\\right]}\\prod_{j=0}^{p-1}\\exp{\\left(-\\frac{\\vert\\beta_j\\vert}{\\tau}\\right)}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "8b0dc761", + "metadata": { + "editable": true + }, + "source": [ + "Taking the negative\n", + "logarithm of the posterior probability and leaving out the\n", + "constants terms that do not depend on $\\beta$, we have" + ] + }, + { + "cell_type": "markdown", + "id": "81709208", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "C(\\boldsymbol{\\beta}=\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})\\vert\\vert_2^2}{2\\sigma^2}+\\frac{1}{\\tau}\\vert\\vert\\boldsymbol{\\beta}\\vert\\vert_1,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "757cbc8c", + "metadata": { + "editable": true + }, + "source": [ + "and replacing $1/\\tau$ with $\\lambda$ we have" + ] + }, + { + "cell_type": "markdown", + "id": "337a92ec", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "C(\\boldsymbol{\\beta}=\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})\\vert\\vert_2^2}{2\\sigma^2}+\\lambda\\vert\\vert\\boldsymbol{\\beta}\\vert\\vert_1,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "170ec18c", + "metadata": { + "editable": true + }, + "source": [ + "which is our Lasso cost function!" + ] + }, + { + "cell_type": "markdown", + "id": "1919001a", + "metadata": { + "editable": true + }, + "source": [ + "## Why resampling methods\n", + "\n", + "Before we proceed, we need to rethink what we have been doing. In our\n", + "eager to fit the data, we have omitted several important elements in\n", + "our regression analysis. In what follows we will\n", + "1. look at statistical properties, including a discussion of mean values, variance and the so-called bias-variance tradeoff\n", + "\n", + "2. introduce resampling techniques like cross-validation, bootstrapping and jackknife and more\n", + "\n", + "and discuss how to select a given model (one of the difficult parts in machine learning)." + ] + }, + { + "cell_type": "markdown", + "id": "861c96a1", + "metadata": { + "editable": true + }, + "source": [ + "## Resampling methods\n", + "Resampling methods are an indispensable tool in modern\n", + "statistics. They involve repeatedly drawing samples from a training\n", + "set and refitting a model of interest on each sample in order to\n", + "obtain additional information about the fitted model. For example, in\n", + "order to estimate the variability of a linear regression fit, we can\n", + "repeatedly draw different samples from the training data, fit a linear\n", + "regression to each new sample, and then examine the extent to which\n", + "the resulting fits differ. Such an approach may allow us to obtain\n", + "information that would not be available from fitting the model only\n", + "once using the original training sample.\n", + "\n", + "Two resampling methods are often used in Machine Learning analyses,\n", + "1. The **bootstrap method**\n", + "\n", + "2. and **Cross-Validation**\n", + "\n", + "In addition there are several other methods such as the Jackknife and the Blocking methods. We will discuss in particular\n", + "cross-validation and the bootstrap method." + ] + }, + { + "cell_type": "markdown", + "id": "9e8d9abb", + "metadata": { + "editable": true + }, + "source": [ + "## Resampling approaches can be computationally expensive\n", + "\n", + "Resampling approaches can be computationally expensive, because they\n", + "involve fitting the same statistical method multiple times using\n", + "different subsets of the training data. However, due to recent\n", + "advances in computing power, the computational requirements of\n", + "resampling methods generally are not prohibitive. In this chapter, we\n", + "discuss two of the most commonly used resampling methods,\n", + "cross-validation and the bootstrap. Both methods are important tools\n", + "in the practical application of many statistical learning\n", + "procedures. For example, cross-validation can be used to estimate the\n", + "test error associated with a given statistical learning method in\n", + "order to evaluate its performance, or to select the appropriate level\n", + "of flexibility. The process of evaluating a model’s performance is\n", + "known as model assessment, whereas the process of selecting the proper\n", + "level of flexibility for a model is known as model selection. The\n", + "bootstrap is widely used." + ] + }, + { + "cell_type": "markdown", + "id": "cca36e61", + "metadata": { + "editable": true + }, + "source": [ + "## Why resampling methods ?\n", + "**Statistical analysis.**\n", + "\n", + "* Our simulations can be treated as *computer experiments*. This is particularly the case for Monte Carlo methods which are widely used in statistical analyses.\n", + "\n", + "* The results can be analysed with the same statistical tools as we would use when analysing experimental data.\n", + "\n", + "* As in all experiments, we are looking for expectation values and an estimate of how accurate they are, i.e., possible sources for errors." + ] + }, + { + "cell_type": "markdown", + "id": "060a4427", + "metadata": { + "editable": true + }, + "source": [ + "## Statistical analysis\n", + "\n", + "* As in other experiments, many numerical experiments have two classes of errors:\n", + "\n", + " * Statistical errors\n", + "\n", + " * Systematical errors\n", + "\n", + "* Statistical errors can be estimated using standard tools from statistics\n", + "\n", + "* Systematical errors are method specific and must be treated differently from case to case." + ] + }, + { + "cell_type": "markdown", + "id": "bc631501", + "metadata": { + "editable": true + }, + "source": [ + "## Resampling methods\n", + "\n", + "With all these analytical equations for both the OLS and Ridge\n", + "regression, we will now outline how to assess a given model. This will\n", + "lead to a discussion of the so-called bias-variance tradeoff (see\n", + "below) and so-called resampling methods.\n", + "\n", + "One of the quantities we have discussed as a way to measure errors is\n", + "the mean-squared error (MSE), mainly used for fitting of continuous\n", + "functions. Another choice is the absolute error.\n", + "\n", + "In the discussions below we will focus on the MSE and in particular since we will split the data into test and training data,\n", + "we discuss the\n", + "1. prediction error or simply the **test error** $\\mathrm{Err_{Test}}$, where we have a fixed training set and the test error is the MSE arising from the data reserved for testing. We discuss also the \n", + "\n", + "2. training error $\\mathrm{Err_{Train}}$, which is the average loss over the training data.\n", + "\n", + "As our model becomes more and more complex, more of the training data tends to used. The training may thence adapt to more complicated structures in the data. This may lead to a decrease in the bias (see below for code example) and a slight increase of the variance for the test error.\n", + "For a certain level of complexity the test error will reach minimum, before starting to increase again. The\n", + "training error reaches a saturation." + ] + }, + { + "cell_type": "markdown", + "id": "65212453", + "metadata": { + "editable": true + }, + "source": [ + "## Resampling methods: Bootstrap\n", + "Bootstrapping is a [non-parametric approach](https://en.wikipedia.org/wiki/Nonparametric_statistics) to statistical inference\n", + "that substitutes computation for more traditional distributional\n", + "assumptions and asymptotic results. Bootstrapping offers a number of\n", + "advantages: \n", + "1. The bootstrap is quite general, although there are some cases in which it fails. \n", + "\n", + "2. Because it does not require distributional assumptions (such as normally distributed errors), the bootstrap can provide more accurate inferences when the data are not well behaved or when the sample size is small. \n", + "\n", + "3. It is possible to apply the bootstrap to statistics with sampling distributions that are difficult to derive, even asymptotically. \n", + "\n", + "4. It is relatively simple to apply the bootstrap to complex data-collection plans (such as stratified and clustered samples).\n", + "\n", + "The textbook by [Davison on the Bootstrap Methods and their Applications](https://www.cambridge.org/core/books/bootstrap-methods-and-their-application/ED2FD043579F27952363566DC09CBD6A) provides many more insights and proofs. In this course we will take a more practical approach and use the results and theorems provided in the literature. For those interested in reading more about the bootstrap methods, we recommend the above text and the one by [Efron and Tibshirani](https://www.routledge.com/An-Introduction-to-the-Bootstrap/Efron-Tibshirani/p/book/9780412042317).\n", + "\n", + "Before we proceed however, we need to remind ourselves about a central theorem in statistics, namely the so-called **central limit theorem**." + ] + }, + { + "cell_type": "markdown", + "id": "ce801e18", + "metadata": { + "editable": true + }, + "source": [ + "## The Central Limit Theorem\n", + "\n", + "Suppose we have a PDF $p(x)$ from which we generate a series $N$\n", + "of averages $\\mathbb{E}[x_i]$. Each mean value $\\mathbb{E}[x_i]$\n", + "is viewed as the average of a specific measurement, e.g., throwing \n", + "dice 100 times and then taking the average value, or producing a certain\n", + "amount of random numbers. \n", + "For notational ease, we set $\\mathbb{E}[x_i]=x_i$ in the discussion\n", + "which follows. We do the same for $\\mathbb{E}[z]=z$.\n", + "\n", + "If we compute the mean $z$ of $m$ such mean values $x_i$" + ] + }, + { + "cell_type": "markdown", + "id": "927e2be5", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "z=\\frac{x_1+x_2+\\dots+x_m}{m},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "fe6c7817", + "metadata": { + "editable": true + }, + "source": [ + "the question we pose is which is the PDF of the new variable $z$." + ] + }, + { + "cell_type": "markdown", + "id": "b0ae80c3", + "metadata": { + "editable": true + }, + "source": [ + "## Finding the Limit\n", + "\n", + "The probability of obtaining an average value $z$ is the product of the \n", + "probabilities of obtaining arbitrary individual mean values $x_i$,\n", + "but with the constraint that the average is $z$. We can express this through\n", + "the following expression" + ] + }, + { + "cell_type": "markdown", + "id": "b8bf320d", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\tilde{p}(z)=\\int dx_1p(x_1)\\int dx_2p(x_2)\\dots\\int dx_mp(x_m)\n", + " \\delta(z-\\frac{x_1+x_2+\\dots+x_m}{m}),\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "62def127", + "metadata": { + "editable": true + }, + "source": [ + "where the $\\delta$-function enbodies the constraint that the mean is $z$.\n", + "All measurements that lead to each individual $x_i$ are expected to\n", + "be independent, which in turn means that we can express $\\tilde{p}$ as the \n", + "product of individual $p(x_i)$. The independence assumption is important in the derivation of the central limit theorem." + ] + }, + { + "cell_type": "markdown", + "id": "71d882fb", + "metadata": { + "editable": true + }, + "source": [ + "## Rewriting the $\\delta$-function\n", + "\n", + "If we use the integral expression for the $\\delta$-function" + ] + }, + { + "cell_type": "markdown", + "id": "37f348c8", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\delta(z-\\frac{x_1+x_2+\\dots+x_m}{m})=\\frac{1}{2\\pi}\\int_{-\\infty}^{\\infty}\n", + " dq\\exp{\\left(iq(z-\\frac{x_1+x_2+\\dots+x_m}{m})\\right)},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "0b949710", + "metadata": { + "editable": true + }, + "source": [ + "and inserting $e^{i\\mu q-i\\mu q}$ where $\\mu$ is the mean value\n", + "we arrive at" + ] + }, + { + "cell_type": "markdown", + "id": "673d5c06", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\tilde{p}(z)=\\frac{1}{2\\pi}\\int_{-\\infty}^{\\infty}\n", + " dq\\exp{\\left(iq(z-\\mu)\\right)}\\left[\\int_{-\\infty}^{\\infty}\n", + " dxp(x)\\exp{\\left(iq(\\mu-x)/m\\right)}\\right]^m,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "81c0beaf", + "metadata": { + "editable": true + }, + "source": [ + "with the integral over $x$ resulting in" + ] + }, + { + "cell_type": "markdown", + "id": "e83202fb", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\int_{-\\infty}^{\\infty}dxp(x)\\exp{\\left(iq(\\mu-x)/m\\right)}=\n", + " \\int_{-\\infty}^{\\infty}dxp(x)\n", + " \\left[1+\\frac{iq(\\mu-x)}{m}-\\frac{q^2(\\mu-x)^2}{2m^2}+\\dots\\right].\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "27744da9", + "metadata": { + "editable": true + }, + "source": [ + "## Identifying Terms\n", + "\n", + "The second term on the rhs disappears since this is just the mean and \n", + "employing the definition of $\\sigma^2$ we have" + ] + }, + { + "cell_type": "markdown", + "id": "420c8688", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\int_{-\\infty}^{\\infty}dxp(x)e^{\\left(iq(\\mu-x)/m\\right)}=\n", + " 1-\\frac{q^2\\sigma^2}{2m^2}+\\dots,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "591e95ca", + "metadata": { + "editable": true + }, + "source": [ + "resulting in" + ] + }, + { + "cell_type": "markdown", + "id": "a044c8a4", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\left[\\int_{-\\infty}^{\\infty}dxp(x)\\exp{\\left(iq(\\mu-x)/m\\right)}\\right]^m\\approx\n", + " \\left[1-\\frac{q^2\\sigma^2}{2m^2}+\\dots \\right]^m,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "22b21609", + "metadata": { + "editable": true + }, + "source": [ + "and in the limit $m\\rightarrow \\infty$ we obtain" + ] + }, + { + "cell_type": "markdown", + "id": "461ba192", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\tilde{p}(z)=\\frac{1}{\\sqrt{2\\pi}(\\sigma/\\sqrt{m})}\n", + " \\exp{\\left(-\\frac{(z-\\mu)^2}{2(\\sigma/\\sqrt{m})^2}\\right)},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "97d21082", + "metadata": { + "editable": true + }, + "source": [ + "which is the normal distribution with variance\n", + "$\\sigma^2_m=\\sigma^2/m$, where $\\sigma$ is the variance of the PDF $p(x)$\n", + "and $\\mu$ is also the mean of the PDF $p(x)$." + ] + }, + { + "cell_type": "markdown", + "id": "1231f2f0", + "metadata": { + "editable": true + }, + "source": [ + "## Wrapping it up\n", + "\n", + "Thus, the central limit theorem states that the PDF $\\tilde{p}(z)$ of\n", + "the average of $m$ random values corresponding to a PDF $p(x)$ \n", + "is a normal distribution whose mean is the \n", + "mean value of the PDF $p(x)$ and whose variance is the variance\n", + "of the PDF $p(x)$ divided by $m$, the number of values used to compute $z$.\n", + "\n", + "The central limit theorem leads to the well-known expression for the\n", + "standard deviation, given by" + ] + }, + { + "cell_type": "markdown", + "id": "def2d3ca", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\sigma_m=\n", + "\\frac{\\sigma}{\\sqrt{m}}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "acdeb582", + "metadata": { + "editable": true + }, + "source": [ + "The latter is true only if the average value is known exactly. This is obtained in the limit\n", + "$m\\rightarrow \\infty$ only. Because the mean and the variance are measured quantities we obtain \n", + "the familiar expression in statistics (the so-called Bessel correction)" + ] + }, + { + "cell_type": "markdown", + "id": "ad0ce315", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\sigma_m\\approx \n", + "\\frac{\\sigma}{\\sqrt{m-1}}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "6be519fc", + "metadata": { + "editable": true + }, + "source": [ + "In many cases however the above estimate for the standard deviation,\n", + "in particular if correlations are strong, may be too simplistic. Keep\n", + "in mind that we have assumed that the variables $x$ are independent\n", + "and identically distributed. This is obviously not always the\n", + "case. For example, the random numbers (or better pseudorandom numbers)\n", + "we generate in various calculations do always exhibit some\n", + "correlations.\n", + "\n", + "The theorem is satisfied by a large class of PDFs. Note however that for a\n", + "finite $m$, it is not always possible to find a closed form /analytic expression for\n", + "$\\tilde{p}(x)$." + ] + }, + { + "cell_type": "markdown", + "id": "72497b42", + "metadata": { + "editable": true + }, + "source": [ + "## Confidence Intervals\n", + "\n", + "Confidence intervals are used in statistics and represent a type of estimate\n", + "computed from the observed data. This gives a range of values for an\n", + "unknown parameter such as the parameters $\\boldsymbol{\\beta}$ from linear regression.\n", + "\n", + "With the OLS expressions for the parameters $\\boldsymbol{\\beta}$ we found \n", + "$\\mathbb{E}(\\boldsymbol{\\beta}) = \\boldsymbol{\\beta}$, which means that the estimator of the regression parameters is unbiased.\n", + "\n", + "We found also that the variance of the estimate of the $j$-th regression coefficient is\n", + "$\\boldsymbol{\\sigma}^2 (\\boldsymbol{\\beta}_j ) = \\boldsymbol{\\sigma}^2 [(\\mathbf{X}^{T} \\mathbf{X})^{-1}]_{jj} $.\n", + "\n", + "This quantity will be used to\n", + "construct a confidence interval for the estimates." + ] + }, + { + "cell_type": "markdown", + "id": "7d663e8f", + "metadata": { + "editable": true + }, + "source": [ + "## Standard Approach based on the Normal Distribution\n", + "\n", + "We will assume that the parameters $\\beta$ follow a normal\n", + "distribution. We can then define the confidence interval. Here we will be using as\n", + "shorthands $\\mu_{\\beta}$ for the above mean value and $\\sigma_{\\beta}$\n", + "for the standard deviation. We have then a confidence interval" + ] + }, + { + "cell_type": "markdown", + "id": "4925ba6e", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\left(\\mu_{\\beta}\\pm \\frac{z\\sigma_{\\beta}}{\\sqrt{n}}\\right),\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "9fbe8108", + "metadata": { + "editable": true + }, + "source": [ + "where $z$ defines the level of certainty (or confidence). For a normal\n", + "distribution typical parameters are $z=2.576$ which corresponds to a\n", + "confidence of $99\\%$ while $z=1.96$ corresponds to a confidence of\n", + "$95\\%$. A confidence level of $95\\%$ is commonly used and it is\n", + "normally referred to as a *two-sigmas* confidence level, that is we\n", + "approximate $z\\approx 2$.\n", + "\n", + "For more discussions of confidence intervals (and in particular linked with a discussion of the bootstrap method), see chapter 5 of the textbook by [Davison on the Bootstrap Methods and their Applications](https://www.cambridge.org/core/books/bootstrap-methods-and-their-application/ED2FD043579F27952363566DC09CBD6A)\n", + "\n", + "In this text you will also find an in-depth discussion of the\n", + "Bootstrap method, why it works and various theorems related to it." + ] + }, + { + "cell_type": "markdown", + "id": "b6b2b234", + "metadata": { + "editable": true + }, + "source": [ + "## Resampling methods: Bootstrap background\n", + "\n", + "Since $\\widehat{\\beta} = \\widehat{\\beta}(\\boldsymbol{X})$ is a function of random variables,\n", + "$\\widehat{\\beta}$ itself must be a random variable. Thus it has\n", + "a pdf, call this function $p(\\boldsymbol{t})$. The aim of the bootstrap is to\n", + "estimate $p(\\boldsymbol{t})$ by the relative frequency of\n", + "$\\widehat{\\beta}$. You can think of this as using a histogram\n", + "in the place of $p(\\boldsymbol{t})$. If the relative frequency closely\n", + "resembles $p(\\vec{t})$, then using numerics, it is straight forward to\n", + "estimate all the interesting parameters of $p(\\boldsymbol{t})$ using point\n", + "estimators." + ] + }, + { + "cell_type": "markdown", + "id": "82bd2034", + "metadata": { + "editable": true + }, + "source": [ + "## Resampling methods: More Bootstrap background\n", + "\n", + "In the case that $\\widehat{\\beta}$ has\n", + "more than one component, and the components are independent, we use the\n", + "same estimator on each component separately. If the probability\n", + "density function of $X_i$, $p(x)$, had been known, then it would have\n", + "been straightforward to do this by: \n", + "1. Drawing lots of numbers from $p(x)$, suppose we call one such set of numbers $(X_1^*, X_2^*, \\cdots, X_n^*)$. \n", + "\n", + "2. Then using these numbers, we could compute a replica of $\\widehat{\\beta}$ called $\\widehat{\\beta}^*$. \n", + "\n", + "By repeated use of the above two points, many\n", + "estimates of $\\widehat{\\beta}$ can be obtained. The\n", + "idea is to use the relative frequency of $\\widehat{\\beta}^*$\n", + "(think of a histogram) as an estimate of $p(\\boldsymbol{t})$." + ] + }, + { + "cell_type": "markdown", + "id": "61a94d24", + "metadata": { + "editable": true + }, + "source": [ + "## Resampling methods: Bootstrap approach\n", + "\n", + "But\n", + "unless there is enough information available about the process that\n", + "generated $X_1,X_2,\\cdots,X_n$, $p(x)$ is in general\n", + "unknown. Therefore, [Efron in 1979](https://projecteuclid.org/euclid.aos/1176344552) asked the\n", + "question: What if we replace $p(x)$ by the relative frequency\n", + "of the observation $X_i$?\n", + "\n", + "If we draw observations in accordance with\n", + "the relative frequency of the observations, will we obtain the same\n", + "result in some asymptotic sense? The answer is yes." + ] + }, + { + "cell_type": "markdown", + "id": "fd22fd14", + "metadata": { + "editable": true + }, + "source": [ + "## Resampling methods: Bootstrap steps\n", + "\n", + "The independent bootstrap works like this: \n", + "\n", + "1. Draw with replacement $n$ numbers for the observed variables $\\boldsymbol{x} = (x_1,x_2,\\cdots,x_n)$. \n", + "\n", + "2. Define a vector $\\boldsymbol{x}^*$ containing the values which were drawn from $\\boldsymbol{x}$. \n", + "\n", + "3. Using the vector $\\boldsymbol{x}^*$ compute $\\widehat{\\beta}^*$ by evaluating $\\widehat \\beta$ under the observations $\\boldsymbol{x}^*$. \n", + "\n", + "4. Repeat this process $k$ times. \n", + "\n", + "When you are done, you can draw a histogram of the relative frequency\n", + "of $\\widehat \\beta^*$. This is your estimate of the probability\n", + "distribution $p(t)$. Using this probability distribution you can\n", + "estimate any statistics thereof. In principle you never draw the\n", + "histogram of the relative frequency of $\\widehat{\\beta}^*$. Instead\n", + "you use the estimators corresponding to the statistic of interest. For\n", + "example, if you are interested in estimating the variance of $\\widehat\n", + "\\beta$, apply the etsimator $\\widehat \\sigma^2$ to the values\n", + "$\\widehat \\beta^*$." + ] + }, + { + "cell_type": "markdown", + "id": "3497401f", + "metadata": { + "editable": true + }, + "source": [ + "## Code example for the Bootstrap method\n", + "\n", + "The following code starts with a Gaussian distribution with mean value\n", + "$\\mu =100$ and variance $\\sigma=15$. We use this to generate the data\n", + "used in the bootstrap analysis. The bootstrap analysis returns a data\n", + "set after a given number of bootstrap operations (as many as we have\n", + "data points). This data set consists of estimated mean values for each\n", + "bootstrap operation. The histogram generated by the bootstrap method\n", + "shows that the distribution for these mean values is also a Gaussian,\n", + "centered around the mean value $\\mu=100$ but with standard deviation\n", + "$\\sigma/\\sqrt{n}$, where $n$ is the number of bootstrap samples (in\n", + "this case the same as the number of original data points). The value\n", + "of the standard deviation is what we expect from the central limit\n", + "theorem." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "3ef8772f", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "\n", + "import numpy as np\n", + "from time import time\n", + "from scipy.stats import norm\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Returns mean of bootstrap samples \n", + "# Bootstrap algorithm\n", + "def bootstrap(data, datapoints):\n", + " t = np.zeros(datapoints)\n", + " n = len(data)\n", + " # non-parametric bootstrap \n", + " for i in range(datapoints):\n", + " t[i] = np.mean(data[np.random.randint(0,n,n)])\n", + " # analysis \n", + " print(\"Bootstrap Statistics :\")\n", + " print(\"original bias std. error\")\n", + " print(\"%8g %8g %14g %15g\" % (np.mean(data), np.std(data),np.mean(t),np.std(t)))\n", + " return t\n", + "\n", + "# We set the mean value to 100 and the standard deviation to 15\n", + "mu, sigma = 100, 15\n", + "datapoints = 10000\n", + "# We generate random numbers according to the normal distribution\n", + "x = mu + sigma*np.random.randn(datapoints)\n", + "# bootstrap returns the data sample \n", + "t = bootstrap(x, datapoints)" + ] + }, + { + "cell_type": "markdown", + "id": "ffe9e08b", + "metadata": { + "editable": true + }, + "source": [ + "We see that our new variance and from that the standard deviation, agrees with the central limit theorem." + ] + }, + { + "cell_type": "markdown", + "id": "c8770096", + "metadata": { + "editable": true + }, + "source": [ + "## Plotting the Histogram" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "ac35a65b", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "# the histogram of the bootstrapped data (normalized data if density = True)\n", + "n, binsboot, patches = plt.hist(t, 50, density=True, facecolor='red', alpha=0.75)\n", + "# add a 'best fit' line \n", + "y = norm.pdf(binsboot, np.mean(t), np.std(t))\n", + "lt = plt.plot(binsboot, y, 'b', linewidth=1)\n", + "plt.xlabel('x')\n", + "plt.ylabel('Probability')\n", + "plt.grid(True)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "e4ad71a5", + "metadata": { + "editable": true + }, + "source": [ + "## The bias-variance tradeoff\n", + "\n", + "We will discuss the bias-variance tradeoff in the context of\n", + "continuous predictions such as regression. However, many of the\n", + "intuitions and ideas discussed here also carry over to classification\n", + "tasks. Consider a dataset $\\mathcal{D}$ consisting of the data\n", + "$\\mathbf{X}_\\mathcal{D}=\\{(y_j, \\boldsymbol{x}_j), j=0\\ldots n-1\\}$. \n", + "\n", + "Let us assume that the true data is generated from a noisy model" + ] + }, + { + "cell_type": "markdown", + "id": "edcf8b5c", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\boldsymbol{y}=f(\\boldsymbol{x}) + \\boldsymbol{\\epsilon}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "77b70dca", + "metadata": { + "editable": true + }, + "source": [ + "where $\\epsilon$ is normally distributed with mean zero and standard deviation $\\sigma^2$.\n", + "\n", + "In our derivation of the ordinary least squares method we defined then\n", + "an approximation to the function $f$ in terms of the parameters\n", + "$\\boldsymbol{\\beta}$ and the design matrix $\\boldsymbol{X}$ which embody our model,\n", + "that is $\\boldsymbol{\\tilde{y}}=\\boldsymbol{X}\\boldsymbol{\\beta}$. \n", + "\n", + "Thereafter we found the parameters $\\boldsymbol{\\beta}$ by optimizing the means squared error via the so-called cost function" + ] + }, + { + "cell_type": "markdown", + "id": "07cccff6", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "C(\\boldsymbol{X},\\boldsymbol{\\beta}) =\\frac{1}{n}\\sum_{i=0}^{n-1}(y_i-\\tilde{y}_i)^2=\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right].\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "b04fa9bd", + "metadata": { + "editable": true + }, + "source": [ + "We can rewrite this as" + ] + }, + { + "cell_type": "markdown", + "id": "c79570c2", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\frac{1}{n}\\sum_i(f_i-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2+\\frac{1}{n}\\sum_i(\\tilde{y}_i-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2+\\sigma^2.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "9a8a6a3b", + "metadata": { + "editable": true + }, + "source": [ + "The three terms represent the square of the bias of the learning\n", + "method, which can be thought of as the error caused by the simplifying\n", + "assumptions built into the method. The second term represents the\n", + "variance of the chosen model and finally the last terms is variance of\n", + "the error $\\boldsymbol{\\epsilon}$.\n", + "\n", + "To derive this equation, we need to recall that the variance of $\\boldsymbol{y}$ and $\\boldsymbol{\\epsilon}$ are both equal to $\\sigma^2$. The mean value of $\\boldsymbol{\\epsilon}$ is by definition equal to zero. Furthermore, the function $f$ is not a stochastics variable, idem for $\\boldsymbol{\\tilde{y}}$.\n", + "We use a more compact notation in terms of the expectation value" + ] + }, + { + "cell_type": "markdown", + "id": "a9a892c2", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\mathbb{E}\\left[(\\boldsymbol{f}+\\boldsymbol{\\epsilon}-\\boldsymbol{\\tilde{y}})^2\\right],\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "0057120a", + "metadata": { + "editable": true + }, + "source": [ + "and adding and subtracting $\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right]$ we get" + ] + }, + { + "cell_type": "markdown", + "id": "9e9b0c0f", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\mathbb{E}\\left[(\\boldsymbol{f}+\\boldsymbol{\\epsilon}-\\boldsymbol{\\tilde{y}}+\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right]-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2\\right],\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "4b28d5f5", + "metadata": { + "editable": true + }, + "source": [ + "which, using the abovementioned expectation values can be rewritten as" + ] + }, + { + "cell_type": "markdown", + "id": "3fbb0a03", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\mathbb{E}\\left[(\\boldsymbol{y}-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2\\right]+\\mathrm{Var}\\left[\\boldsymbol{\\tilde{y}}\\right]+\\sigma^2,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "c367d950", + "metadata": { + "editable": true + }, + "source": [ + "that is the rewriting in terms of the so-called bias, the variance of the model $\\boldsymbol{\\tilde{y}}$ and the variance of $\\boldsymbol{\\epsilon}$." + ] + }, + { + "cell_type": "markdown", + "id": "e71acf60", + "metadata": { + "editable": true + }, + "source": [ + "## A way to Read the Bias-Variance Tradeoff\n", + "\n", + "\n", + "\n", + "\n", + "

Figure 1:

\n", + "" + ] + }, + { + "cell_type": "markdown", + "id": "93070f01", + "metadata": { + "editable": true + }, + "source": [ + "## Example code for Bias-Variance tradeoff" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "a46b37f7", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "from sklearn.linear_model import LinearRegression, Ridge, Lasso\n", + "from sklearn.preprocessing import PolynomialFeatures\n", + "from sklearn.model_selection import train_test_split\n", + "from sklearn.pipeline import make_pipeline\n", + "from sklearn.utils import resample\n", + "\n", + "np.random.seed(2018)\n", + "\n", + "n = 500\n", + "n_boostraps = 100\n", + "degree = 18 # A quite high value, just to show.\n", + "noise = 0.1\n", + "\n", + "# Make data set.\n", + "x = np.linspace(-1, 3, n).reshape(-1, 1)\n", + "y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2) + np.random.normal(0, 0.1, x.shape)\n", + "\n", + "# Hold out some test data that is never used in training.\n", + "x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2)\n", + "\n", + "# Combine x transformation and model into one operation.\n", + "# Not neccesary, but convenient.\n", + "model = make_pipeline(PolynomialFeatures(degree=degree), LinearRegression(fit_intercept=False))\n", + "\n", + "# The following (m x n_bootstraps) matrix holds the column vectors y_pred\n", + "# for each bootstrap iteration.\n", + "y_pred = np.empty((y_test.shape[0], n_boostraps))\n", + "for i in range(n_boostraps):\n", + " x_, y_ = resample(x_train, y_train)\n", + "\n", + " # Evaluate the new model on the same test data each time.\n", + " y_pred[:, i] = model.fit(x_, y_).predict(x_test).ravel()\n", + "\n", + "# Note: Expectations and variances taken w.r.t. different training\n", + "# data sets, hence the axis=1. Subsequent means are taken across the test data\n", + "# set in order to obtain a total value, but before this we have error/bias/variance\n", + "# calculated per data point in the test set.\n", + "# Note 2: The use of keepdims=True is important in the calculation of bias as this \n", + "# maintains the column vector form. Dropping this yields very unexpected results.\n", + "error = np.mean( np.mean((y_test - y_pred)**2, axis=1, keepdims=True) )\n", + "bias = np.mean( (y_test - np.mean(y_pred, axis=1, keepdims=True))**2 )\n", + "variance = np.mean( np.var(y_pred, axis=1, keepdims=True) )\n", + "print('Error:', error)\n", + "print('Bias^2:', bias)\n", + "print('Var:', variance)\n", + "print('{} >= {} + {} = {}'.format(error, bias, variance, bias+variance))\n", + "\n", + "plt.plot(x[::5, :], y[::5, :], label='f(x)')\n", + "plt.scatter(x_test, y_test, label='Data points')\n", + "plt.scatter(x_test, np.mean(y_pred, axis=1), label='Pred')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "152a6857", + "metadata": { + "editable": true + }, + "source": [ + "## Understanding what happens" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "c385948e", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "from sklearn.linear_model import LinearRegression, Ridge, Lasso\n", + "from sklearn.preprocessing import PolynomialFeatures\n", + "from sklearn.model_selection import train_test_split\n", + "from sklearn.pipeline import make_pipeline\n", + "from sklearn.utils import resample\n", + "\n", + "np.random.seed(2018)\n", + "\n", + "n = 40\n", + "n_boostraps = 100\n", + "maxdegree = 14\n", + "\n", + "\n", + "# Make data set.\n", + "x = np.linspace(-3, 3, n).reshape(-1, 1)\n", + "y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)+ np.random.normal(0, 0.1, x.shape)\n", + "error = np.zeros(maxdegree)\n", + "bias = np.zeros(maxdegree)\n", + "variance = np.zeros(maxdegree)\n", + "polydegree = np.zeros(maxdegree)\n", + "x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2)\n", + "\n", + "for degree in range(maxdegree):\n", + " model = make_pipeline(PolynomialFeatures(degree=degree), LinearRegression(fit_intercept=False))\n", + " y_pred = np.empty((y_test.shape[0], n_boostraps))\n", + " for i in range(n_boostraps):\n", + " x_, y_ = resample(x_train, y_train)\n", + " y_pred[:, i] = model.fit(x_, y_).predict(x_test).ravel()\n", + "\n", + " polydegree[degree] = degree\n", + " error[degree] = np.mean( np.mean((y_test - y_pred)**2, axis=1, keepdims=True) )\n", + " bias[degree] = np.mean( (y_test - np.mean(y_pred, axis=1, keepdims=True))**2 )\n", + " variance[degree] = np.mean( np.var(y_pred, axis=1, keepdims=True) )\n", + " print('Polynomial degree:', degree)\n", + " print('Error:', error[degree])\n", + " print('Bias^2:', bias[degree])\n", + " print('Var:', variance[degree])\n", + " print('{} >= {} + {} = {}'.format(error[degree], bias[degree], variance[degree], bias[degree]+variance[degree]))\n", + "\n", + "plt.plot(polydegree, error, label='Error')\n", + "plt.plot(polydegree, bias, label='bias')\n", + "plt.plot(polydegree, variance, label='Variance')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "a6ddc62c", + "metadata": { + "editable": true + }, + "source": [ + "## Summing up\n", + "\n", + "The bias-variance tradeoff summarizes the fundamental tension in\n", + "machine learning, particularly supervised learning, between the\n", + "complexity of a model and the amount of training data needed to train\n", + "it. Since data is often limited, in practice it is often useful to\n", + "use a less-complex model with higher bias, that is a model whose asymptotic\n", + "performance is worse than another model because it is easier to\n", + "train and less sensitive to sampling noise arising from having a\n", + "finite-sized training dataset (smaller variance). \n", + "\n", + "The above equations tell us that in\n", + "order to minimize the expected test error, we need to select a\n", + "statistical learning method that simultaneously achieves low variance\n", + "and low bias. Note that variance is inherently a nonnegative quantity,\n", + "and squared bias is also nonnegative. Hence, we see that the expected\n", + "test MSE can never lie below $Var(\\epsilon)$, the irreducible error.\n", + "\n", + "What do we mean by the variance and bias of a statistical learning\n", + "method? The variance refers to the amount by which our model would change if we\n", + "estimated it using a different training data set. Since the training\n", + "data are used to fit the statistical learning method, different\n", + "training data sets will result in a different estimate. But ideally the\n", + "estimate for our model should not vary too much between training\n", + "sets. However, if a method has high variance then small changes in\n", + "the training data can result in large changes in the model. In general, more\n", + "flexible statistical methods have higher variance.\n", + "\n", + "You may also find this recent [article](https://www.pnas.org/content/116/32/15849) of interest." + ] + }, + { + "cell_type": "markdown", + "id": "3ff69bcd", + "metadata": { + "editable": true + }, + "source": [ + "## Another Example from Scikit-Learn's Repository" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "16bd46aa", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "\"\"\"\n", + "============================\n", + "Underfitting vs. Overfitting\n", + "============================\n", + "\n", + "This example demonstrates the problems of underfitting and overfitting and\n", + "how we can use linear regression with polynomial features to approximate\n", + "nonlinear functions. The plot shows the function that we want to approximate,\n", + "which is a part of the cosine function. In addition, the samples from the\n", + "real function and the approximations of different models are displayed. The\n", + "models have polynomial features of different degrees. We can see that a\n", + "linear function (polynomial with degree 1) is not sufficient to fit the\n", + "training samples. This is called **underfitting**. A polynomial of degree 4\n", + "approximates the true function almost perfectly. However, for higher degrees\n", + "the model will **overfit** the training data, i.e. it learns the noise of the\n", + "training data.\n", + "We evaluate quantitatively **overfitting** / **underfitting** by using\n", + "cross-validation. We calculate the mean squared error (MSE) on the validation\n", + "set, the higher, the less likely the model generalizes correctly from the\n", + "training data.\n", + "\"\"\"\n", + "\n", + "print(__doc__)\n", + "\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from sklearn.pipeline import Pipeline\n", + "from sklearn.preprocessing import PolynomialFeatures\n", + "from sklearn.linear_model import LinearRegression\n", + "from sklearn.model_selection import cross_val_score\n", + "\n", + "\n", + "def true_fun(X):\n", + " return np.cos(1.5 * np.pi * X)\n", + "\n", + "np.random.seed(0)\n", + "\n", + "n_samples = 30\n", + "degrees = [1, 4, 15]\n", + "\n", + "X = np.sort(np.random.rand(n_samples))\n", + "y = true_fun(X) + np.random.randn(n_samples) * 0.1\n", + "\n", + "plt.figure(figsize=(14, 5))\n", + "for i in range(len(degrees)):\n", + " ax = plt.subplot(1, len(degrees), i + 1)\n", + " plt.setp(ax, xticks=(), yticks=())\n", + "\n", + " polynomial_features = PolynomialFeatures(degree=degrees[i],\n", + " include_bias=False)\n", + " linear_regression = LinearRegression()\n", + " pipeline = Pipeline([(\"polynomial_features\", polynomial_features),\n", + " (\"linear_regression\", linear_regression)])\n", + " pipeline.fit(X[:, np.newaxis], y)\n", + "\n", + " # Evaluate the models using crossvalidation\n", + " scores = cross_val_score(pipeline, X[:, np.newaxis], y,\n", + " scoring=\"neg_mean_squared_error\", cv=10)\n", + "\n", + " X_test = np.linspace(0, 1, 100)\n", + " plt.plot(X_test, pipeline.predict(X_test[:, np.newaxis]), label=\"Model\")\n", + " plt.plot(X_test, true_fun(X_test), label=\"True function\")\n", + " plt.scatter(X, y, edgecolor='b', s=20, label=\"Samples\")\n", + " plt.xlabel(\"x\")\n", + " plt.ylabel(\"y\")\n", + " plt.xlim((0, 1))\n", + " plt.ylim((-2, 2))\n", + " plt.legend(loc=\"best\")\n", + " plt.title(\"Degree {}\\nMSE = {:.2e}(+/- {:.2e})\".format(\n", + " degrees[i], -scores.mean(), scores.std()))\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "d898e22e", + "metadata": { + "editable": true + }, + "source": [ + "## Various steps in cross-validation\n", + "\n", + "When the repetitive splitting of the data set is done randomly,\n", + "samples may accidently end up in a fast majority of the splits in\n", + "either training or test set. Such samples may have an unbalanced\n", + "influence on either model building or prediction evaluation. To avoid\n", + "this $k$-fold cross-validation structures the data splitting. The\n", + "samples are divided into $k$ more or less equally sized exhaustive and\n", + "mutually exclusive subsets. In turn (at each split) one of these\n", + "subsets plays the role of the test set while the union of the\n", + "remaining subsets constitutes the training set. Such a splitting\n", + "warrants a balanced representation of each sample in both training and\n", + "test set over the splits. Still the division into the $k$ subsets\n", + "involves a degree of randomness. This may be fully excluded when\n", + "choosing $k=n$. This particular case is referred to as leave-one-out\n", + "cross-validation (LOOCV)." + ] + }, + { + "cell_type": "markdown", + "id": "b3c4bc74", + "metadata": { + "editable": true + }, + "source": [ + "## Cross-validation in brief\n", + "\n", + "For the various values of $k$\n", + "\n", + "1. shuffle the dataset randomly.\n", + "\n", + "2. Split the dataset into $k$ groups.\n", + "\n", + "3. For each unique group:\n", + "\n", + "a. Decide which group to use as set for test data\n", + "\n", + "b. Take the remaining groups as a training data set\n", + "\n", + "c. Fit a model on the training set and evaluate it on the test set\n", + "\n", + "d. Retain the evaluation score and discard the model\n", + "\n", + "5. Summarize the model using the sample of model evaluation scores" + ] + }, + { + "cell_type": "markdown", + "id": "35277af5", + "metadata": { + "editable": true + }, + "source": [ + "## Code Example for Cross-validation and $k$-fold Cross-validation\n", + "\n", + "The code here uses Ridge regression with cross-validation (CV) resampling and $k$-fold CV in order to fit a specific polynomial." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "6e8a01e6", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from sklearn.model_selection import KFold\n", + "from sklearn.linear_model import Ridge\n", + "from sklearn.model_selection import cross_val_score\n", + "from sklearn.preprocessing import PolynomialFeatures\n", + "\n", + "# A seed just to ensure that the random numbers are the same for every run.\n", + "# Useful for eventual debugging.\n", + "np.random.seed(3155)\n", + "\n", + "# Generate the data.\n", + "nsamples = 100\n", + "x = np.random.randn(nsamples)\n", + "y = 3*x**2 + np.random.randn(nsamples)\n", + "\n", + "## Cross-validation on Ridge regression using KFold only\n", + "\n", + "# Decide degree on polynomial to fit\n", + "poly = PolynomialFeatures(degree = 6)\n", + "\n", + "# Decide which values of lambda to use\n", + "nlambdas = 500\n", + "lambdas = np.logspace(-3, 5, nlambdas)\n", + "\n", + "# Initialize a KFold instance\n", + "k = 5\n", + "kfold = KFold(n_splits = k)\n", + "\n", + "# Perform the cross-validation to estimate MSE\n", + "scores_KFold = np.zeros((nlambdas, k))\n", + "\n", + "i = 0\n", + "for lmb in lambdas:\n", + " ridge = Ridge(alpha = lmb)\n", + " j = 0\n", + " for train_inds, test_inds in kfold.split(x):\n", + " xtrain = x[train_inds]\n", + " ytrain = y[train_inds]\n", + "\n", + " xtest = x[test_inds]\n", + " ytest = y[test_inds]\n", + "\n", + " Xtrain = poly.fit_transform(xtrain[:, np.newaxis])\n", + " ridge.fit(Xtrain, ytrain[:, np.newaxis])\n", + "\n", + " Xtest = poly.fit_transform(xtest[:, np.newaxis])\n", + " ypred = ridge.predict(Xtest)\n", + "\n", + " scores_KFold[i,j] = np.sum((ypred - ytest[:, np.newaxis])**2)/np.size(ypred)\n", + "\n", + " j += 1\n", + " i += 1\n", + "\n", + "\n", + "estimated_mse_KFold = np.mean(scores_KFold, axis = 1)\n", + "\n", + "## Cross-validation using cross_val_score from sklearn along with KFold\n", + "\n", + "# kfold is an instance initialized above as:\n", + "# kfold = KFold(n_splits = k)\n", + "\n", + "estimated_mse_sklearn = np.zeros(nlambdas)\n", + "i = 0\n", + "for lmb in lambdas:\n", + " ridge = Ridge(alpha = lmb)\n", + "\n", + " X = poly.fit_transform(x[:, np.newaxis])\n", + " estimated_mse_folds = cross_val_score(ridge, X, y[:, np.newaxis], scoring='neg_mean_squared_error', cv=kfold)\n", + "\n", + " # cross_val_score return an array containing the estimated negative mse for every fold.\n", + " # we have to the the mean of every array in order to get an estimate of the mse of the model\n", + " estimated_mse_sklearn[i] = np.mean(-estimated_mse_folds)\n", + "\n", + " i += 1\n", + "\n", + "## Plot and compare the slightly different ways to perform cross-validation\n", + "\n", + "plt.figure()\n", + "\n", + "plt.plot(np.log10(lambdas), estimated_mse_sklearn, label = 'cross_val_score')\n", + "plt.plot(np.log10(lambdas), estimated_mse_KFold, 'r--', label = 'KFold')\n", + "\n", + "plt.xlabel('log10(lambda)')\n", + "plt.ylabel('mse')\n", + "\n", + "plt.legend()\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "addf22bf", + "metadata": { + "editable": true + }, + "source": [ + "## More examples on bootstrap and cross-validation and errors" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "f1af3e2c", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "# Common imports\n", + "import os\n", + "import numpy as np\n", + "import pandas as pd\n", + "import matplotlib.pyplot as plt\n", + "from sklearn.linear_model import LinearRegression, Ridge, Lasso\n", + "from sklearn.model_selection import train_test_split\n", + "from sklearn.utils import resample\n", + "from sklearn.metrics import mean_squared_error\n", + "# Where to save the figures and data files\n", + "PROJECT_ROOT_DIR = \"Results\"\n", + "FIGURE_ID = \"Results/FigureFiles\"\n", + "DATA_ID = \"DataFiles/\"\n", + "\n", + "if not os.path.exists(PROJECT_ROOT_DIR):\n", + " os.mkdir(PROJECT_ROOT_DIR)\n", + "\n", + "if not os.path.exists(FIGURE_ID):\n", + " os.makedirs(FIGURE_ID)\n", + "\n", + "if not os.path.exists(DATA_ID):\n", + " os.makedirs(DATA_ID)\n", + "\n", + "def image_path(fig_id):\n", + " return os.path.join(FIGURE_ID, fig_id)\n", + "\n", + "def data_path(dat_id):\n", + " return os.path.join(DATA_ID, dat_id)\n", + "\n", + "def save_fig(fig_id):\n", + " plt.savefig(image_path(fig_id) + \".png\", format='png')\n", + "\n", + "infile = open(data_path(\"EoS.csv\"),'r')\n", + "\n", + "# Read the EoS data as csv file and organize the data into two arrays with density and energies\n", + "EoS = pd.read_csv(infile, names=('Density', 'Energy'))\n", + "EoS['Energy'] = pd.to_numeric(EoS['Energy'], errors='coerce')\n", + "EoS = EoS.dropna()\n", + "Energies = EoS['Energy']\n", + "Density = EoS['Density']\n", + "# The design matrix now as function of various polytrops\n", + "\n", + "Maxpolydegree = 30\n", + "X = np.zeros((len(Density),Maxpolydegree))\n", + "X[:,0] = 1.0\n", + "testerror = np.zeros(Maxpolydegree)\n", + "trainingerror = np.zeros(Maxpolydegree)\n", + "polynomial = np.zeros(Maxpolydegree)\n", + "\n", + "trials = 100\n", + "for polydegree in range(1, Maxpolydegree):\n", + " polynomial[polydegree] = polydegree\n", + " for degree in range(polydegree):\n", + " X[:,degree] = Density**(degree/3.0)\n", + "\n", + "# loop over trials in order to estimate the expectation value of the MSE\n", + " testerror[polydegree] = 0.0\n", + " trainingerror[polydegree] = 0.0\n", + " for samples in range(trials):\n", + " x_train, x_test, y_train, y_test = train_test_split(X, Energies, test_size=0.2)\n", + " model = LinearRegression(fit_intercept=False).fit(x_train, y_train)\n", + " ypred = model.predict(x_train)\n", + " ytilde = model.predict(x_test)\n", + " testerror[polydegree] += mean_squared_error(y_test, ytilde)\n", + " trainingerror[polydegree] += mean_squared_error(y_train, ypred) \n", + "\n", + " testerror[polydegree] /= trials\n", + " trainingerror[polydegree] /= trials\n", + " print(\"Degree of polynomial: %3d\"% polynomial[polydegree])\n", + " print(\"Mean squared error on training data: %.8f\" % trainingerror[polydegree])\n", + " print(\"Mean squared error on test data: %.8f\" % testerror[polydegree])\n", + "\n", + "plt.plot(polynomial, np.log10(trainingerror), label='Training Error')\n", + "plt.plot(polynomial, np.log10(testerror), label='Test Error')\n", + "plt.xlabel('Polynomial degree')\n", + "plt.ylabel('log10[MSE]')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "c05b2a3a", + "metadata": { + "editable": true + }, + "source": [ + "Note that we kept the intercept column in the fitting here. This means that we need to set the **intercept** in the call to the **Scikit-Learn** function as **False**. Alternatively, we could have set up the design matrix $X$ without the first column of ones." + ] + }, + { + "cell_type": "markdown", + "id": "be50bfa2", + "metadata": { + "editable": true + }, + "source": [ + "## The same example but now with cross-validation\n", + "\n", + "In this example we keep the intercept column again but add cross-validation in order to estimate the best possible value of the means squared error." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "33fb2f51", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "# Common imports\n", + "import os\n", + "import numpy as np\n", + "import pandas as pd\n", + "import matplotlib.pyplot as plt\n", + "from sklearn.linear_model import LinearRegression, Ridge, Lasso\n", + "from sklearn.metrics import mean_squared_error\n", + "from sklearn.model_selection import KFold\n", + "from sklearn.model_selection import cross_val_score\n", + "\n", + "\n", + "# Where to save the figures and data files\n", + "PROJECT_ROOT_DIR = \"Results\"\n", + "FIGURE_ID = \"Results/FigureFiles\"\n", + "DATA_ID = \"DataFiles/\"\n", + "\n", + "if not os.path.exists(PROJECT_ROOT_DIR):\n", + " os.mkdir(PROJECT_ROOT_DIR)\n", + "\n", + "if not os.path.exists(FIGURE_ID):\n", + " os.makedirs(FIGURE_ID)\n", + "\n", + "if not os.path.exists(DATA_ID):\n", + " os.makedirs(DATA_ID)\n", + "\n", + "def image_path(fig_id):\n", + " return os.path.join(FIGURE_ID, fig_id)\n", + "\n", + "def data_path(dat_id):\n", + " return os.path.join(DATA_ID, dat_id)\n", + "\n", + "def save_fig(fig_id):\n", + " plt.savefig(image_path(fig_id) + \".png\", format='png')\n", + "\n", + "infile = open(data_path(\"EoS.csv\"),'r')\n", + "\n", + "# Read the EoS data as csv file and organize the data into two arrays with density and energies\n", + "EoS = pd.read_csv(infile, names=('Density', 'Energy'))\n", + "EoS['Energy'] = pd.to_numeric(EoS['Energy'], errors='coerce')\n", + "EoS = EoS.dropna()\n", + "Energies = EoS['Energy']\n", + "Density = EoS['Density']\n", + "# The design matrix now as function of various polytrops\n", + "\n", + "Maxpolydegree = 30\n", + "X = np.zeros((len(Density),Maxpolydegree))\n", + "X[:,0] = 1.0\n", + "estimated_mse_sklearn = np.zeros(Maxpolydegree)\n", + "polynomial = np.zeros(Maxpolydegree)\n", + "k =5\n", + "kfold = KFold(n_splits = k)\n", + "\n", + "for polydegree in range(1, Maxpolydegree):\n", + " polynomial[polydegree] = polydegree\n", + " for degree in range(polydegree):\n", + " X[:,degree] = Density**(degree/3.0)\n", + " OLS = LinearRegression(fit_intercept=False)\n", + "# loop over trials in order to estimate the expectation value of the MSE\n", + " estimated_mse_folds = cross_val_score(OLS, X, Energies, scoring='neg_mean_squared_error', cv=kfold)\n", + "#[:, np.newaxis]\n", + " estimated_mse_sklearn[polydegree] = np.mean(-estimated_mse_folds)\n", + "\n", + "plt.plot(polynomial, np.log10(estimated_mse_sklearn), label='Test Error')\n", + "plt.xlabel('Polynomial degree')\n", + "plt.ylabel('log10[MSE]')\n", + "plt.legend()\n", + "plt.show()" + ] + } + ], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/doc/LectureNotes/_build/html/chapter1.html b/doc/LectureNotes/_build/html/chapter1.html index 743ba1f0e..f7a949576 100644 --- a/doc/LectureNotes/_build/html/chapter1.html +++ b/doc/LectureNotes/_build/html/chapter1.html @@ -278,6 +278,28 @@ const thebe_selector_output = ".output, .cell_output" Week 36: Statistical interpretation of Linear Regression and Resampling techniques +
  • + + Exercises week 37 + +
    • +
  • + + Week 37: Statitsitcal interpretations and Resampling Methods + +
    • + +

    + + Projects + +

    + @@ -994,13 +1016,13 @@ example of the functionality of Scikit-Learn.

    The intercept alpha: 
- [2.05177695]
+ [1.89563529]
 Coefficient beta : 
- [[5.05971574]]
-Mean squared error: 0.28
-Variance score: 0.88
+ [[5.26512016]]
+Mean squared error: 0.27
+Variance score: 0.87
 Mean squared log error: 0.01
-Mean absolute error: 0.45
+Mean absolute error: 0.41
    _images/chapter1_19_1.png @@ -1100,7 +1122,7 @@ a linear \(x\)-dependence we s
    _images/chapter1_33_0.png -
    0.004999999999999997
+
    0.0049999999999999845
    diff --git a/doc/LectureNotes/_build/html/chapter10.html b/doc/LectureNotes/_build/html/chapter10.html index 8421d3a58..796a1d331 100644 --- a/doc/LectureNotes/_build/html/chapter10.html +++ b/doc/LectureNotes/_build/html/chapter10.html @@ -278,6 +278,28 @@ const thebe_selector_output = ".output, .cell_output" Week 36: Statistical interpretation of Linear Regression and Resampling techniques +
  • + + Exercises week 37 + +
    • +
  • + + Week 37: Statitsitcal interpretations and Resampling Methods + +
    • + +

    + + Projects + +

    +
    @@ -1311,7 +1333,7 @@ the Hadamard product, meaning element-wise multiplication.

    Old accuracy on training data: 0.1440501043841336
    -
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -1645,7 +1667,7 @@ Lambda =  10.0
 Accuracy score on test set:  0.19166666666666668
    -
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -1654,7 +1676,7 @@ Lambda =  1e-05
 Accuracy score on test set:  0.10555555555555556
    -
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -1663,7 +1685,7 @@ Lambda =  0.0001
 Accuracy score on test set:  0.08611111111111111
    -
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -1672,7 +1694,7 @@ Lambda =  0.001
 Accuracy score on test set:  0.10555555555555556
    -
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -1681,7 +1703,7 @@ Lambda =  0.01
 Accuracy score on test set:  0.08888888888888889
    -
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -1690,7 +1712,7 @@ Lambda =  0.1
 Accuracy score on test set:  0.08611111111111111
    -
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -1699,7 +1721,7 @@ Lambda =  1.0
 Accuracy score on test set:  0.08888888888888889
    -
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -1708,11 +1730,11 @@ Lambda =  10.0
 Accuracy score on test set:  0.09166666666666666
    -
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -1721,11 +1743,11 @@ Lambda =  1e-05
 Accuracy score on test set:  0.07777777777777778
    -
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -1734,11 +1756,11 @@ Lambda =  0.0001
 Accuracy score on test set:  0.07777777777777778
    -
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -1747,11 +1769,11 @@ Lambda =  0.001
 Accuracy score on test set:  0.07777777777777778
    -
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -1760,11 +1782,11 @@ Lambda =  0.01
 Accuracy score on test set:  0.07777777777777778
    -
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -1773,7 +1795,7 @@ Lambda =  0.1
 Accuracy score on test set:  0.07777777777777778
    -
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -1782,11 +1804,11 @@ Lambda =  1.0
 Accuracy score on test set:  0.10555555555555556
    -
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -1795,11 +1817,11 @@ Lambda =  10.0
 Accuracy score on test set:  0.07777777777777778
    -
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -1808,11 +1830,11 @@ Lambda =  1e-05
 Accuracy score on test set:  0.07777777777777778
    -
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -1821,11 +1843,11 @@ Lambda =  0.0001
 Accuracy score on test set:  0.07777777777777778
    -
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -1834,11 +1856,11 @@ Lambda =  0.001
 Accuracy score on test set:  0.07777777777777778
    -
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -1847,11 +1869,11 @@ Lambda =  0.01
 Accuracy score on test set:  0.07777777777777778
    -
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -1860,11 +1882,11 @@ Lambda =  0.1
 Accuracy score on test set:  0.07777777777777778
    -
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -1873,11 +1895,11 @@ Lambda =  1.0
 Accuracy score on test set:  0.07777777777777778
    -
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -1930,15 +1952,15 @@ Accuracy score on test set:  0.07777777777777778
    -
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -2258,26 +2280,26 @@ Accuracy score on test set:  0.17777777777777778
 Learning rate  =  1.0
 Lambda =  0.1
 Accuracy score on test set:  0.08333333333333333
-
-Learning rate  =  1.0
-Lambda =  1.0
-Accuracy score on test set:  0.08888888888888889
 
    Learning rate  =  1.0
+Lambda =  1.0
+Accuracy score on test set:  0.08888888888888889
+
+Learning rate  =  1.0
 Lambda =  10.0
 Accuracy score on test set:  0.09444444444444444
 
 Learning rate  =  10.0
 Lambda =  1e-05
 Accuracy score on test set:  0.17222222222222222
-
-Learning rate  =  10.0
-Lambda =  0.0001
-Accuracy score on test set:  0.11666666666666667
 
    Learning rate  =  10.0
+Lambda =  0.0001
+Accuracy score on test set:  0.11666666666666667
+
+Learning rate  =  10.0
 Lambda =  0.001
 Accuracy score on test set:  0.10555555555555556
 
diff --git a/doc/LectureNotes/_build/html/chapter11.html b/doc/LectureNotes/_build/html/chapter11.html
index 6f0a465b2..92d140dec 100644
--- a/doc/LectureNotes/_build/html/chapter11.html
+++ b/doc/LectureNotes/_build/html/chapter11.html
@@ -278,6 +278,28 @@ const thebe_selector_output = ".output, .cell_output"
    Week 36: Statistical interpretation of Linear Regression and Resampling techniques
   
  
+ 
  • 
+  
+   Exercises week 37
+  
+ 
    • 
+ 
  • 
+  
+   Week 37: Statitsitcal interpretations and Resampling Methods
+  
+ 
    • 
+
+
    
+ 
+  Projects
+ 
+
    
+
    @@ -2653,31 +2675,25 @@ Using TensorFlow results in a much better execution time. Try it!

    22 for parent, ingrad in zip(node.parents, ingrads): 23 outgrads[parent] = add_outgrads(outgrads.get(parent), ingrad) -File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:78, in defvjp.<locals>.vjp_argnums.<locals>.<lambda>(g) - 76 vjp_0 = vjp_0_fun(ans, *args, **kwargs) - 77 vjp_1 = vjp_1_fun(ans, *args, **kwargs) ----> 78 return lambda g: (vjp_0(g), vjp_1(g)) - 79 else: - 80 vjps = [vjps_dict[argnum](ans, *args, **kwargs) for argnum in argnums] +File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:67, in defvjp.<locals>.vjp_argnums.<locals>.<lambda>(g) + 64 raise NotImplementedError( + 65 "VJP of {} wrt argnum 0 not defined".format(fun.__name__)) + 66 vjp = vjpfun(ans, *args, **kwargs) +---> 67 return lambda g: (vjp(g),) + 68 elif L == 2: + 69 argnum_0, argnum_1 = argnums -File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:660, in unbroadcast_f.<locals>.<lambda>(g) - 658 def unbroadcast_f(target, f): - 659 target_meta = anp.metadata(target) ---> 660 return lambda g: unbroadcast(f(g), target_meta) +File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:423, in matmul_vjp_1.<locals>.<lambda>(g) + 421 A_ndim = anp.ndim(A) + 422 B_meta = anp.metadata(B) +--> 423 return lambda g: matmul_adjoint_1(A, g, A_ndim, B_meta) -File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:35, in <lambda>(g) - 30 # ----- Binary ufuncs ----- - 32 defvjp(anp.add, lambda ans, x, y : unbroadcast_f(x, lambda g: g), - 33 lambda ans, x, y : unbroadcast_f(y, lambda g: g)) - 34 defvjp(anp.multiply, lambda ans, x, y : unbroadcast_f(x, lambda g: y * g), ----> 35 lambda ans, x, y : unbroadcast_f(y, lambda g: x * g)) - 36 defvjp(anp.subtract, lambda ans, x, y : unbroadcast_f(x, lambda g: g), - 37 lambda ans, x, y : unbroadcast_f(y, lambda g: -g)) - 38 defvjp(anp.divide, lambda ans, x, y : unbroadcast_f(x, lambda g: g / y), - 39 lambda ans, x, y : unbroadcast_f(y, lambda g: - g * x / y**2)) - -File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_boxes.py:35, in ArrayBox.__rmul__(self, other) ----> 35 def __rmul__(self, other): return anp.multiply(other, self) +File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:410, in matmul_adjoint_1(A, G, A_ndim, B_meta) + 408 else: # We need to swap the last two axes of A + 409 A = anp.swapaxes(A, A_ndim - 2, A_ndim - 1) +--> 410 result = anp.matmul(A, G) + 411 if B_is_vec: + 412 result = anp.squeeze(result, anp.ndim(G) - 1) File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:45, in primitive.<locals>.f_wrapped(*args, **kwargs) 43 argnums = tuple(argnum for argnum, _ in boxed_args) @@ -2692,13 +2708,30 @@ Using TensorFlow results in a much better execution time. Try it!

    35 .format(fun_name, parent_argnums)) ---> 36 self.vjp = vjpmaker(parent_argnums, value, args, kwargs) -File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:56, in defvjp.<locals>.vjp_argnums(argnums, ans, args, kwargs) - 53 argnums = kwargs.get('argnums', count()) - 54 vjps_dict = {argnum : translate_vjp(vjpmaker, fun, argnum) - 55 for argnum, vjpmaker in zip(argnums, vjpmakers)} ----> 56 def vjp_argnums(argnums, ans, args, kwargs): - 57 L = len(argnums) - 58 # These first two cases are just optimizations +File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:77, in defvjp.<locals>.vjp_argnums(argnums, ans, args, kwargs) + 74 raise NotImplementedError( + 75 "VJP of {} wrt argnums 0, 1 not defined".format(fun.__name__)) + 76 vjp_0 = vjp_0_fun(ans, *args, **kwargs) +---> 77 vjp_1 = vjp_1_fun(ans, *args, **kwargs) + 78 return lambda g: (vjp_0(g), vjp_1(g)) + 79 else: + +File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:422, in matmul_vjp_1(ans, A, B) + 420 def matmul_vjp_1(ans, A, B): + 421 A_ndim = anp.ndim(A) +--> 422 B_meta = anp.metadata(B) + 423 return lambda g: matmul_adjoint_1(A, g, A_ndim, B_meta) + +File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:61, in notrace_primitive.<locals>.f_wrapped(*args, **kwargs) + 58 @wraps(f_raw) + 59 def f_wrapped(*args, **kwargs): + 60 argvals = map(getval, args) +---> 61 return f_raw(*argvals, **kwargs) + +File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_wrapper.py:148, in metadata(A) + 146 @notrace_primitive + 147 def metadata(A): +--> 148 return _np.shape(A), _np.ndim(A), _np.result_type(A), _np.iscomplexobj(A) KeyboardInterrupt:
    diff --git a/doc/LectureNotes/_build/html/chapter12.html b/doc/LectureNotes/_build/html/chapter12.html index 08ef4f16d..f969e3b51 100644 --- a/doc/LectureNotes/_build/html/chapter12.html +++ b/doc/LectureNotes/_build/html/chapter12.html @@ -278,6 +278,28 @@ const thebe_selector_output = ".output, .cell_output" Week 36: Statistical interpretation of Linear Regression and Resampling techniques +
  • + + Exercises week 37 + +
    • +
  • + + Week 37: Statitsitcal interpretations and Resampling Methods + +
    • + +

    + + Projects + +

    +
    diff --git a/doc/LectureNotes/_build/html/chapter13.html b/doc/LectureNotes/_build/html/chapter13.html index 6b8dd6b5b..81f1db1a4 100644 --- a/doc/LectureNotes/_build/html/chapter13.html +++ b/doc/LectureNotes/_build/html/chapter13.html @@ -278,6 +278,28 @@ const thebe_selector_output = ".output, .cell_output" Week 36: Statistical interpretation of Linear Regression and Resampling techniques +
  • + + Exercises week 37 + +
    • +
  • + + Week 37: Statitsitcal interpretations and Resampling Methods + +
    • + +

    + + Projects + +

    +
    diff --git a/doc/LectureNotes/_build/html/chapter2.html b/doc/LectureNotes/_build/html/chapter2.html index 224ea1380..7834f4242 100644 --- a/doc/LectureNotes/_build/html/chapter2.html +++ b/doc/LectureNotes/_build/html/chapter2.html @@ -278,6 +278,28 @@ const thebe_selector_output = ".output, .cell_output" Week 36: Statistical interpretation of Linear Regression and Resampling techniques +
  • + + Exercises week 37 + +
    • +
  • + + Week 37: Statitsitcal interpretations and Resampling Methods + +
    • + +

    + + Projects + +

    + @@ -1243,10 +1265,10 @@ covariance matrix through the np.linalg.eig() function.

    -
    0.01354598394614281
-4.037503978471253
-[[0.95927495 2.85834701]
- [2.85834701 9.70233292]]
+
    0.003788445263115483
+3.859628021353642
+[[0.93725291 2.8143782 ]
+ [2.8143782  9.64008343]]
    @@ -1283,10 +1305,10 @@ a more brute force way. Here we scale the mean values for each column of the des
    -
    0.09309965420717024
-1.6546329613199204
-[[1.         0.57867898]
- [0.57867898 1.        ]]
+
    0.07783152589039466
+2.06282378894371
+[[1.         0.66124684]
+ [0.66124684 1.        ]]
    @@ -1316,30 +1338,30 @@ this matrix we easily see that it is a positive definite matrix.

    -
    [[-0.49352496 -2.38394242]
- [ 0.18849928  0.73454039]
- [-1.58104393 -5.16350368]
- [ 0.34695383  0.23472346]
- [ 0.95953339  2.95819409]
- [ 1.31331481  3.59914165]
- [ 0.14846308  1.1180677 ]
- [ 0.26022531  0.23496851]
- [-0.12178678 -0.11868087]
- [-1.02063403 -1.21350883]]
+
    [[-0.15499979 -0.6924788 ]
+ [-0.50456256 -2.98248681]
+ [ 1.97264311  4.4533029 ]
+ [ 0.03286166 -0.27108228]
+ [-0.97421755 -3.08891672]
+ [-0.3744637   0.62223681]
+ [ 1.18655084  4.67392051]
+ [-0.51719273 -1.14648903]
+ [-0.51793145 -1.51975002]
+ [-0.14868784 -0.04825655]]
           0         1
-0 -0.493525 -2.383942
-1  0.188499  0.734540
-2 -1.581044 -5.163504
-3  0.346954  0.234723
-4  0.959533  2.958194
-5  1.313315  3.599142
-6  0.148463  1.118068
-7  0.260225  0.234969
-8 -0.121787 -0.118681
-9 -1.020634 -1.213509
+0 -0.155000 -0.692479
+1 -0.504563 -2.982487
+2  1.972643  4.453303
+3  0.032862 -0.271082
+4 -0.974218 -3.088917
+5 -0.374464  0.622237
+6  1.186551  4.673921
+7 -0.517193 -1.146489
+8 -0.517931 -1.519750
+9 -0.148688 -0.048257
           0         1
-0  1.000000  0.949087
-1  0.949087  1.000000
+0  1.000000  0.929612
+1  0.929612  1.000000
    @@ -1396,37 +1418,37 @@ this matrix we easily see that it is a positive definite matrix.

         0         1         2         3         4         5         6         7   \
 0   0.0  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000   
-1   0.0  0.072254  0.074732  0.075050  0.075400  0.075727  0.068297  0.068215   
-2   0.0  0.074732  0.078265  0.076259  0.077107  0.077954  0.068418  0.068622   
-3   0.0  0.075050  0.076259  0.082604  0.082322  0.081988  0.078133  0.077663   
-4   0.0  0.075400  0.077107  0.082322  0.082315  0.082269  0.077387  0.077091   
-5   0.0  0.075727  0.077954  0.081988  0.082269  0.082525  0.076570  0.076454   
-6   0.0  0.068297  0.068418  0.078133  0.077387  0.076570  0.075952  0.075224   
-7   0.0  0.068215  0.068622  0.077663  0.077091  0.076454  0.075224  0.074613   
-8   0.0  0.068168  0.068876  0.077210  0.076818  0.076371  0.074495  0.074004   
-9   0.0  0.068163  0.069190  0.076775  0.076573  0.076324  0.073764  0.073398   
-10  0.0  0.060924  0.060401  0.071600  0.070601  0.069522  0.071006  0.070141   
-11  0.0  0.060711  0.060369  0.071122  0.070241  0.069283  0.070364  0.069583   
-12  0.0  0.060534  0.060381  0.070671  0.069911  0.069080  0.069738  0.069042   
-13  0.0  0.060394  0.060441  0.070245  0.069612  0.068912  0.069125  0.068517   
-14  0.0  0.060291  0.060550  0.069845  0.069343  0.068782  0.068524  0.068007   
+1   0.0  0.079729  0.074983  0.077280  0.078995  0.080168  0.068546  0.070577   
+2   0.0  0.074983  0.071314  0.073127  0.075035  0.076519  0.065106  0.067183   
+3   0.0  0.077280  0.073127  0.080979  0.082487  0.083517  0.075422  0.077387   
+4   0.0  0.078995  0.075035  0.082487  0.084199  0.085447  0.076612  0.078725   
+5   0.0  0.080168  0.076519  0.083517  0.085447  0.086942  0.077411  0.079671   
+6   0.0  0.068546  0.065106  0.075422  0.076612  0.077411  0.072522  0.074203   
+7   0.0  0.070577  0.067183  0.077387  0.078725  0.079671  0.074203  0.076007   
+8   0.0  0.072638  0.069315  0.079368  0.080867  0.081977  0.075887  0.077825   
+9   0.0  0.074671  0.071455  0.081315  0.082991  0.084282  0.077536  0.079615   
+10  0.0  0.060425  0.057463  0.068676  0.069583  0.070161  0.067515  0.068912   
+11  0.0  0.062197  0.059245  0.070486  0.071501  0.072183  0.069129  0.070625   
+12  0.0  0.064048  0.061113  0.072365  0.073497  0.074293  0.070797  0.072398   
+13  0.0  0.065974  0.063066  0.074310  0.075569  0.076491  0.072515  0.074230   
+14  0.0  0.067967  0.065101  0.076313  0.077711  0.078771  0.074276  0.076112   
 
           8         9         10        11        12        13        14  
 0   0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  
-1   0.068168  0.068163  0.060924  0.060711  0.060534  0.060394  0.060291  
-2   0.068876  0.069190  0.060401  0.060369  0.060381  0.060441  0.060550  
-3   0.077210  0.076775  0.071600  0.071122  0.070671  0.070245  0.069845  
-4   0.076818  0.076573  0.070601  0.070241  0.069911  0.069612  0.069343  
-5   0.076371  0.076324  0.069522  0.069283  0.069080  0.068912  0.068782  
-6   0.074495  0.073764  0.071006  0.070364  0.069738  0.069125  0.068524  
-7   0.074004  0.073398  0.070141  0.069583  0.069042  0.068517  0.068007  
-8   0.073520  0.073044  0.069265  0.068792  0.068339  0.067905  0.067489  
-9   0.073044  0.072705  0.068375  0.067990  0.067628  0.067288  0.066969  
-10  0.069265  0.068375  0.067400  0.066672  0.065952  0.065237  0.064526  
-11  0.068792  0.067990  0.066672  0.066006  0.065350  0.064701  0.064057  
-12  0.068339  0.067628  0.065952  0.065350  0.064759  0.064176  0.063600  
-13  0.067905  0.067288  0.065237  0.064701  0.064176  0.063661  0.063155  
-14  0.067489  0.066969  0.064526  0.064057  0.063600  0.063155  0.062721  
+1   0.072638  0.074671  0.060425  0.062197  0.064048  0.065974  0.067967  
+2   0.069315  0.071455  0.057463  0.059245  0.061113  0.063066  0.065101  
+3   0.079368  0.081315  0.068676  0.070486  0.072365  0.074310  0.076313  
+4   0.080867  0.082991  0.069583  0.071501  0.073497  0.075569  0.077711  
+5   0.081977  0.084282  0.070161  0.072183  0.074293  0.076491  0.078771  
+6   0.075887  0.077536  0.067515  0.069129  0.070797  0.072515  0.074276  
+7   0.077825  0.079615  0.068912  0.070625  0.072398  0.074230  0.076112  
+8   0.079786  0.081728  0.070305  0.072122  0.074007  0.075958  0.077970  
+9   0.081728  0.083834  0.071659  0.073585  0.075587  0.077666  0.079814  
+10  0.070305  0.071659  0.063876  0.065268  0.066700  0.068170  0.069669  
+11  0.072122  0.073585  0.065268  0.066742  0.068261  0.069823  0.071420  
+12  0.074007  0.075587  0.066700  0.068261  0.069873  0.071534  0.073236  
+13  0.075958  0.077666  0.068170  0.069823  0.071534  0.073300  0.075115  
+14  0.077970  0.079814  0.069669  0.071420  0.073236  0.075115  0.077050
    diff --git a/doc/LectureNotes/_build/html/chapter3.html b/doc/LectureNotes/_build/html/chapter3.html index 907f755d4..2194b7987 100644 --- a/doc/LectureNotes/_build/html/chapter3.html +++ b/doc/LectureNotes/_build/html/chapter3.html @@ -278,6 +278,28 @@ const thebe_selector_output = ".output, .cell_output" Week 36: Statistical interpretation of Linear Regression and Resampling techniques +
  • + + Exercises week 37 + +
    • +
  • + + Week 37: Statitsitcal interpretations and Resampling Methods + +
    • + +

    + + Projects + +

    +
    @@ -797,10 +819,10 @@ number \(i\) is left out. Usin
    -
    Runtime: 0.0907788 sec
+
    Runtime: 0.101292 sec
 Jackknife Statistics :
 original           bias      std. error
- 100.022        100.012        0.148734
+ 99.9618        99.9518        0.148771
    @@ -1019,7 +1041,7 @@ theorem.

    Bootstrap Statistics :
 original           bias      std. error
- 99.7522  14.9594        99.7525        0.149991
+ 99.9169   14.873        99.9169        0.147934
    @@ -1273,9 +1295,7 @@ Error: 0.021592704588021178 Bias^2: 0.010516485576646504 Var: 0.01107621901137467 0.021592704588021178 >= 0.010516485576646504 + 0.01107621901137467 = 0.021592704588021174 -
    -
    -
    Polynomial degree: 11
+Polynomial degree: 11
 Error: 0.07160048164232538
 Bias^2: 0.014436800088896381
 Var: 0.05716368155342902
@@ -1285,7 +1305,9 @@ Error: 0.11547777218876518
 Bias^2: 0.016285782696017142
 Var: 0.09919198949274803
 0.11547777218876518 >= 0.016285782696017142 + 0.09919198949274803 = 0.11547777218876518
-Polynomial degree: 13
+
    +
    +
    Polynomial degree: 13
 Error: 0.2284246870217162
 Bias^2: 0.01975416527168255
 Var: 0.20867052175003364
@@ -1545,12 +1567,12 @@ Mean squared error on test data: 0.17446471
 Degree of polynomial:  13
 Mean squared error on training data: 0.00759119
 Mean squared error on test data: 1.08131003
-Degree of polynomial:  14
-Mean squared error on training data: 0.00472199
-Mean squared error on test data: 0.81333804
    -
    Degree of polynomial:  15
+
    Degree of polynomial:  14
+Mean squared error on training data: 0.00472199
+Mean squared error on test data: 0.81333804
+Degree of polynomial:  15
 Mean squared error on training data: 0.00410478
 Mean squared error on test data: 92.09172409
 Degree of polynomial:  16
@@ -1588,12 +1610,12 @@ Mean squared error on test data: 128664.31650694
 Degree of polynomial:  26
 Mean squared error on training data: 0.00076905
 Mean squared error on test data: 19003.94822514
-
    
-
    
-
    Degree of polynomial:  27
+Degree of polynomial:  27
 Mean squared error on training data: 0.00068946
 Mean squared error on test data: 2379.66219404
-Degree of polynomial:  28
+
    
+
    
+
    Degree of polynomial:  28
 Mean squared error on training data: 0.00062595
 Mean squared error on test data: 4082.19983530
 Degree of polynomial:  29
@@ -1601,9 +1623,9 @@ Mean squared error on training data: 0.00060705
 Mean squared error on test data: 3250.17647619
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16213/626635268.py:73: RuntimeWarning: divide by zero encountered in log10
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/626635268.py:73: RuntimeWarning: divide by zero encountered in log10
   plt.plot(polynomial, np.log10(trainingerror), label='Training Error')
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16213/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
   plt.plot(polynomial, np.log10(testerror), label='Test Error')
 
    
 
    
@@ -1837,7 +1859,7 @@ cross-validation (LOOCV).
    
 
    
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16213/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10
   plt.plot(polynomial, np.log10(estimated_mse_sklearn), label='Test Error')
 
    
 
    
@@ -2726,9 +2748,9 @@ linear system as an equation would reduce this down to
 
    
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16213/4162706317.py:6: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/4162706317.py:6: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
   cb = fig.colorbar(im)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16213/4162706317.py:7: UserWarning: FixedFormatter should only be used together with FixedLocator
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/4162706317.py:7: UserWarning: FixedFormatter should only be used together with FixedLocator
   cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
 
    
 
    
@@ -2872,9 +2894,9 @@ with the form utilized in linear regression, viz.
    
 
    
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16213/3777801602.py:6: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/3777801602.py:6: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
   cb = fig.colorbar(im)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16213/3777801602.py:7: UserWarning: FixedFormatter should only be used together with FixedLocator
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/3777801602.py:7: UserWarning: FixedFormatter should only be used together with FixedLocator
   cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
 
    
 
    
@@ -2914,9 +2936,9 @@ cost function is given by
    
 
    
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16213/438060758.py:9: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/438060758.py:9: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
   cb = fig.colorbar(im)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16213/438060758.py:10: UserWarning: FixedFormatter should only be used together with FixedLocator
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/438060758.py:10: UserWarning: FixedFormatter should only be used together with FixedLocator
   cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
 
    
 
    
@@ -2951,9 +2973,9 @@ cost function is given by
    
 
    
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16213/3544313922.py:8: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/3544313922.py:8: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
   cb = fig.colorbar(im)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16213/3544313922.py:9: UserWarning: FixedFormatter should only be used together with FixedLocator
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/3544313922.py:9: UserWarning: FixedFormatter should only be used together with FixedLocator
   cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
 
    
 
    
@@ -3006,43 +3028,43 @@ constant as opposed to ridge and OLS. We get a sparse solution with
 
    
 
    
 
    
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    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_coordinate_descent.py:647: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations, check the scale of the features or consider increasing regularisation. Duality gap: 3.924e+00, tolerance: 1.797e+00
   model = cd_fast.enet_coordinate_descent(
 
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@@ -3189,9 +3211,9 @@ which polynomial fits the data best.
    
 
    
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16213/3980313467.py:9: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/3980313467.py:9: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().
   ax = fig.gca(projection='3d')
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16213/3980313467.py:37: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/3980313467.py:37: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
   fig.colorbar(surf, shrink=0.5, aspect=5)
 
    
 
    
diff --git a/doc/LectureNotes/_build/html/chapter4.html b/doc/LectureNotes/_build/html/chapter4.html
index 0b527a199..eb5cd3b1c 100644
--- a/doc/LectureNotes/_build/html/chapter4.html
+++ b/doc/LectureNotes/_build/html/chapter4.html
@@ -278,6 +278,28 @@ const thebe_selector_output = ".output, .cell_output"
    Week 36: Statistical interpretation of Linear Regression and Resampling techniques
   
  
+ 
  • 
+  
+   Exercises week 37
+  
+ 
    • 
+ 
  • 
+  
+   Week 37: Statitsitcal interpretations and Resampling Methods
+  
+ 
    • 
+
+
    
+ 
+  Projects
+ 
+
    
+
 
     
    
diff --git a/doc/LectureNotes/_build/html/chapter5.html b/doc/LectureNotes/_build/html/chapter5.html
index 399f156ce..a5a6f181e 100644
--- a/doc/LectureNotes/_build/html/chapter5.html
+++ b/doc/LectureNotes/_build/html/chapter5.html
@@ -278,6 +278,28 @@ const thebe_selector_output = ".output, .cell_output"
    Week 36: Statistical interpretation of Linear Regression and Resampling techniques
   
  
+ 
  • 
+  
+   Exercises week 37
+  
+ 
    • 
+ 
  • 
+  
+   Week 37: Statitsitcal interpretations and Resampling Methods
+  
+ 
    • 
+
+
    
+ 
+  Projects
+ 
+
    
+
 
     
    
diff --git a/doc/LectureNotes/_build/html/chapter6.html b/doc/LectureNotes/_build/html/chapter6.html
index f7124abd2..05e5bf3e6 100644
--- a/doc/LectureNotes/_build/html/chapter6.html
+++ b/doc/LectureNotes/_build/html/chapter6.html
@@ -278,6 +278,28 @@ const thebe_selector_output = ".output, .cell_output"
    Week 36: Statistical interpretation of Linear Regression and Resampling techniques
   
  
+ 
  • 
+  
+   Exercises week 37
+  
+ 
    • 
+ 
  • 
+  
+   Week 37: Statitsitcal interpretations and Resampling Methods
+  
+ 
    • 
+
+
    
+ 
+  Projects
+ 
+
    
+
 
     
    
@@ -725,9 +747,9 @@ predicting the target features of query instances is as follows:
    
 
    
 
    
 
    2nd degree coefficients:
-zero power:  -6.548110376991839
-first power:  0.2232822462117919
-second power:  -0.0007480407244119591
+zero power:  4.0618352118150005
+first power:  0.004339135748752641
+second power:  1.9543538503067644e-05
 
    
 
    
 _images/chapter6_1_1.png
diff --git a/doc/LectureNotes/_build/html/chapter7.html b/doc/LectureNotes/_build/html/chapter7.html
index eee3e2dd3..d613340fb 100644
--- a/doc/LectureNotes/_build/html/chapter7.html
+++ b/doc/LectureNotes/_build/html/chapter7.html
@@ -278,6 +278,28 @@ const thebe_selector_output = ".output, .cell_output"
    Week 36: Statistical interpretation of Linear Regression and Resampling techniques
   
  
+ 
  • 
+  
+   Exercises week 37
+  
+ 
    • 
+ 
  • 
+  
+   Week 37: Statitsitcal interpretations and Resampling Methods
+  
+ 
    • 
+
+
    
+ 
+  Projects
+ 
+
    
+
 
     
    
diff --git a/doc/LectureNotes/_build/html/chapter8.html b/doc/LectureNotes/_build/html/chapter8.html
index 465d13b8e..2ce06ffd3 100644
--- a/doc/LectureNotes/_build/html/chapter8.html
+++ b/doc/LectureNotes/_build/html/chapter8.html
@@ -278,6 +278,28 @@ const thebe_selector_output = ".output, .cell_output"
    Week 36: Statistical interpretation of Linear Regression and Resampling techniques
   
  
+ 
  • 
+  
+   Exercises week 37
+  
+ 
    • 
+ 
  • 
+  
+   Week 37: Statitsitcal interpretations and Resampling Methods
+  
+ 
    • 
+
+
    
+ 
+  Projects
+ 
+
    
+
 
     
    
@@ -679,10 +701,10 @@ covariance matrix through the np.linalg.eig() function.
    
 
    
 
    
 
    
-
    0.26662339374864535
-4.736115211426478
-[[ 1.20561803  3.63264564]
- [ 3.63264564 12.10207647]]
+
    0.03822007730337899
+3.989393825676568
+[[0.90044211 2.80659468]
+ [2.80659468 9.73667253]]
 
    
 
    
 
    
@@ -722,10 +744,10 @@ a more brute force way. Here we scale the mean values for each column of the des
 
    
 
    
 
    
-
    0.09318696260700278
-1.9096305360355206
-[[1.         0.65907898]
- [0.65907898 1.        ]]
+
    0.07864140367329474
+2.0511284278960114
+[[1.         0.68282072]
+ [0.68282072 1.        ]]
 
    
 
    
 
    
@@ -754,30 +776,30 @@ this matrix we easily see that it is a positive definite matrix.
    
 
    
 
    
 
    
-
    [[ 0.32360769  2.53264317]
- [ 0.04531375 -0.70569833]
- [ 0.17001895 -0.49570819]
- [ 1.60938882  4.69896355]
- [ 0.14052537  1.37535105]
- [-0.12909917  1.25781559]
- [-0.03016916  0.01780471]
- [-0.38816656 -0.82894017]
- [-0.34591885 -3.1893772 ]
- [-1.39550083 -4.66285417]]
+
    [[ 0.21424133 -1.00310568]
+ [ 1.84955363  5.92472578]
+ [ 0.43773101  1.60738434]
+ [ 0.94910711  2.53617977]
+ [-1.00106025 -3.87889126]
+ [-0.2544356  -0.48005485]
+ [-0.72117282 -1.4229538 ]
+ [-0.48783291  0.5970842 ]
+ [-0.17565241 -0.84643086]
+ [-0.8104791  -3.03393764]]
           0         1
-0  0.323608  2.532643
-1  0.045314 -0.705698
-2  0.170019 -0.495708
-3  1.609389  4.698964
-4  0.140525  1.375351
-5 -0.129099  1.257816
-6 -0.030169  0.017805
-7 -0.388167 -0.828940
-8 -0.345919 -3.189377
-9 -1.395501 -4.662854
-          0         1
-0  1.000000  0.899734
-1  0.899734  1.000000
+0  0.214241 -1.003106
+1  1.849554  5.924726
+2  0.437731  1.607384
+3  0.949107  2.536180
+4 -1.001060 -3.878891
+5 -0.254436 -0.480055
+6 -0.721173 -1.422954
+7 -0.487833  0.597084
+8 -0.175652 -0.846431
+9 -0.810479 -3.033938
+         0        1
+0  1.00000  0.93503
+1  0.93503  1.00000
 
    
 
    
 
    
@@ -834,37 +856,37 @@ this matrix we easily see that it is a positive definite matrix.
    
 
    
 
         0         1         2         3         4         5         6         7   \
 0   0.0  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000   
-1   0.0  0.086358  0.084977  0.084028  0.085456  0.086705  0.073624  0.075225   
-2   0.0  0.084977  0.085778  0.080455  0.082791  0.085242  0.069320  0.071314   
-3   0.0  0.084028  0.080455  0.086647  0.086999  0.086904  0.078715  0.079856   
-4   0.0  0.085456  0.082791  0.086999  0.087848  0.088361  0.078426  0.079839   
-5   0.0  0.086705  0.085242  0.086904  0.088361  0.089641  0.077606  0.079333   
-6   0.0  0.073624  0.069320  0.078715  0.078426  0.077606  0.073298  0.074046   
-7   0.0  0.075225  0.071314  0.079856  0.079839  0.079333  0.074046  0.074971   
-8   0.0  0.076867  0.073465  0.080914  0.081223  0.081100  0.074653  0.075779   
-9   0.0  0.078521  0.075782  0.081827  0.082527  0.082877  0.075047  0.076403   
-10  0.0  0.063766  0.059453  0.069855  0.069291  0.068201  0.066209  0.066728   
-11  0.0  0.065175  0.061037  0.071105  0.070700  0.069782  0.067233  0.067873   
-12  0.0  0.066656  0.062742  0.072370  0.072150  0.071437  0.068239  0.069013   
-13  0.0  0.068206  0.064577  0.073634  0.073630  0.073163  0.069203  0.070127   
-14  0.0  0.069816  0.066556  0.074868  0.075121  0.074951  0.070092  0.071185   
+1   0.0  0.082232  0.082339  0.080863  0.080028  0.078987  0.072334  0.071321   
+2   0.0  0.082339  0.085298  0.084636  0.085154  0.085104  0.077849  0.077521   
+3   0.0  0.080863  0.084636  0.085290  0.086290  0.086690  0.079860  0.079858   
+4   0.0  0.080028  0.085154  0.086290  0.088026  0.088995  0.081970  0.082385   
+5   0.0  0.078987  0.085104  0.086690  0.088995  0.090424  0.083319  0.084079   
+6   0.0  0.072334  0.077849  0.079860  0.081970  0.083319  0.077182  0.077910   
+7   0.0  0.071321  0.077521  0.079858  0.082385  0.084079  0.077910  0.078901   
+8   0.0  0.070302  0.077012  0.079649  0.082509  0.084487  0.078333  0.079546   
+9   0.0  0.069312  0.076408  0.079319  0.082449  0.084666  0.078555  0.079958   
+10  0.0  0.063977  0.070119  0.072959  0.075620  0.077491  0.072176  0.073337   
+11  0.0  0.063115  0.069617  0.072682  0.075590  0.077676  0.072384  0.073717   
+12  0.0  0.062295  0.069072  0.072344  0.075455  0.077724  0.072474  0.073955   
+13  0.0  0.061529  0.068521  0.071982  0.075263  0.077690  0.072492  0.074102   
+14  0.0  0.060822  0.067984  0.071619  0.075045  0.077611  0.072468  0.074193   
 
           8         9         10        11        12        13        14  
 0   0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  
-1   0.076867  0.078521  0.063766  0.065175  0.066656  0.068206  0.069816  
-2   0.073465  0.075782  0.059453  0.061037  0.062742  0.064577  0.066556  
-3   0.080914  0.081827  0.069855  0.071105  0.072370  0.073634  0.074868  
-4   0.081223  0.082527  0.069291  0.070700  0.072150  0.073630  0.075121  
-5   0.081100  0.082877  0.068201  0.069782  0.071437  0.073163  0.074951  
-6   0.074653  0.075047  0.066209  0.067233  0.068239  0.069203  0.070092  
-7   0.075779  0.076403  0.066728  0.067873  0.069013  0.070127  0.071185  
-8   0.076819  0.077713  0.067089  0.068365  0.069654  0.070936  0.072186  
-9   0.077713  0.078926  0.067224  0.068643  0.070096  0.071567  0.073038  
-10  0.067089  0.067224  0.060603  0.061468  0.062298  0.063070  0.063750  
-11  0.068365  0.068643  0.061468  0.062424  0.063353  0.064232  0.065030  
-12  0.069654  0.070096  0.062298  0.063353  0.064390  0.065389  0.066317  
-13  0.070936  0.071567  0.063070  0.064232  0.065389  0.066519  0.067593  
-14  0.072186  0.073038  0.063750  0.065030  0.066317  0.067593  0.068832  
+1   0.070302  0.069312  0.063977  0.063115  0.062295  0.061529  0.060822  
+2   0.077012  0.076408  0.070119  0.069617  0.069072  0.068521  0.067984  
+3   0.079649  0.079319  0.072959  0.072682  0.072344  0.071982  0.071619  
+4   0.082509  0.082449  0.075620  0.075590  0.075455  0.075263  0.075045  
+5   0.084487  0.084666  0.077491  0.077676  0.077724  0.077690  0.077611  
+6   0.078333  0.078555  0.072176  0.072384  0.072474  0.072492  0.072468  
+7   0.079546  0.079958  0.073337  0.073717  0.073955  0.074102  0.074193  
+8   0.080384  0.080965  0.074161  0.074692  0.075064  0.075330  0.075529  
+9   0.080965  0.081699  0.074752  0.075418  0.075911  0.076288  0.076588  
+10  0.074161  0.074752  0.068701  0.069233  0.069621  0.069911  0.070139  
+11  0.074692  0.075418  0.069233  0.069886  0.070381  0.070769  0.071086  
+12  0.075064  0.075911  0.069621  0.070381  0.070975  0.071453  0.071853  
+13  0.075330  0.076288  0.069911  0.070769  0.071453  0.072016  0.072493  
+14  0.075529  0.076588  0.070139  0.071086  0.071853  0.072493  0.073045  
 
    
 
    
 
    
@@ -1053,10 +1075,10 @@ We can write our own code or simply use either the functionaly of numpy<
 
    
 
    
 
              0         1
-0  4.059118  2.009163
-1  2.009163  2.004788
-[[4.05911793 2.00916336]
- [2.00916336 2.00478786]]
+0  3.965838  1.971865
+1  1.971865  1.997830
+[[3.96583833 1.97186457]
+ [1.97186457 1.99783004]]
 
    
 
    
 
    
@@ -1083,8 +1105,8 @@ Our own code here is not very elegant and asks for obvious improvements. It is t
 
    
 
    
 
    Centered covariance using own code
-[[4.05911793 2.00916336]
- [2.00916336 2.00478786]]
+[[3.96583833 1.97186457]
+ [1.97186457 1.99783004]]
 
    
 
    
 _images/chapter8_65_1.png
@@ -1144,16 +1166,16 @@ questions.
    
 
    
 
    
 
    Eigenvalues of Covariance matrix
-5.288455813429108
-0.7754499790100834
+5.185584177293881
+0.7780841853755783
 First eigenvector
-[0.85299536 0.52191849]
+[0.85044503 0.52606392]
 Second eigenvector
-[-0.52191849  0.85299536]
+[-0.52606392  0.85044503]
 
    
 
    
 
    Eigenvector of largest eigenvalue
-[0.85299536 0.52191849]
+[0.85044503 0.52606392]
 
    
 
    
 
    
diff --git a/doc/LectureNotes/_build/html/chapter9.html b/doc/LectureNotes/_build/html/chapter9.html
index 4bca6f831..dafec4bb9 100644
--- a/doc/LectureNotes/_build/html/chapter9.html
+++ b/doc/LectureNotes/_build/html/chapter9.html
@@ -278,6 +278,28 @@ const thebe_selector_output = ".output, .cell_output"
    Week 36: Statistical interpretation of Linear Regression and Resampling techniques
   
  
+ 
  • 
+  
+   Exercises week 37
+  
+ 
    • 
+ 
  • 
+  
+   Week 37: Statitsitcal interpretations and Resampling Methods
+  
+ 
    • 
+
+
    
+ 
+  Projects
+ 
+
    
+
 
     
    
diff --git a/doc/LectureNotes/_build/html/chapteroptimization.html b/doc/LectureNotes/_build/html/chapteroptimization.html
index 048ba187e..3e60c521e 100644
--- a/doc/LectureNotes/_build/html/chapteroptimization.html
+++ b/doc/LectureNotes/_build/html/chapteroptimization.html
@@ -278,6 +278,28 @@ const thebe_selector_output = ".output, .cell_output"
    Week 36: Statistical interpretation of Linear Regression and Resampling techniques
   
  
+ 
  • 
+  
+   Exercises week 37
+  
+ 
    • 
+ 
  • 
+  
+   Week 37: Statitsitcal interpretations and Resampling Methods
+  
+ 
    • 
+
+
    
+ 
+  Projects
+ 
+
    
+
 
     
    
@@ -975,11 +997,11 @@ which equals
    
 
    
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16261/483257001.py:18: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7714/483257001.py:18: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().
   ax = fig.gca(projection="3d")
 
    
 
    
-
    <mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x138098070>
+
    <mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x11e77b070>
 
    
 
    
 _images/chapteroptimization_61_2.png
@@ -1037,7 +1059,7 @@ which equals
    
 
    
 
    
 
    
-
    [<matplotlib.lines.Line2D at 0x1387541c0>]
+
    [<matplotlib.lines.Line2D at 0x11ecf9850>]
 
    
 
    
 _images/chapteroptimization_69_1.png
@@ -1294,11 +1316,11 @@ when \(||\nabla_\beta C(\beta_k) || \
 
    
 
    
 
    
-
    [0.28836053 4.52113415]
-[[4.19528375]
- [2.90383424]]
-[[4.19528375]
- [2.90383424]]
+
    [0.33196524 4.36593124]
+[[4.09963157]
+ [2.99760425]]
+[[4.09963157]
+ [2.99760425]]
 
    
 
    
 _images/chapteroptimization_123_1.png
@@ -1327,9 +1349,9 @@ when \(||\nabla_\beta C(\beta_k) || \
 
    
 
    
 
    
-
    [[4.16575256]
- [2.8620652 ]]
-[4.11520281] [2.85097049]
+
    [[4.21639245]
+ [2.82985482]]
+[4.15172236] [2.79589065]
 
    
 
    
 
    
@@ -1400,10 +1422,10 @@ C_{\text{ridge}}(\beta) = \frac{1}{n}||X\beta -\mathbf{y}||^2 + \lambda ||\beta|
 
    
 
    
 
    
-
    [[4.20793824]
- [2.75460639]]
-[[4.106971  ]
- [2.83724637]]
+
    [[3.98919197]
+ [2.94015598]]
+[[3.94925462]
+ [2.97087408]]
 
    
 
    
 _images/chapteroptimization_132_1.png
@@ -1653,15 +1675,15 @@ function.
    
 
    
 
    
 
    Own inversion
-[[4.31347523]
- [2.69915639]]
-Eigenvalues of Hessian Matrix:[0.28457442 4.43693489]
+[[4.5424657 ]
+ [2.40026896]]
+Eigenvalues of Hessian Matrix:[0.29830651 3.89658408]
 theta from own gd
-[[4.31347523]
- [2.69915639]]
+[[4.5424657 ]
+ [2.40026896]]
 theta from own sdg
-[[4.2891298 ]
- [2.67783138]]
+[[4.55687658]
+ [2.41165766]]
 
    
 
    
 _images/chapteroptimization_148_1.png
diff --git a/doc/LectureNotes/_build/html/clustering.html b/doc/LectureNotes/_build/html/clustering.html
index 077fbf904..86656c216 100644
--- a/doc/LectureNotes/_build/html/clustering.html
+++ b/doc/LectureNotes/_build/html/clustering.html
@@ -278,6 +278,28 @@ const thebe_selector_output = ".output, .cell_output"
    Week 36: Statistical interpretation of Linear Regression and Resampling techniques
   
  
+ 
  • 
+  
+   Exercises week 37
+  
+ 
    • 
+ 
  • 
+  
+   Week 37: Statitsitcal interpretations and Resampling Methods
+  
+ 
    • 
+
+
    
+ 
+  Projects
+ 
+
    
+
 
     
    
diff --git a/doc/LectureNotes/_build/html/exercisesweek34.html b/doc/LectureNotes/_build/html/exercisesweek34.html
index 06c5ea5d0..6650984ac 100644
--- a/doc/LectureNotes/_build/html/exercisesweek34.html
+++ b/doc/LectureNotes/_build/html/exercisesweek34.html
@@ -278,6 +278,28 @@ const thebe_selector_output = ".output, .cell_output"
    Week 36: Statistical interpretation of Linear Regression and Resampling techniques
   
  
+ 
  • 
+  
+   Exercises week 37
+  
+ 
    • 
+ 
  • 
+  
+   Week 37: Statitsitcal interpretations and Resampling Methods
+  
+ 
    • 
+
+
    
+ 
+  Projects
+ 
+
    
+
 
     
    
diff --git a/doc/LectureNotes/_build/html/exercisesweek35.html b/doc/LectureNotes/_build/html/exercisesweek35.html
index b9dd5219b..ff9b213a1 100644
--- a/doc/LectureNotes/_build/html/exercisesweek35.html
+++ b/doc/LectureNotes/_build/html/exercisesweek35.html
@@ -278,6 +278,28 @@ const thebe_selector_output = ".output, .cell_output"
    Week 36: Statistical interpretation of Linear Regression and Resampling techniques
   
  
+ 
  • 
+  
+   Exercises week 37
+  
+ 
    • 
+ 
  • 
+  
+   Week 37: Statitsitcal interpretations and Resampling Methods
+  
+ 
    • 
+
+
    
+ 
+  Projects
+ 
+
    
+
 
     
    
diff --git a/doc/LectureNotes/_build/html/exercisesweek36.html b/doc/LectureNotes/_build/html/exercisesweek36.html
index a534ed99f..ea4f6bff3 100644
--- a/doc/LectureNotes/_build/html/exercisesweek36.html
+++ b/doc/LectureNotes/_build/html/exercisesweek36.html
@@ -278,6 +278,16 @@ const thebe_selector_output = ".output, .cell_output"
    Week 36: Statistical interpretation of Linear Regression and Resampling techniques
   
  
+ 
  • 
+  
+   Exercises week 37
+  
+ 
    • 
+ 
  • 
+  
+   Week 37: Statitsitcal interpretations and Resampling Methods
+  
+ 
    • 
 
 
    
  
diff --git a/doc/LectureNotes/_build/html/exercisesweek37.html b/doc/LectureNotes/_build/html/exercisesweek37.html
new file mode 100644
index 000000000..3075b4c77
--- /dev/null
+++ b/doc/LectureNotes/_build/html/exercisesweek37.html
@@ -0,0 +1,566 @@
+
+
+
+
+  
+    
+    
+    Exercises week 37 — Applied Data Analysis and Machine Learning
+    
+  
+  
+
+    
+  
+  
+  
+
+    
+      
+
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+  
+
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+
+    
+    
+  
+  
+    
+    
    
+
+    
+
+    
    
+      
    
+          
+
+
+
+          
+
+
+          
+
    
+    
+    
    
+    
    
+        
    
+        
    
+            
+            
+            
+            
+
    
+    
+
+    
    
+        
+        
+        
+        
+        
+        
+    
    
+
    
+
+            
+
+            
+
+
+
+            
+
+        
    
+
+        
+        
    
+            
+            
    
+                 Contents
+            
    
+            
+        
    
+    
    
+
    
+    
    
+        
    
+            
+            
    
+                
    Exercises week 37
    
+                
+                
    
+                    
+                
    
+            
    
+            
+              
    
+                
+  
+
    
+
    Exercises week 37
    
+
    September 11-15, 2023
    
+
    Date: Deadline is Sunday September 17 at midnight
    
+
    
+
    Overarching aims of the exercises this week
    
+
    This exercise deals with various mean values and variances in  linear regression method (here it may be useful to look up chapter 3, equation (3.8) of Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer). The exercise is also a part of project 1 and can be reused in the theory part of the project.
    
+
    For more discussions on Ridge regression and calculation of expectation values, Wessel van Wieringen’s article is highly recommended.
    
+
    The assumption we have made is
+that there exists a continuous function \(f(\boldsymbol{x})\) and  a normal distributed error \(\boldsymbol{\varepsilon}\sim N(0, \sigma^2)\)
+which describes our data
    
+
    
+\[
+\boldsymbol{y} = f(\boldsymbol{x})+\boldsymbol{\varepsilon}
+\]
    
+
    We then approximate this function \(f(\boldsymbol{x})\) with our model \(\boldsymbol{\tilde{y}}\) from the solution of the linear regression equations (ordinary least squares OLS), that is our
+function \(f\) is approximated by \(\boldsymbol{\tilde{y}}\) where we minimized  \((\boldsymbol{y}-\boldsymbol{\tilde{y}})^2\), with
    
+
    
+\[
+\boldsymbol{\tilde{y}} = \boldsymbol{X}\boldsymbol{\beta}.
+\]
    
+
    The matrix \(\boldsymbol{X}\) is the so-called design or feature matrix.
    
+
    
+
    
+
    Exercise 1: Expectation values for ordinary least squares expressions
    
+
    Show that  the expectation value of \(\boldsymbol{y}\) for a given element \(i\)
    
+
    
+\[
+\mathbb{E}(y_i)  =\sum_{j}x_{ij} \beta_j=\mathbf{X}_{i, \ast} \, \boldsymbol{\beta},
+\]
    
+
    and that
+its variance is
    
+
    
+\[
+\mbox{Var}(y_i)  = \sigma^2.
+\]
    
+
    Hence, \(y_i \sim N( \mathbf{X}_{i, \ast} \, \boldsymbol{\beta}, \sigma^2)\), that is \(\boldsymbol{y}\) follows a normal distribution with
+mean value \(\boldsymbol{X}\boldsymbol{\beta}\) and variance \(\sigma^2\).
    
+
    With the OLS expressions for the optimal parameters \(\boldsymbol{\hat{\beta}}\) show that
    
+
    
+\[
+\mathbb{E}(\boldsymbol{\hat{\beta}}) = \boldsymbol{\beta}.
+\]
    
+
    Show finally that the variance of \(\boldsymbol{\beta}\) is
    
+
    
+\[
+\mbox{Var}(\boldsymbol{\hat{\beta}}) = \sigma^2 \, (\mathbf{X}^{T} \mathbf{X})^{-1}.
+\]
    
+
    We can use the last expression when we define a so-called confidence interval for the parameters \(\beta\).
+A given parameter \(\beta_j\) is given by the diagonal matrix element of the above matrix.
    
+
    
+
    
+
    Exercise 2: Expectation values for Ridge regression
    
+
    Show that
    
+
    
+\[
+\mathbb{E} \big[ \boldsymbol{\beta}^{\mathrm{Ridge}} \big]=(\mathbf{X}^{T} \mathbf{X} + \lambda \mathbf{I}_{pp})^{-1} (\mathbf{X}^{\top} \mathbf{X})\
+\boldsymbol{\beta}^{\mathrm{OLS}}.
+\]
    
+
    We see clearly that
+\(\mathbb{E} \big[ \boldsymbol{\beta}^{\mathrm{Ridge}} \big] \not= \boldsymbol{\beta}^{\mathrm{OLS}}\) for any \(\lambda > 0\).
    
+
    Show also that the variance is
    
+
    
+\[
+\mbox{Var}[\boldsymbol{\beta}^{\mathrm{Ridge}}]=\sigma^2[  \mathbf{X}^{T} \mathbf{X} + \lambda \mathbf{I} ]^{-1}  \mathbf{X}^{T} \mathbf{X} \{ [  \m\
+athbf{X}^{\top} \mathbf{X} + \lambda \mathbf{I} ]^{-1}\}^{T},
+\]
    
+
    and it is easy to see that if the parameter \(\lambda\) goes to infinity then the variance of Ridge parameters \(\boldsymbol{\beta}\) goes to zero.
    
+
    
+
    
+
+    
+    
+
+              
    
+              
+            
+                
+
     
+    
+        
+        
    
+            
    previous
    
+            
    Week 36: Statistical interpretation of Linear Regression and Resampling techniques
    
+        
    
+        
+    
+    
    
+        
    next
    
+        
    Week 37: Statitsitcal interpretations and Resampling Methods
    
+    
    
+    
+        
+
    
+            
+        
    
+    
    
+    
    
+  
    
+    
+      By Morten Hjorth-Jensen
    
+    
+        © Copyright 2021.
    
+  
    
+
    
+
    
+
+
+      
    
+    
    
+  
+  
+
+  
+
\ No newline at end of file
diff --git a/doc/LectureNotes/_build/html/genindex.html b/doc/LectureNotes/_build/html/genindex.html
index cceeb3127..3510efc2b 100644
--- a/doc/LectureNotes/_build/html/genindex.html
+++ b/doc/LectureNotes/_build/html/genindex.html
@@ -274,6 +274,16 @@ const thebe_selector_output = ".output, .cell_output"
    Week 36: Statistical interpretation of Linear Regression and Resampling techniques
   
  
+ 
  • 
+  
+   Exercises week 37
+  
+ 
    • 
+ 
  • 
+  
+   Week 37: Statitsitcal interpretations and Resampling Methods
+  
+ 
    • 
 
 
    
  
diff --git a/doc/LectureNotes/_build/html/intro.html b/doc/LectureNotes/_build/html/intro.html
index f470da79f..1780e369c 100644
--- a/doc/LectureNotes/_build/html/intro.html
+++ b/doc/LectureNotes/_build/html/intro.html
@@ -275,6 +275,16 @@ const thebe_selector_output = ".output, .cell_output"
    Week 36: Statistical interpretation of Linear Regression and Resampling techniques
   
  
+ 
  • 
+  
+   Exercises week 37
+  
+ 
    • 
+ 
  • 
+  
+   Week 37: Statitsitcal interpretations and Resampling Methods
+  
+ 
    • 
 
 
    
  
diff --git a/doc/LectureNotes/_build/html/linalg.html b/doc/LectureNotes/_build/html/linalg.html
index eaabfff04..78ec45d58 100644
--- a/doc/LectureNotes/_build/html/linalg.html
+++ b/doc/LectureNotes/_build/html/linalg.html
@@ -278,6 +278,28 @@ const thebe_selector_output = ".output, .cell_output"
    Week 36: Statistical interpretation of Linear Regression and Resampling techniques
   
  
+ 
  • 
+  
+   Exercises week 37
+  
+ 
    • 
+ 
  • 
+  
+   Week 37: Statitsitcal interpretations and Resampling Methods
+  
+ 
    • 
+
+
    
+ 
+  Projects
+ 
+
    
+
 
     
    
@@ -581,8 +603,8 @@ matrices and vectors.
    
 
    
 
    
 
    
-
    [-0.87136737  1.4300745  -0.3322326  -0.66758934 -1.00283636 -0.27625974
-  1.89249454 -0.25006757  0.73565195  0.33697405]
+
    [-0.28587856 -0.73509675  0.35559283 -0.62819534 -0.15254784 -0.44792888
+  1.5393681  -0.81784072  0.53476918  1.02055673]
 
    
 
    
 
    
@@ -803,26 +825,26 @@ as (recall that we user lowercase letters for vectors and uppercase letters for
 
    
 
    
 
    
-
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+ [0.21089449 0.0402861  0.12611267 0.49197115 0.59203799 0.74577306
+  0.14491591 0.71135895 0.84723978 0.03416188]]
 
    
 
    
 
    
@@ -882,13 +904,13 @@ covariance matrix through the np.linalg.eig() function.
    
 
    
 
    
 
    
-
    0.03499693245669077
-4.187268182169147
--0.19627430151896047
-[[ 1.0622197   3.16232481  2.98018358]
- [ 3.16232481 10.48442771  8.58039072]
- [ 2.98018358  8.58039072 13.66351927]]
-[21.70244042  0.07978179  3.42794448]
+
    0.041129694365319464
+4.025325212488352
+0.010687707010849668
+[[ 1.23319332  3.73704762  4.12446443]
+ [ 3.73704762 12.59095724 12.81409445]
+ [ 4.12446443 12.81409445 20.04983109]]
+[30.70850263  0.10254846  3.06293056]
 
    
 
    
 
    
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diff --git a/doc/LectureNotes/_build/html/project1.html b/doc/LectureNotes/_build/html/project1.html
index 430ee97af..e10cdfbc1 100644
--- a/doc/LectureNotes/_build/html/project1.html
+++ b/doc/LectureNotes/_build/html/project1.html
@@ -55,7 +55,7 @@ const thebe_selector_output = ".output, .cell_output"
     
     
     
-    
+    
     
     
     
@@ -277,6 +277,16 @@ const thebe_selector_output = ".output, .cell_output"
    Week 36: Statistical interpretation of Linear Regression and Resampling techniques
   
  
+ 
  • 
+  
+   Exercises week 37
+  
+ 
    • 
+ 
  • 
+  
+   Week 37: Statitsitcal interpretations and Resampling Methods
+  
+ 
    • 
 
 
    
  
@@ -639,7 +649,7 @@ which polynomial fits the data best.
    
 
    
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_19350/39730396.py:11: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7740/39730396.py:11: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().
   ax = fig.gca(projection='3d')
 
    
 
    
@@ -998,11 +1008,11 @@ of code developers and contributors keeps increasing.
    
             
                 
 
     
-    
+    
         
         
    
             
    previous
    
-            
    Week 36: Statistical interpretation of Linear Regression and Resampling techniques
    
+            
    Week 37: Statitsitcal interpretations and Resampling Methods
    
         
    
         
 
    
diff --git a/doc/LectureNotes/_build/html/schedule.html b/doc/LectureNotes/_build/html/schedule.html
index a8fe16c41..632c2fd70 100644
--- a/doc/LectureNotes/_build/html/schedule.html
+++ b/doc/LectureNotes/_build/html/schedule.html
@@ -276,6 +276,28 @@ const thebe_selector_output = ".output, .cell_output"
    Week 36: Statistical interpretation of Linear Regression and Resampling techniques
   
  
+ 
  • 
+  
+   Exercises week 37
+  
+ 
    • 
+ 
  • 
+  
+   Week 37: Statitsitcal interpretations and Resampling Methods
+  
+ 
    • 
+
+
    
+ 
+  Projects
+ 
+
    
+
 
     
    
diff --git a/doc/LectureNotes/_build/html/search.html b/doc/LectureNotes/_build/html/search.html
index 502590f1b..b63f5bcae 100644
--- a/doc/LectureNotes/_build/html/search.html
+++ b/doc/LectureNotes/_build/html/search.html
@@ -280,6 +280,16 @@ const thebe_selector_output = ".output, .cell_output"
    Week 36: Statistical interpretation of Linear Regression and Resampling techniques
   
  
+ 
  • 
+  
+   Exercises week 37
+  
+ 
    • 
+ 
  • 
+  
+   Week 37: Statitsitcal interpretations and Resampling Methods
+  
+ 
    • 
 
 
    
  
diff --git a/doc/LectureNotes/_build/html/searchindex.js b/doc/LectureNotes/_build/html/searchindex.js
index f2daa6b24..e06c4446e 100644
--- a/doc/LectureNotes/_build/html/searchindex.js
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Linear Regression","14. Building a Feed Forward Neural Network","15. Solving Differential Equations  with Deep Learning","16. Convolutional Neural Networks","17. Recurrent neural networks: Overarching view","4. Ridge and Lasso Regression","5. Resampling Methods","6. Logistic Regression","8. Support Vector Machines, overarching aims","9. Decision trees, overarching aims","10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods","11. Basic ideas of the Principal Component Analysis (PCA)","13. Neural networks","7. Optimization, the central part of any Machine Learning algortithm","12. Clustering and Unsupervised Learning","Exercises week 34","Exercises week 35","Exercises week 36","Exercises week 37","Applied Data Analysis and Machine Learning","2. Linear Algebra, Handling of Arrays and more Python Features","Project 1 on Machine Learning, deadline October 9 (midnight), 2023","Teaching schedule with links to material","1. Elements of Probability Theory and Statistical Data Analysis","Teachers and Grading","Textbooks","Week 34: Introduction to the course, Logistics and Practicalities","Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression","Week 36: Statistical interpretation of Linear Regression and Resampling techniques","Week 37: Statitsitcal interpretations and Resampling Methods"],titleterms:{"1":[0,15,16,17,18,21,26,27],"10":[],"11":[],"12":[],"13":[],"14":29,"15":[],"16":[],"17":[],"18":[],"19":[],"2":[0,15,16,17,18,26,27],"20":[],"2021":[],"2022":[],"2023":[21,24],"21":[],"22":[],"23":[],"24":[],"25":[],"26":[],"27":[],"28":[],"29":[],"3":[0,15,16,26,27],"30":[],"31":27,"34":[15,26],"35":[16,27],"36":[17,28],"37":[18,29],"38":[],"39":[],"4":[0,27],"40":[],"41":[],"4155":[],"42":[],"43":[],"44":[],"45":[],"46":[],"47":[],"5":0,"6":[],"7":28,"8":[],"9":21,"case":[8,10,23,27,28],"do":[1,26,28,29],"final":[12,27,28],"function":[0,1,6,7,8,10,11,12,13,21,23,26,27,28,29],"import":[5,20,26,27],"new":[4,28,29],A:[0,1,4,8,9,26,28,29],And:[26,27,28],In:24,Ising:6,The:[0,1,2,3,5,6,7,8,9,11,12,17,19,26,27,28,29],To:[26,27],With:[4,28],about:[26,27],abov:28,activ:[1,12,28],actual:[],ad:[0,6,17,21,26,27],adaboost:10,adagrad:13,adam:13,adapt:10,adjust:1,adversari:4,again:[3,9],ai:26,aim:[8,9,17,18,26],aka:[26,27],algebra:[20,26],algorithm:[9,10,11,12,27],algortithm:13,all:8,an:[0,4,10,26],analys:[5,27],analysi:[0,5,6,11,19,21,23,26,27,28,29],analyt:[0,16,17],ani:13,anoth:[9,28,29],appli:19,approach:[0,8,14,26,29],approxim:12,architectur:1,arrai:[20,26],assist:24,assumpt:[28,29],august:27,autocorrel:23,autograd:[2,13],automat:13,b:[17,21],back:[1,11,12],background:[19,21,29],bag:10,base:[13,29],basic:[0,5,7,9,10,11,20,27,28,29],batch:1,bay:[5,28,29],befor:11,beta:[28,29],better:8,bia:[6,21,29],binari:1,bind:26,binomi:[],bird:10,block:[],boldsymbol:[27,28,29],boost:10,bootstrap:[6,10,29],boston:[0,27],breast:1,brief:[26,29],bring:12,build:[1,3,9],c:[21,26],calcul:27,can:[26,29],cancer:[1,7,9,11],cart:9,center:27,central:[13,19,23,29],chain:12,chang:10,channel:26,chi:[0,26],choos:1,cifar01:3,classic:11,classif:[1,9,10],classifi:8,clip:1,cluster:14,cnn:3,code:[0,1,2,5,9,11,12,13,14,26,27,28,29],collect:[1,3],commun:26,compar:[2,10],comparison:28,complet:27,complex:[0,6,21,27],complic:6,compon:11,comput:9,computation:29,computerlab:26,con:9,concept:23,condit:[28,29],confid:29,conjug:13,continu:[],contn:26,convex:[8,13],convolut:[3,12],correctli:[28,29],correl:[11,27],cost:[1,10,27,28,29],cours:[19,25,26],covari:[5,11,23,27],cover:26,cross:[6,21,29],cumul:[],cython:26,d:21,data:[0,1,3,6,7,9,11,15,16,19,21,23,26,27],dataset:[1,3],deadlin:[21,26],decai:2,decis:[9,10],decomposit:[5,11,17,20,27],deep:[1,2],defin:[1,26],definit:[],degre:[0,27],deliveri:21,delta:29,demonstr:[],dens:[0,26],deriv:[5,12,27,28,29],descent:[2,10,13],descript:21,design:27,detail:[3,26],develop:1,deviat:[],diagon:11,dice:[],differ:8,differenti:[2,13],diffus:2,dimension:[2,3,8,21,27],disadvantag:9,discret:23,disguis:[],distribut:[5,23,28,29],distrubut:[28,29],doe:[27,28],domain:23,down:1,dropout:1,e:21,economi:27,electron:21,element:[0,23,26],elimin:20,energi:26,ensembl:10,entropi:9,environ:[0,15,26],equat:[0,2,12,26,27,28],error:[0,10,26,27,29],essenti:26,estim:[28,29],etc:26,euler:2,evalu:1,event:[],exampl:[0,1,2,3,4,6,7,8,9,10,26,27,28,29],exercis:[0,6,15,16,17,18,26,27,29],expect:[18,23,28,29],expens:29,experi:23,explor:[0,15,16,26],exponenti:2,express:[17,18,26,27],extrapol:4,extrem:[10,26],ey:10,f:21,fall:24,famili:[1,26,27],famou:20,fantast:27,featur:[9,20,27],feed:[1,12],find:29,fine:1,first:[4,12,26,27,28],fit:[0,10,26,28],fix:27,fold:29,forc:3,forest:10,format:[21,26],forward:[1,2,12],fourier:3,frank:[6,21,27],freedom:[0,27],frequent:27,frequentist:[0,26],from:[5,10,12,27,28,29],full:2,further:[3,5,27],fy:[],g:21,gan:4,gaussian:20,gd:13,gener:[4,9,26],geometr:11,gini:9,good:[0,26],grade:[24,26],gradient:[1,2,10,13],growth:2,ha:19,handl:[20,26,27],happen:[28,29],have:26,heard:26,hessian:27,hidden:2,histogram:29,hous:[0,27],how:[],hyperparamet:1,hyperplan:8,i:1,id3:9,idea:11,ident:[28,29],identifi:29,ii:26,iid:[28,29],illustr:28,implement:1,implic:[5,27],improv:1,includ:13,increment:11,independ:[28,29],index:9,inform:24,input:2,instal:[19,21,26],instructor:24,intercept:27,interpret:[5,11,26,27,28,29],interv:29,introduc:[11,13,27],introduct:[0,6,19,20,21,26],invers:[5,20,28],invert:27,invok:28,iter:10,its:27,jackknif:[],jacobian:27,jax:13,julia:26,jungl:10,k:29,kera:[1,3],kernel:[8,11],lagrangian:8,lasso:[5,6,21,27,28,29],last:[27,29],later:[5,27],layer:[1,2,3,12],learn:[0,1,2,11,13,14,15,16,19,21,26,27,28,29],least:[5,6,18,21,26,27,28],lectur:[26,27,28,29],level:10,librari:[19,26],likelihood:[7,28,29],limit:[1,13,23,29],linear:[0,8,13,20,26,27,28],link:[5,11,22,25,27,28,29],literatur:21,logist:[7,26],loss:27,lu:20,machin:[0,8,13,19,21,26],made:[28,29],mai:26,main:23,make:[0,9,10,15,16,26,27],mani:[10,12],manipul:27,margin:[28,29],mass:26,materi:[22,26,27,28,29],math:[5,27],mathemat:[3,5,8,27],matric:[5,20,26,28],matrix:[1,5,11,12,20,26,27,28],matter:[0,26],max:27,maximum:[28,29],mean:[0,26,27,28],meet:[5,10,23,26,27],mercer:8,mersenn:[],method:[6,9,10,13,21,29],midnight:21,min:27,minim:26,ml:26,mle:[28,29],mlp:12,mnist:[3,4],model:[0,1,4,6,12,26],moment:[],momentum:13,moon:[8,9],more:[3,6,20,21,26,27,28,29],multila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\ No newline at end of file
diff --git a/doc/LectureNotes/_build/html/statistics.html b/doc/LectureNotes/_build/html/statistics.html
index a45121dc4..9ec036575 100644
--- a/doc/LectureNotes/_build/html/statistics.html
+++ b/doc/LectureNotes/_build/html/statistics.html
@@ -278,6 +278,28 @@ const thebe_selector_output = ".output, .cell_output"
    Week 36: Statistical interpretation of Linear Regression and Resampling techniques
   
  
+ 
  • 
+  
+   Exercises week 37
+  
+ 
    • 
+ 
  • 
+  
+   Week 37: Statitsitcal interpretations and Resampling Methods
+  
+ 
    • 
+
+
    
+ 
+  Projects
+ 
+
    
+
 
     
    
@@ -953,27 +975,27 @@ uncorrelated.
    
 
    
 
    
 
    
-
    1.9474044318317307
-[[16.27404277  4.07430684  4.90189742  9.80462258  9.27412395  4.40264255
-   5.15060311 17.7265799  -0.62769765  9.00658717]
- [ 4.07430684  1.02002781  1.22722021  2.45464765  2.32183405  1.10222868
-   1.28948521  4.43795846 -0.15714797  2.25485457]
- [ 4.90189742  1.22722021  1.47649841  2.95324615  2.79345488  1.32611807
-   1.55141095  5.33941551 -0.18906854  2.71287025]
- [ 9.80462258  2.45464765  2.95324615  5.90699099  5.58738148  2.65246006
-   3.10308387 10.67973263 -0.37816901  5.42619859]
- [ 9.27412395  2.32183405  2.79345488  5.58738148  5.28506507  2.50894343
-   2.93518534 10.10188442 -0.35770742  5.13260331]
- [ 4.40264255  1.10222868  1.32611807  2.65246006  2.50894343  1.19105386
-   1.39340081  4.79559972 -0.16981204  2.43656628]
- [ 5.15060311  1.28948521  1.55141095  3.10308387  2.93518534  1.39340081
-   1.63012429  5.61031939 -0.19866124  2.85051211]
- [17.7265799   4.43795846  5.33941551 10.67973263 10.10188442  4.79559972
-   5.61031939 19.308763   -0.68372271  9.8104687 ]
- [-0.62769765 -0.15714797 -0.18906854 -0.37816901 -0.35770742 -0.16981204
-  -0.19866124 -0.68372271  0.0242106  -0.3473884 ]
- [ 9.00658717  2.25485457  2.71287025  5.42619859  5.13260331  2.43656628
-   2.85051211  9.8104687  -0.3473884   4.98453971]]
+
    2.0543653729690416
+[[ 8.75352505  9.52812155  6.26350283  2.23593659  5.0058263  12.34270689
+   3.69987647 18.4524458   5.51178587  5.67743788]
+ [ 9.52812155 10.37126183  6.8177581   2.43379387  5.44879019 13.43490889
+   4.0272773  20.08529655  5.99952195  6.17983246]
+ [ 6.26350283  6.8177581   4.48179077  1.59990347  3.58187211  8.83170827
+   2.64741194 13.2034747   3.94390673  4.06243748]
+ [ 2.23593659  2.43379387  1.59990347  0.57113133  1.27865175  3.15273101
+   0.94506946  4.71335815  1.40789038  1.45020332]
+ [ 5.0058263   5.44879019  3.58187211  1.27865175  2.86265211  7.05835037
+   2.11582635 10.55229041  3.1519922   3.24672263]
+ [12.34270689 13.43490889  8.83170827  3.15273101  7.05835037 17.40355028
+   5.21692581 26.01844727  7.77176703  8.00534085]
+ [ 3.69987647  4.0272773   2.64741194  0.94506946  2.11582635  5.21692581
+   1.56383695  7.79934594  2.32968167  2.39969826]
+ [18.4524458  20.08529655 13.2034747   4.71335815 10.55229041 26.01844727
+   7.79934594 38.89778737 11.61885405 11.96804878]
+ [ 5.51178587  5.99952195  3.94390673  1.40789038  3.1519922   7.77176703
+   2.32968167 11.61885405  3.47057708  3.57488231]
+ [ 5.67743788  6.17983246  4.06243748  1.45020332  3.24672263  8.00534085
+   2.39969826 11.96804878  3.57488231  3.68232235]]
 
    
 
    
 
    
@@ -1241,15 +1263,15 @@ more practically oriented methods like the blocking technique.
    
 
    
 
    
 
    
-
    0.08549632935144091
-4.438111004052204
-0.15485374225770068
-0.8225325933960339 7.887392472315955 7.062734874360835
-2.364244035362507 1.814860456269878 5.4421034379901165
-[[0.82253259 2.36424404 1.81486046]
- [2.36424404 7.88739247 5.44210344]
- [1.81486046 5.44210344 7.06273487]]
-[13.62123034  0.09662862  2.05480098]
+
    0.1999902359008225
+4.487000566129411
+1.3211480515121596
+1.0120561022775605 9.785157020098348 24.0365416391166
+2.9740940821517547 3.838584583553216 11.184094793957168
+[[ 1.0120561   2.97409408  3.83858458]
+ [ 2.97409408  9.78515702 11.18409479]
+ [ 3.83858458 11.18409479 24.03654164]]
+[30.9410965   0.08502185  3.80763641]
 
    
 
    
 
    
@@ -1579,7 +1601,7 @@ assumption for approximating \(\sigma
 
    
 
    
 
    
-
    0.029574060388349064 0.9577775794806141
+
    -0.026121042099059435 1.0617129312534124
 
    
 
    
 _images/statistics_188_1.png
diff --git a/doc/LectureNotes/_build/html/teachers.html b/doc/LectureNotes/_build/html/teachers.html
index bebb743b2..f45a16b34 100644
--- a/doc/LectureNotes/_build/html/teachers.html
+++ b/doc/LectureNotes/_build/html/teachers.html
@@ -276,6 +276,28 @@ const thebe_selector_output = ".output, .cell_output"
    Week 36: Statistical interpretation of Linear Regression and Resampling techniques
   
  
+ 
  • 
+  
+   Exercises week 37
+  
+ 
    • 
+ 
  • 
+  
+   Week 37: Statitsitcal interpretations and Resampling Methods
+  
+ 
    • 
+
+
    
+ 
+  Projects
+ 
+
    
+
 
     
    
diff --git a/doc/LectureNotes/_build/html/textbooks.html b/doc/LectureNotes/_build/html/textbooks.html
index d41a9ad55..6f37b6882 100644
--- a/doc/LectureNotes/_build/html/textbooks.html
+++ b/doc/LectureNotes/_build/html/textbooks.html
@@ -276,6 +276,28 @@ const thebe_selector_output = ".output, .cell_output"
    Week 36: Statistical interpretation of Linear Regression and Resampling techniques
   
  
+ 
  • 
+  
+   Exercises week 37
+  
+ 
    • 
+ 
  • 
+  
+   Week 37: Statitsitcal interpretations and Resampling Methods
+  
+ 
    • 
+
+
    
+ 
+  Projects
+ 
+
    
+
 
     
    
diff --git a/doc/LectureNotes/_build/html/week34.html b/doc/LectureNotes/_build/html/week34.html
index 69b9b0409..ff28d5d16 100644
--- a/doc/LectureNotes/_build/html/week34.html
+++ b/doc/LectureNotes/_build/html/week34.html
@@ -278,6 +278,28 @@ const thebe_selector_output = ".output, .cell_output"
    Week 36: Statistical interpretation of Linear Regression and Resampling techniques
   
  
+ 
  • 
+  
+   Exercises week 37
+  
+ 
    • 
+ 
  • 
+  
+   Week 37: Statitsitcal interpretations and Resampling Methods
+  
+ 
    • 
+
+
    
+ 
+  Projects
+ 
+
    
+
 
     
    
@@ -1743,8 +1765,8 @@ developed in the 1970s, namely EISPACK and LINPACK.  We describe them shortly he
 
    
 
    
 
    
-
    [-0.75408649 -0.05177092 -0.07339251  1.49372893 -1.21467644  0.24712854
-  0.67554302 -0.45143018  0.34212496  0.63262164]
+
    [-1.79544237 -0.19322111  0.14623399  0.65045925 -0.73133982 -1.90092179
+  0.45359479  1.04800573 -1.16171326  1.30577095]
 
    
 
    
 
    
@@ -1969,26 +1991,26 @@ lowercase letters for vectors and uppercase letters for matrices)
    
 
    
 
    
 
    
-
    [[0.11167579 0.88778091 0.24908246 0.32566092 0.37585988 0.61893735
-  0.58574143 0.60081665 0.81065392 0.00509527]
- [0.02840884 0.39600607 0.96810393 0.28213741 0.19237495 0.54219245
-  0.85581869 0.17928538 0.43185254 0.37624303]
- [0.82045496 0.22828694 0.52773891 0.54526769 0.84708672 0.59118929
-  0.18221254 0.94640767 0.25328924 0.03192893]
- [0.98328759 0.68996179 0.81168086 0.08086066 0.10659682 0.66599246
-  0.78035464 0.57403561 0.96995249 0.78990036]
- [0.9909606  0.39920034 0.59813773 0.85982436 0.66665241 0.60522226
-  0.08889302 0.74433499 0.85630009 0.2745333 ]
- [0.60826013 0.94413158 0.32305813 0.27011455 0.38636467 0.02568505
-  0.0610602  0.92275042 0.09189927 0.67177934]
- [0.72097126 0.35819312 0.98060869 0.46573851 0.70482138 0.51749473
-  0.17012048 0.53752634 0.66726905 0.08874264]
- [0.79974359 0.05023564 0.84150451 0.05491301 0.90643349 0.75505597
-  0.7300372  0.57445493 0.39626502 0.22016672]
- [0.44463741 0.01448144 0.01167264 0.85595734 0.09989861 0.81007682
-  0.30844205 0.68075712 0.9067362  0.96317459]
- [0.87327422 0.12086283 0.50504743 0.60715594 0.9440887  0.54041662
-  0.7316348  0.42976761 0.63933182 0.22772039]]
+
    [[0.79725436 0.93166184 0.53462883 0.92250132 0.79313278 0.4185877
+  0.21601417 0.21037404 0.98496212 0.89482188]
+ [0.15696119 0.72299619 0.71846708 0.7506246  0.74409239 0.1280756
+  0.5316382  0.91236018 0.24479698 0.3435384 ]
+ [0.5342745  0.2369833  0.47356208 0.16499193 0.60378214 0.9920084
+  0.80788856 0.36452684 0.23309661 0.33829607]
+ [0.7803076  0.17074761 0.15484848 0.82187419 0.69965466 0.85754328
+  0.35700089 0.70856363 0.44993812 0.48802709]
+ [0.06875458 0.23106527 0.28230186 0.40805354 0.54632096 0.11033412
+  0.51220693 0.07752967 0.58908017 0.78263078]
+ [0.62686358 0.14793475 0.11341291 0.46164895 0.32542732 0.42090072
+  0.25033968 0.33199489 0.25137033 0.17009925]
+ [0.74260356 0.49932184 0.99035178 0.5146617  0.9859105  0.8990231
+  0.38098948 0.10635754 0.21186069 0.07687896]
+ [0.92173899 0.87556429 0.04674926 0.70911476 0.43975616 0.37622356
+  0.79994469 0.22524236 0.10951119 0.04316854]
+ [0.3521478  0.25186426 0.59164202 0.44214614 0.09497154 0.97558913
+  0.40837841 0.56953559 0.36074377 0.95539206]
+ [0.33113182 0.3702755  0.31816439 0.83303886 0.51013506 0.6257439
+  0.89881026 0.55805262 0.79700882 0.14010994]]
 
    
 
    
 
    
@@ -2043,13 +2065,13 @@ covariance matrix through the np.linalg.eig() function.
    
 
    
 
    
 
    
-
    -0.05279147850537411
-3.9698377974429513
-0.22403397554517984
-[[ 1.03173163  3.03859372  3.15084741]
- [ 3.03859372  9.96514849  9.33589475]
- [ 3.15084741  9.33589475 15.3141149 ]]
-[23.20313883  0.08502083  3.02283536]
+
    -0.13314597157635316
+3.42745728579187
+-0.1549258803307933
+[[ 1.0457893   3.16754123  2.39769983]
+ [ 3.16754123 10.50453066  7.29238177]
+ [ 2.39769983  7.29238177  8.3431023 ]]
+[17.73772319  0.07333967  2.0823594 ]
 
    
 
    
 
    
@@ -2272,7 +2294,7 @@ Name: Aragorn, dtype: object
 
    
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16293/1326197715.py:6: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7752/1326197715.py:6: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
   data_pandas=data_pandas.append(pd.DataFrame(new_hobbit, index=['Pippin']))
 
    
 
    
diff --git a/doc/LectureNotes/_build/html/week35.html b/doc/LectureNotes/_build/html/week35.html
index 28f234655..b002b3156 100644
--- a/doc/LectureNotes/_build/html/week35.html
+++ b/doc/LectureNotes/_build/html/week35.html
@@ -278,6 +278,28 @@ const thebe_selector_output = ".output, .cell_output"
    Week 36: Statistical interpretation of Linear Regression and Resampling techniques
   
  
+ 
  • 
+  
+   Exercises week 37
+  
+ 
    • 
+ 
  • 
+  
+   Week 37: Statitsitcal interpretations and Resampling Methods
+  
+ 
    • 
+
+
    
+ 
+  Projects
+ 
+
    
+
 
     
    
@@ -1624,7 +1646,7 @@ Since we are not using Scikit-Learn here we can define our own
 
    
 
    
 
    
-
    0.9959033816551833
+
    0.996535469511469
 
    
 
    
 
    
@@ -1641,7 +1663,7 @@ Since we are not using Scikit-Learn here we can define our own
 
    
 
    
 
    
-
    0.009290411029763584
+
    0.0077750600806588575
 
    
 
    
 
    
@@ -1656,23 +1678,23 @@ Since we are not using Scikit-Learn here we can define our own
 
    
 
    
 
    
-
    [0.02126934 0.07602623 0.0014937  0.01294617 0.05421908 0.02237669
- 0.0026081  0.00564956 0.00399247 0.05763394 0.00040953 0.06861085
- 0.0098629  0.01199845 0.0097577  0.03260201 0.020964   0.01933058
- 0.02255062 0.01801774 0.04039087 0.00472303 0.01003763 0.01487742
- 0.05554042 0.00886682 0.05110883 0.02944194 0.00806407 0.01028231
- 0.03613949 0.03352185 0.0512238  0.01525206 0.00660801 0.01073938
- 0.06353697 0.00700232 0.0391902  0.08741274 0.01227458 0.01049472
- 0.04691549 0.00963223 0.0143088  0.05177527 0.00850988 0.01121347
- 0.02768957 0.02259051 0.02233576 0.01322543 0.02143332 0.01400329
- 0.00102864 0.01322099 0.00611932 0.01011376 0.13281267 0.00684221
- 0.05358851 0.02232779 0.00695738 0.03054765 0.00554475 0.05748797
- 0.03507211 0.00563446 0.03123832 0.00033779 0.01122997 0.1098906
- 0.07003926 0.03718926 0.0695405  0.00605451 0.0456042  0.00477722
- 0.01224109 0.01072866 0.04273116 0.01873409 0.02903947 0.01927709
- 0.00819724 0.00628788 0.00086553 0.02341603 0.0525063  0.03546779
- 0.03012368 0.05069808 0.00327082 0.00517074 0.00071305 0.01194406
- 0.05454172 0.02480935 0.00577016 0.02925853]
+
    [0.05751737 0.02644748 0.02533184 0.02193035 0.02521356 0.00712899
+ 0.00857688 0.0101339  0.01097227 0.01132947 0.01644452 0.01655455
+ 0.00771046 0.05177021 0.01374437 0.04208274 0.01667873 0.00228986
+ 0.00749579 0.00852965 0.01628823 0.0341899  0.01178253 0.00626339
+ 0.00514913 0.00791019 0.00363986 0.00471966 0.00390805 0.00910241
+ 0.00232255 0.02670606 0.03224523 0.01637147 0.00918914 0.02705154
+ 0.00321694 0.01904583 0.0177181  0.00538287 0.02291121 0.01028255
+ 0.04566103 0.00954257 0.00011551 0.0283589  0.00953728 0.03399521
+ 0.01205286 0.02251524 0.00353655 0.02344605 0.05288681 0.01950574
+ 0.00330907 0.01492855 0.01472766 0.03952093 0.01491299 0.00187154
+ 0.02897168 0.00072037 0.00895315 0.02775293 0.01547992 0.04117184
+ 0.0116726  0.03330335 0.01515966 0.0070381  0.01317074 0.00654702
+ 0.00329264 0.02502101 0.00226569 0.05029894 0.01929643 0.03028379
+ 0.053994   0.03413302 0.01854824 0.00393744 0.0600658  0.01855624
+ 0.0590702  0.01826743 0.01039549 0.02151219 0.00928016 0.03536062
+ 0.00503218 0.08526352 0.00506765 0.02609885 0.04771105 0.0010059
+ 0.00659545 0.00143188 0.01489692 0.08237141]
 
    
 
    
 
    
@@ -1741,15 +1763,15 @@ but now splitting the data into a training set and a test set.
    
 
    
 
    
 
    
-
    [ 2.04860436 -0.39444293  5.97533203 -0.78980112  0.09575221]
+
    [ 1.95976303  0.48974963  2.82202765  3.79224555 -2.14248744]
 Training R2
-0.9960913291755783
+0.9947613223847728
 Training MSE
-0.008823125370709272
+0.010596520060222926
 Test R2
-0.9906601091977738
+0.989645675273948
 Test MSE
-0.01969004537138309
+0.01889099091713886
 
    
 
    
 
    
diff --git a/doc/LectureNotes/_build/html/week36.html b/doc/LectureNotes/_build/html/week36.html
index 0c17d27f3..3bad39527 100644
--- a/doc/LectureNotes/_build/html/week36.html
+++ b/doc/LectureNotes/_build/html/week36.html
@@ -55,6 +55,7 @@ const thebe_selector_output = ".output, .cell_output"
     
     
     
+    
     
     
     
@@ -277,6 +278,28 @@ const thebe_selector_output = ".output, .cell_output"
    Week 36: Statistical interpretation of Linear Regression and Resampling techniques
   
  
+ 
  • 
+  
+   Exercises week 37
+  
+ 
    • 
+ 
  • 
+  
+   Week 37: Statitsitcal interpretations and Resampling Methods
+  
+ 
    • 
+
+
    
+ 
+  Projects
+ 
+
    
+
 
     
    
@@ -2213,6 +2236,13 @@ C(\boldsymbol{\beta}=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{
             
    Exercises week 36
    
         
    
     
+    
+    
    
+        
    next
    
+        
    Exercises week 37
    
+    
    
+    
+        
 
    
             
         
    
diff --git a/doc/LectureNotes/_build/html/week37.html b/doc/LectureNotes/_build/html/week37.html
new file mode 100644
index 000000000..ba5623255
--- /dev/null
+++ b/doc/LectureNotes/_build/html/week37.html
@@ -0,0 +1,2651 @@
+
+
+
+
+  
+    
+    
+    Week 37: Statitsitcal interpretations and Resampling Methods — Applied Data Analysis and Machine Learning
+    
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+                 Contents
+            
    
+            
+        
    
+    
    
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+    
    
+        
    
+            
+            
    
+                
    Week 37: Statitsitcal interpretations and Resampling Methods
    
+                
+                
    
+                    
    
+                        
+                        
    
+                            
     Contents 
    
+                        
    
+                        
+                    
    
+                
    
+            
    
+            
+              
    
+                
+  
+
    
+
    Week 37: Statitsitcal interpretations and Resampling Methods
    
+
    Morten Hjorth-Jensen, Department of Physics, University of Oslo and Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University
    
+
    Date: Sep 11, 2023
    
+
    Copyright 1999-2023, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
    
+
    
+
    Plans for week 37
    
+
    Material for the active learning sessions on Tuesday and Wednesday.
    
+
      
+
    • Lecture from last week on calculations of expectation values
      • 
+
    • Exercise for week 37
      • 
+
    • Work on project 1
      • 
+
    • See also additional note on scaling (jupyter-notebook) sent separately. This will be discussed during the first hour of each session.
      • 
+
    • For more discussions of Ridge regression and calculation of averages, Wessel van Wieringen’s article is highly recommended.
      • 
+
    
+
    Material for the lecture on Thursday September 7.
    
+
      
+
    • Statistical interpretation of Ridge and Lasso regression
      • 
+
    • Resampling techniques, Bootstrap and cross validation and bias-variance tradeoff
      • 
+
    • Reads and Videos:
      
+
+
      • 
+
    
+
    
+
    
+
    Material from last week and relevant for the weekly exercises
    
+
    
+
    
+
    Linking the regression analysis with a statistical interpretation
    
+
    We will now couple the discussions of ordinary least squares, Ridge
+and Lasso regression with a statistical interpretation, that is we
+move from a linear algebra analysis to a statistical analysis. In
+particular, we will focus on what the regularization terms can result
+in.  We will amongst other things show that the regularization
+parameter can reduce considerably the variance of the parameters
+\(\beta\).
    
+
    The
+advantage of doing linear regression is that we actually end up with
+analytical expressions for several statistical quantities.
    
+Standard least squares and Ridge regression  allow us to
+derive quantities like the variance and other expectation values in a
+rather straightforward way.
    
+
    It is assumed that \(\varepsilon_i
+\sim \mathcal{N}(0, \sigma^2)\) and the \(\varepsilon_{i}\) are
+independent, i.e.:
    
+
    
+\[\begin{split}
+\begin{align*} 
+\mbox{Cov}(\varepsilon_{i_1},
+\varepsilon_{i_2}) & = \left\{ \begin{array}{lcc} \sigma^2 & \mbox{if}
+& i_1 = i_2, \\ 0 & \mbox{if} & i_1 \not= i_2.  \end{array} \right.
+\end{align*}
+\end{split}\]
    
+
    The randomness of \(\varepsilon_i\) implies that
+\(\mathbf{y}_i\) is also a random variable. In particular,
+\(\mathbf{y}_i\) is normally distributed, because \(\varepsilon_i \sim
+\mathcal{N}(0, \sigma^2)\) and \(\mathbf{X}_{i,\ast} \, \boldsymbol{\beta}\) is a
+non-random scalar. To specify the parameters of the distribution of
+\(\mathbf{y}_i\) we need to calculate its first two moments.
    
+
    Recall that \(\boldsymbol{X}\) is a matrix of dimensionality \(n\times p\). The
+notation above \(\mathbf{X}_{i,\ast}\) means that we are looking at the
+row number \(i\) and perform a sum over all values \(p\).
    
+
    
+
    
+
    Assumptions made
    
+
    The assumption we have made here can be summarized as (and this is going to be useful when we discuss the bias-variance trade off)
+that there exists a function \(f(\boldsymbol{x})\) and  a normal distributed error \(\boldsymbol{\varepsilon}\sim \mathcal{N}(0, \sigma^2)\)
+which describe our data
    
+
    
+\[
+\boldsymbol{y} = f(\boldsymbol{x})+\boldsymbol{\varepsilon}
+\]
    
+
    We approximate this function with our model from the solution of the linear regression equations, that is our
+function \(f\) is approximated by \(\boldsymbol{\tilde{y}}\) where we want to minimize \((\boldsymbol{y}-\boldsymbol{\tilde{y}})^2\), our MSE, with
    
+
    
+\[
+\boldsymbol{\tilde{y}} = \boldsymbol{X}\boldsymbol{\beta}.
+\]
    
+
    
+
    
+
    Expectation value and variance
    
+
    We can calculate the expectation value of \(\boldsymbol{y}\) for a given element \(i\)
    
+
    
+\[
+\begin{align*} 
+\mathbb{E}(y_i) & =
+\mathbb{E}(\mathbf{X}_{i, \ast} \, \boldsymbol{\beta}) + \mathbb{E}(\varepsilon_i)
+\, \, \, = \, \, \, \mathbf{X}_{i, \ast} \, \beta, 
+\end{align*}
+\]
    
+
    while
+its variance is
    
+
    
+\[\begin{split}
+\begin{align*} \mbox{Var}(y_i) & = \mathbb{E} \{ [y_i
+- \mathbb{E}(y_i)]^2 \} \, \, \, = \, \, \, \mathbb{E} ( y_i^2 ) -
+[\mathbb{E}(y_i)]^2  \\  & = \mathbb{E} [ ( \mathbf{X}_{i, \ast} \,
+\beta + \varepsilon_i )^2] - ( \mathbf{X}_{i, \ast} \, \boldsymbol{\beta})^2 \\ &
+= \mathbb{E} [ ( \mathbf{X}_{i, \ast} \, \boldsymbol{\beta})^2 + 2 \varepsilon_i
+\mathbf{X}_{i, \ast} \, \boldsymbol{\beta} + \varepsilon_i^2 ] - ( \mathbf{X}_{i,
+\ast} \, \beta)^2 \\  & = ( \mathbf{X}_{i, \ast} \, \boldsymbol{\beta})^2 + 2
+\mathbb{E}(\varepsilon_i) \mathbf{X}_{i, \ast} \, \boldsymbol{\beta} +
+\mathbb{E}(\varepsilon_i^2 ) - ( \mathbf{X}_{i, \ast} \, \boldsymbol{\beta})^2 
+\\ & = \mathbb{E}(\varepsilon_i^2 ) \, \, \, = \, \, \,
+\mbox{Var}(\varepsilon_i) \, \, \, = \, \, \, \sigma^2.  
+\end{align*}
+\end{split}\]
    
+
    Hence, \(y_i \sim \mathcal{N}( \mathbf{X}_{i, \ast} \, \boldsymbol{\beta}, \sigma^2)\), that is \(\boldsymbol{y}\) follows a normal distribution with
+mean value \(\boldsymbol{X}\boldsymbol{\beta}\) and variance \(\sigma^2\) (not be confused with the singular values of the SVD).
    
+
    
+
    
+
    Expectation value and variance for \(\boldsymbol{\beta}\)
    
+
    With the OLS expressions for the optimal parameters \(\boldsymbol{\hat{\beta}}\) we can evaluate the expectation value
    
+
    
+\[
+\mathbb{E}(\boldsymbol{\hat{\beta}}) = \mathbb{E}[ (\mathbf{X}^{\top} \mathbf{X})^{-1}\mathbf{X}^{T} \mathbf{Y}]=(\mathbf{X}^{T} \mathbf{X})^{-1}\mathbf{X}^{T} \mathbb{E}[ \mathbf{Y}]=(\mathbf{X}^{T} \mathbf{X})^{-1} \mathbf{X}^{T}\mathbf{X}\boldsymbol{\beta}=\boldsymbol{\beta}.
+\]
    
+
    This means that the estimator of the regression parameters is unbiased.
    
+
    We can also calculate the variance
    
+
    The variance of the optimal value \(\boldsymbol{\hat{\beta}}\) is
    
+
    
+\[\begin{split}
+\begin{eqnarray*}
+\mbox{Var}(\boldsymbol{\hat{\beta}}) & = & \mathbb{E} \{ [\boldsymbol{\beta} - \mathbb{E}(\boldsymbol{\beta})] [\boldsymbol{\beta} - \mathbb{E}(\boldsymbol{\beta})]^{T} \}
+\\
+& = & \mathbb{E} \{ [(\mathbf{X}^{T} \mathbf{X})^{-1} \, \mathbf{X}^{T} \mathbf{Y} - \boldsymbol{\beta}] \, [(\mathbf{X}^{T} \mathbf{X})^{-1} \, \mathbf{X}^{T} \mathbf{Y} - \boldsymbol{\beta}]^{T} \}
+\\
+% & = & \mathbb{E} \{ [(\mathbf{X}^{T} \mathbf{X})^{-1} \, \mathbf{X}^{T} \mathbf{Y}] \, [(\mathbf{X}^{T} \mathbf{X})^{-1} \, \mathbf{X}^{T} \mathbf{Y}]^{T} \} - \boldsymbol{\beta} \, \boldsymbol{\beta}^{T}
+% \\
+% & = & \mathbb{E} \{ (\mathbf{X}^{T} \mathbf{X})^{-1} \, \mathbf{X}^{T} \mathbf{Y} \, \mathbf{Y}^{T} \, \mathbf{X} \, (\mathbf{X}^{T} \mathbf{X})^{-1}  \} - \boldsymbol{\beta} \, \boldsymbol{\beta}^{T}
+% \\
+& = & (\mathbf{X}^{T} \mathbf{X})^{-1} \, \mathbf{X}^{T} \, \mathbb{E} \{ \mathbf{Y} \, \mathbf{Y}^{T} \} \, \mathbf{X} \, (\mathbf{X}^{T} \mathbf{X})^{-1} - \boldsymbol{\beta} \, \boldsymbol{\beta}^{T}
+\\
+& = & (\mathbf{X}^{T} \mathbf{X})^{-1} \, \mathbf{X}^{T} \, \{ \mathbf{X} \, \boldsymbol{\beta} \, \boldsymbol{\beta}^{T} \,  \mathbf{X}^{T} + \sigma^2 \} \, \mathbf{X} \, (\mathbf{X}^{T} \mathbf{X})^{-1} - \boldsymbol{\beta} \, \boldsymbol{\beta}^{T}
+% \\
+% & = & (\mathbf{X}^T \mathbf{X})^{-1} \, \mathbf{X}^T \, \mathbf{X} \, \boldsymbol{\beta} \, \boldsymbol{\beta}^T \,  \mathbf{X}^T \, \mathbf{X} \, (\mathbf{X}^T % \mathbf{X})^{-1}
+% \\
+% & & + \, \, \sigma^2 \, (\mathbf{X}^T \mathbf{X})^{-1} \, \mathbf{X}^T  \, \mathbf{X} \, (\mathbf{X}^T \mathbf{X})^{-1} - \boldsymbol{\beta} \boldsymbol{\beta}^T
+\\
+& = & \boldsymbol{\beta} \, \boldsymbol{\beta}^{T}  + \sigma^2 \, (\mathbf{X}^{T} \mathbf{X})^{-1} - \boldsymbol{\beta} \, \boldsymbol{\beta}^{T}
+\, \, \, = \, \, \, \sigma^2 \, (\mathbf{X}^{T} \mathbf{X})^{-1},
+\end{eqnarray*}
+\end{split}\]
    
+
    where we have used  that \(\mathbb{E} (\mathbf{Y} \mathbf{Y}^{T}) =
+\mathbf{X} \, \boldsymbol{\beta} \, \boldsymbol{\beta}^{T} \, \mathbf{X}^{T} +
+\sigma^2 \, \mathbf{I}_{nn}\). From \(\mbox{Var}(\boldsymbol{\beta}) = \sigma^2
+\, (\mathbf{X}^{T} \mathbf{X})^{-1}\), one obtains an estimate of the
+variance of the estimate of the \(j\)-th regression coefficient:
+\(\boldsymbol{\sigma}^2 (\boldsymbol{\beta}_j ) = \boldsymbol{\sigma}^2 [(\mathbf{X}^{T} \mathbf{X})^{-1}]_{jj} \). This may be used to
+construct a confidence interval for the estimates.
    
+
    In a similar way, we can obtain analytical expressions for say the
+expectation values of the parameters \(\boldsymbol{\beta}\) and their variance
+when we employ Ridge regression, allowing us again to define a confidence interval.
    
+
    It is rather straightforward to show that
    
+
    
+\[
+\mathbb{E} \big[ \boldsymbol{\beta}^{\mathrm{Ridge}} \big]=(\mathbf{X}^{T} \mathbf{X} + \lambda \mathbf{I}_{pp})^{-1} (\mathbf{X}^{\top} \mathbf{X})\boldsymbol{\beta}^{\mathrm{OLS}}.
+\]
    
+
    We see clearly that
+\(\mathbb{E} \big[ \boldsymbol{\beta}^{\mathrm{Ridge}} \big] \not= \boldsymbol{\beta}^{\mathrm{OLS}}\) for any \(\lambda > 0\).
    
+
    We can also compute the variance as
    
+
    
+\[
+\mbox{Var}[\boldsymbol{\beta}^{\mathrm{Ridge}}]=\sigma^2[  \mathbf{X}^{T} \mathbf{X} + \lambda \mathbf{I} ]^{-1}  \mathbf{X}^{T} \mathbf{X} \{ [  \mathbf{X}^{\top} \mathbf{X} + \lambda \mathbf{I} ]^{-1}\}^{T},
+\]
    
+
    and it is easy to see that if the parameter \(\lambda\) goes to infinity then the variance of Ridge parameters \(\boldsymbol{\beta}\) goes to zero.
    
+
    With this, we can compute the difference
    
+
    
+\[
+\mbox{Var}[\boldsymbol{\beta}^{\mathrm{OLS}}]-\mbox{Var}(\boldsymbol{\beta}^{\mathrm{Ridge}})=\sigma^2 [  \mathbf{X}^{T} \mathbf{X} + \lambda \mathbf{I} ]^{-1}[ 2\lambda\mathbf{I} + \lambda^2 (\mathbf{X}^{T} \mathbf{X})^{-1} ] \{ [  \mathbf{X}^{T} \mathbf{X} + \lambda \mathbf{I} ]^{-1}\}^{T}.
+\]
    
+
    The difference is non-negative definite since each component of the
+matrix product is non-negative definite.
+This means the variance we obtain with the standard OLS will always for \(\lambda > 0\) be larger than the variance of \(\boldsymbol{\beta}\) obtained with the Ridge estimator. This has interesting consequences when we discuss the so-called bias-variance trade-off below.
    
+
    For more discussions of Ridge regression and calculation of averages, Wessel van Wieringen’s article is highly recommended.
    
+
    
+
    
+
    Material for lecture Thursday September 14
    
+
    
+
    
+
    Deriving OLS from a probability distribution
    
+
    Our basic assumption when we derived the OLS equations was to assume
+that our output is determined by a given continuous function
+\(f(\boldsymbol{x})\) and a random noise \(\boldsymbol{\epsilon}\) given by the normal
+distribution with zero mean value and an undetermined variance
+\(\sigma^2\).
    
+
    We found above that the outputs \(\boldsymbol{y}\) have a mean value given by
+\(\boldsymbol{X}\hat{\boldsymbol{\beta}}\) and variance \(\sigma^2\). Since the entries to
+the design matrix are not stochastic variables, we can assume that the
+probability distribution of our targets is also a normal distribution
+but now with mean value \(\boldsymbol{X}\hat{\boldsymbol{\beta}}\). This means that a
+single output \(y_i\) is given by the Gaussian distribution
    
+
    
+\[
+y_i\sim \mathcal{N}(\boldsymbol{X}_{i,*}\boldsymbol{\beta}, \sigma^2)=\frac{1}{\sqrt{2\pi\sigma^2}}\exp{\left[-\frac{(y_i-\boldsymbol{X}_{i,*}\boldsymbol{\beta})^2}{2\sigma^2}\right]}.
+\]
    
+
    
+
    
+
    Independent and Identically Distrubuted (iid)
    
+
    We assume now that the various \(y_i\) values are stochastically distributed according to the above Gaussian distribution.
+We define this distribution as
    
+
    
+\[
+p(y_i, \boldsymbol{X}\vert\boldsymbol{\beta})=\frac{1}{\sqrt{2\pi\sigma^2}}\exp{\left[-\frac{(y_i-\boldsymbol{X}_{i,*}\boldsymbol{\beta})^2}{2\sigma^2}\right]},
+\]
    
+
    which reads as finding the likelihood of an event \(y_i\) with the input variables \(\boldsymbol{X}\) given the parameters (to be determined) \(\boldsymbol{\beta}\).
    
+
    Since these events are assumed to be independent and identicall distributed we can build the probability distribution function (PDF) for all possible event \(\boldsymbol{y}\) as the product of the single events, that is we have
    
+
    
+\[
+p(\boldsymbol{y},\boldsymbol{X}\vert\boldsymbol{\beta})=\prod_{i=0}^{n-1}\frac{1}{\sqrt{2\pi\sigma^2}}\exp{\left[-\frac{(y_i-\boldsymbol{X}_{i,*}\boldsymbol{\beta})^2}{2\sigma^2}\right]}=\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta}).
+\]
    
+
    We will write this in a more compact form reserving \(\boldsymbol{D}\) for the domain of events, including the ouputs (targets) and the inputs. That is
+in case we have a simple one-dimensional input and output case
    
+
    
+\[
+\boldsymbol{D}=[(x_0,y_0), (x_1,y_1),\dots, (x_{n-1},y_{n-1})].
+\]
    
+
    In the more general case the various inputs should be replaced by the possible features represented by the input data set \(\boldsymbol{X}\).
+We can now rewrite the above probability as
    
+
    
+\[
+p(\boldsymbol{D}\vert\boldsymbol{\beta})=\prod_{i=0}^{n-1}\frac{1}{\sqrt{2\pi\sigma^2}}\exp{\left[-\frac{(y_i-\boldsymbol{X}_{i,*}\boldsymbol{\beta})^2}{2\sigma^2}\right]}.
+\]
    
+
    It is a conditional probability (see below) and reads as the likelihood of a domain of events \(\boldsymbol{D}\) given a set of parameters \(\boldsymbol{\beta}\).
    
+
    
+
    
+
    Maximum Likelihood Estimation (MLE)
    
+
    In statistics, maximum likelihood estimation (MLE) is a method of
+estimating the parameters of an assumed probability distribution,
+given some observed data. This is achieved by maximizing a likelihood
+function so that, under the assumed statistical model, the observed
+data is the most probable.
    
+
    We will assume here that our events are given by the above Gaussian
+distribution and we will determine the optimal parameters \(\beta\) by
+maximizing the above PDF. However, computing the derivatives of a
+product function is cumbersome and can easily lead to overflow and/or
+underflowproblems, with potentials for loss of numerical precision.
    
+
    In practice, it is more convenient to maximize the logarithm of the
+PDF because it is a monotonically increasing function of the argument.
+Alternatively, and this will be our option, we will minimize the
+negative of the logarithm since this is a monotonically decreasing
+function.
    
+
    Note also that maximization/minimization of the logarithm of the PDF
+is equivalent to the maximization/minimization of the function itself.
    
+
    
+
    
+
    A new Cost Function
    
+
    We could now define a new cost function to minimize, namely the negative logarithm of the above PDF
    
+
    
+\[
+C(\boldsymbol{\beta}=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})},
+\]
    
+
    which becomes
    
+
    
+\[
+C(\boldsymbol{\beta}=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}.
+\]
    
+
    Taking the derivative of the new cost function with respect to the parameters \(\beta\) we recognize our familiar OLS equation, namely
    
+
    
+\[
+\boldsymbol{X}^T\left(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right) =0,
+\]
    
+
    which leads to the well-known OLS equation for the optimal paramters \(\beta\)
    
+
    
+\[
+\hat{\boldsymbol{\beta}}^{\mathrm{OLS}}=\left(\boldsymbol{X}^T\boldsymbol{X}\right)^{-1}\boldsymbol{X}^T\boldsymbol{y}!
+\]
    
+
    Before we make a similar analysis for Ridge and Lasso regression, we need a short reminder on statistics.
    
+
    
+
    
+
    More basic Statistics and Bayes’ theorem
    
+
    A central theorem in statistics is Bayes’ theorem. This theorem plays a similar role as the good old Pythagoras’ theorem in geometry.
+Bayes’ theorem is extremely simple to derive. But to do so we need some basic axioms from statistics.
    
+
    Assume we have two domains of events \(X=[x_0,x_1,\dots,x_{n-1}]\) and \(Y=[y_0,y_1,\dots,y_{n-1}]\).
    
+
    We define also the likelihood for \(X\) and \(Y\) as \(p(X)\) and \(p(Y)\) respectively.
+The likelihood of a specific event \(x_i\) (or \(y_i\)) is then written as \(p(X=x_i)\) or just \(p(x_i)=p_i\).
    
+
    Union of events is given by.
    
+
    
+\[
+p(X \cup Y)= p(X)+p(Y)-p(X \cap Y).
+\]
    
+
    The product rule (aka joint probability) is given by.
    
+
    
+\[
+p(X \cup Y)= p(X,Y)= p(X\vert Y)p(Y)=p(Y\vert X)p(X),
+\]
    
+
    where we read \(p(X\vert Y)\) as the likelihood of obtaining \(X\) given \(Y\).
    
+
    If we have independent events then \(p(X,Y)=p(X)p(Y)\).
    
+
    
+
    
+
    Marginal Probability
    
+
    The marginal probability is defined in terms of only one of the set of variables \(X,Y\). For a discrete probability we have
    
+
    
+\[
+p(X)=\sum_{i=0}^{n-1}p(X,Y=y_i)=\sum_{i=0}^{n-1}p(X\vert Y=y_i)p(Y=y_i)=\sum_{i=0}^{n-1}p(X\vert y_i)p(y_i).
+\]
    
+
    
+
    
+
    Conditional  Probability
    
+
    The conditional  probability, if \(p(Y) > 0\), is
    
+
    
+\[
+p(X\vert Y)= \frac{p(X,Y)}{p(Y)}=\frac{p(X,Y)}{\sum_{i=0}^{n-1}p(Y\vert X=x_i)p(x_i)}.
+\]
    
+
    
+
    
+
    Bayes’ Theorem
    
+
    If we combine the conditional probability with the marginal probability and the standard product rule, we have
    
+
    
+\[
+p(X\vert Y)= \frac{p(X,Y)}{p(Y)},
+\]
    
+
    which we can rewrite as
    
+
    
+\[
+p(X\vert Y)= \frac{p(X,Y)}{\sum_{i=0}^{n-1}p(Y\vert X=x_i)p(x_i)}=\frac{p(Y\vert X)p(X)}{\sum_{i=0}^{n-1}p(Y\vert X=x_i)p(x_i)},
+\]
    
+
    which is Bayes’ theorem. It allows us to evaluate the uncertainty in in \(X\) after we have observed \(Y\). We can easily interchange \(X\) with \(Y\).
    
+
    
+
    
+
    Interpretations of Bayes’ Theorem
    
+
    The quantity \(p(Y\vert X)\) on the right-hand side of the theorem is
+evaluated for the observed data \(Y\) and can be viewed as a function of
+the parameter space represented by \(X\). This function is not
+necesseraly normalized and is normally called the likelihood function.
    
+
    The function \(p(X)\) on the right hand side is called the prior while the function on the left hand side is the called the posterior probability. The denominator on the right hand side serves as a normalization factor for the posterior distribution.
    
+
    Let us try to illustrate Bayes’ theorem through an example.
    
+
    
+
    
+
    Example of Usage of Bayes’ theorem
    
+
    Let us suppose that you are undergoing a series of mammography scans in
+order to rule out possible breast cancer cases.  We define the
+sensitivity for a positive event by the variable \(X\). It takes binary
+values with \(X=1\) representing a positive event and \(X=0\) being a
+negative event. We reserve \(Y\) as a classification parameter for
+either a negative or a positive breast cancer confirmation. (Short note on wordings: positive here means having breast cancer, although none of us would consider this being a  positive thing).
    
+
    We let \(Y=1\) represent the the case of having breast cancer and \(Y=0\) as not.
    
+
    Let us assume that if you have breast cancer, the test will be positive with a probability of \(0.8\), that is we have
    
+
    
+\[
+p(X=1\vert Y=1) =0.8.
+\]
    
+
    This obviously sounds  scary since many would conclude that if the test is positive, there is a likelihood of \(80\%\) for having cancer.
+It is however not correct, as the following Bayesian analysis shows.
    
+
    
+
    
+
    Doing it correctly
    
+
    If we look at various national surveys on breast cancer, the general likelihood of developing breast cancer is a very small number.
+Let us assume that the prior probability in the population as a whole is
    
+
    
+\[
+p(Y=1) =0.004.
+\]
    
+
    We need also to account for the fact that the test may produce a false positive result (false alarm). Let us here assume that we have
    
+
    
+\[
+p(X=1\vert Y=0) =0.1.
+\]
    
+
    Using Bayes’ theorem we can then find the posterior probability that the person has breast cancer in case of a positive test, that is we can compute
    
+
    
+\[
+p(Y=1\vert X=1)=\frac{p(X=1\vert Y=1)p(Y=1)}{p(X=1\vert Y=1)p(Y=1)+p(X=1\vert Y=0)p(Y=0)}=\frac{0.8\times 0.004}{0.8\times 0.004+0.1\times 0.996}=0.031.
+\]
    
+
    That is, in case of a positive test, there is only a \(3\%\) chance of having breast cancer!
    
+
    
+
    
+
    Bayes’ Theorem and Ridge and Lasso Regression
    
+
    Using Bayes’ theorem we can gain a better intuition about Ridge and Lasso regression.
    
+
    For ordinary least squares we postulated that the maximum likelihood for the doamin of events \(\boldsymbol{D}\) (one-dimensional case)
    
+
    
+\[
+\boldsymbol{D}=[(x_0,y_0), (x_1,y_1),\dots, (x_{n-1},y_{n-1})],
+\]
    
+
    is given by
    
+
    
+\[
+p(\boldsymbol{D}\vert\boldsymbol{\beta})=\prod_{i=0}^{n-1}\frac{1}{\sqrt{2\pi\sigma^2}}\exp{\left[-\frac{(y_i-\boldsymbol{X}_{i,*}\boldsymbol{\beta})^2}{2\sigma^2}\right]}.
+\]
    
+
    In Bayes’ theorem this function plays the role of the so-called likelihood. We could now ask the question what is the posterior probability of a parameter set \(\boldsymbol{\beta}\) given a domain of events \(\boldsymbol{D}\)?  That is, how can we define the posterior probability
    
+
    
+\[
+p(\boldsymbol{\beta}\vert\boldsymbol{D}).
+\]
    
+
    Bayes’ theorem comes to our rescue here since (omitting the normalization constant)
    
+
    
+\[
+p(\boldsymbol{\beta}\vert\boldsymbol{D})\propto p(\boldsymbol{D}\vert\boldsymbol{\beta})p(\boldsymbol{\beta}).
+\]
    
+
    We have a model for \(p(\boldsymbol{D}\vert\boldsymbol{\beta})\) but need one for the prior \(p(\boldsymbol{\beta}\)!
    
+
    
+
    
+
    Ridge and Bayes
    
+
    With the posterior probability defined by a likelihood which we have
+already modeled and an unknown prior, we are now ready to make
+additional models for the prior.
    
+
    We can, based on our discussions of the variance of \(\boldsymbol{\beta}\) and the mean value, assume that the prior for the values \(\boldsymbol{\beta}\) is given by a Gaussian with mean value zero and variance \(\tau^2\), that is
    
+
    
+\[
+p(\boldsymbol{\beta})=\prod_{j=0}^{p-1}\exp{\left(-\frac{\beta_j^2}{2\tau^2}\right)}.
+\]
    
+
    Our posterior probability becomes then (omitting the normalization factor which is just a constant)
    
+
    
+\[
+p(\boldsymbol{\beta\vert\boldsymbol{D})}=\prod_{i=0}^{n-1}\frac{1}{\sqrt{2\pi\sigma^2}}\exp{\left[-\frac{(y_i-\boldsymbol{X}_{i,*}\boldsymbol{\beta})^2}{2\sigma^2}\right]}\prod_{j=0}^{p-1}\exp{\left(-\frac{\beta_j^2}{2\tau^2}\right)}.
+\]
    
+
    We can now optimize this quantity with respect to \(\boldsymbol{\beta}\). As we
+did for OLS, this is most conveniently done by taking the negative
+logarithm of the posterior probability. Doing so and leaving out the
+constants terms that do not depend on \(\beta\), we have
    
+
    
+\[
+C(\boldsymbol{\beta})=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}+\frac{1}{2\tau^2}\vert\vert\boldsymbol{\beta}\vert\vert_2^2,
+\]
    
+
    and replacing \(1/2\tau^2\) with \(\lambda\) we have
    
+
    
+\[
+C(\boldsymbol{\beta})=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}+\lambda\vert\vert\boldsymbol{\beta}\vert\vert_2^2,
+\]
    
+
    which is our Ridge cost function!  Nice, isn’t it?
    
+
    
+
    
+
    Lasso and Bayes
    
+
    To derive the Lasso cost function, we simply replace the Gaussian prior with an exponential distribution (Laplace in this case) with zero mean value,  that is
    
+
    
+\[
+p(\boldsymbol{\beta})=\prod_{j=0}^{p-1}\exp{\left(-\frac{\vert\beta_j\vert}{\tau}\right)}.
+\]
    
+
    Our posterior probability becomes then (omitting the normalization factor which is just a constant)
    
+
    
+\[
+p(\boldsymbol{\beta}\vert\boldsymbol{D})=\prod_{i=0}^{n-1}\frac{1}{\sqrt{2\pi\sigma^2}}\exp{\left[-\frac{(y_i-\boldsymbol{X}_{i,*}\boldsymbol{\beta})^2}{2\sigma^2}\right]}\prod_{j=0}^{p-1}\exp{\left(-\frac{\vert\beta_j\vert}{\tau}\right)}.
+\]
    
+
    Taking the negative
+logarithm of the posterior probability and leaving out the
+constants terms that do not depend on \(\beta\), we have
    
+
    
+\[
+C(\boldsymbol{\beta}=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}+\frac{1}{\tau}\vert\vert\boldsymbol{\beta}\vert\vert_1,
+\]
    
+
    and replacing \(1/\tau\) with \(\lambda\) we have
    
+
    
+\[
+C(\boldsymbol{\beta}=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}+\lambda\vert\vert\boldsymbol{\beta}\vert\vert_1,
+\]
    
+
    which is our Lasso cost function!
    
+
    
+
    
+
    Why resampling methods
    
+
    Before we proceed, we need to rethink what we have been doing. In our
+eager to fit the data, we have omitted several important elements in
+our regression analysis. In what follows we will
    
+
      
+
    1. look at statistical properties, including a discussion of mean values, variance and the so-called bias-variance tradeoff
      2. 
+
    2. introduce resampling techniques like cross-validation, bootstrapping and jackknife and more
      3. 
+
    
+
    and discuss how to select a given model (one of the difficult parts in machine learning).
    
+
    
+
    
+
    Resampling methods
    
+
    Resampling methods are an indispensable tool in modern
+statistics. They involve repeatedly drawing samples from a training
+set and refitting a model of interest on each sample in order to
+obtain additional information about the fitted model. For example, in
+order to estimate the variability of a linear regression fit, we can
+repeatedly draw different samples from the training data, fit a linear
+regression to each new sample, and then examine the extent to which
+the resulting fits differ. Such an approach may allow us to obtain
+information that would not be available from fitting the model only
+once using the original training sample.
    
+
    Two resampling methods are often used in Machine Learning analyses,
    
+
      
+
    1. The bootstrap method
      2. 
+
    2. and Cross-Validation
      3. 
+
    
+
    In addition there are several other methods such as the Jackknife and the Blocking methods. We will discuss in particular
+cross-validation and the bootstrap method.
    
+
    
+
    
+
    Resampling approaches can be computationally expensive
    
+
    Resampling approaches can be computationally expensive, because they
+involve fitting the same statistical method multiple times using
+different subsets of the training data. However, due to recent
+advances in computing power, the computational requirements of
+resampling methods generally are not prohibitive. In this chapter, we
+discuss two of the most commonly used resampling methods,
+cross-validation and the bootstrap. Both methods are important tools
+in the practical application of many statistical learning
+procedures. For example, cross-validation can be used to estimate the
+test error associated with a given statistical learning method in
+order to evaluate its performance, or to select the appropriate level
+of flexibility. The process of evaluating a model’s performance is
+known as model assessment, whereas the process of selecting the proper
+level of flexibility for a model is known as model selection. The
+bootstrap is widely used.
    
+
    
+
    
+
    Why resampling methods ?
    
+
    Statistical analysis.
    
+
      
+
    • Our simulations can be treated as computer experiments. This is particularly the case for Monte Carlo methods which are widely used in statistical analyses.
      • 
+
    • The results can be analysed with the same statistical tools as we would use when analysing experimental data.
      • 
+
    • As in all experiments, we are looking for expectation values and an estimate of how accurate they are, i.e., possible sources for errors.
      • 
+
    
+
    
+
    
+
    Statistical analysis
    
+
      
+
    • As in other experiments, many numerical  experiments have two classes of errors:
      
+
        
+
      • Statistical errors
        • 
+
      • Systematical errors
        • 
+
      
+
      • 
+
    • Statistical errors can be estimated using standard tools from statistics
      • 
+
    • Systematical errors are method specific and must be treated differently from case to case.
      • 
+
    
+
    
+
    
+
    Resampling methods
    
+
    With all these analytical equations for both the OLS and Ridge
+regression, we will now outline how to assess a given model. This will
+lead to a discussion of the so-called bias-variance tradeoff (see
+below) and so-called resampling methods.
    
+
    One of the quantities we have discussed as a way to measure errors is
+the mean-squared error (MSE), mainly used for fitting of continuous
+functions. Another choice is the absolute error.
    
+
    In the discussions below we will focus on the MSE and in particular since we will split the data into test and training data,
+we discuss the
    
+
      
+
    1. prediction error or simply the test error \(\mathrm{Err_{Test}}\), where we have a fixed training set and the test error is the MSE arising from the data reserved for testing. We discuss also the
      2. 
+
    2. training error \(\mathrm{Err_{Train}}\), which is the average loss over the training data.
      3. 
+
    
+
    As our model becomes more and more complex, more of the training data tends to  used. The training may thence adapt to more complicated structures in the data. This may lead to a decrease in the bias (see below for code example) and a slight increase of the variance for the test error.
+For a certain level of complexity the test error will reach minimum, before starting to increase again. The
+training error reaches a saturation.
    
+
    
+
    
+
    Resampling methods: Bootstrap
    
+
    Bootstrapping is a non-parametric approach to statistical inference
+that substitutes computation for more traditional distributional
+assumptions and asymptotic results. Bootstrapping offers a number of
+advantages:
    
+
      
+
    1. The bootstrap is quite general, although there are some cases in which it fails.
      2. 
+
    2. Because it does not require distributional assumptions (such as normally distributed errors), the bootstrap can provide more accurate inferences when the data are not well behaved or when the sample size is small.
      3. 
+
    3. It is possible to apply the bootstrap to statistics with sampling distributions that are difficult to derive, even asymptotically.
      4. 
+
    4. It is relatively simple to apply the bootstrap to complex data-collection plans (such as stratified and clustered samples).
      5. 
+
    
+
    The textbook by Davison on the Bootstrap Methods and their Applications provides many more insights and proofs. In this course we will take a more practical approach and use the results and theorems provided in the literature. For those interested in reading more about the bootstrap methods, we recommend the above text and the one by Efron and Tibshirani.
    
+
    Before we proceed however, we need to remind ourselves about a central theorem in statistics, namely the so-called central limit theorem.
    
+
    
+
    
+
    The Central Limit Theorem
    
+
    Suppose we have a PDF \(p(x)\) from which we generate  a series \(N\)
+of averages \(\mathbb{E}[x_i]\). Each mean value \(\mathbb{E}[x_i]\)
+is viewed as the average of a specific measurement, e.g., throwing
+dice 100 times and then taking the average value, or producing a certain
+amount of random numbers.
+For notational ease, we set \(\mathbb{E}[x_i]=x_i\) in the discussion
+which follows. We do the same for \(\mathbb{E}[z]=z\).
    
+
    If we compute the mean \(z\) of \(m\) such mean values \(x_i\)
    
+
    
+\[
+z=\frac{x_1+x_2+\dots+x_m}{m},
+\]
    
+
    the question we pose is which is the PDF of the new variable \(z\).
    
+
    
+
    
+
    Finding the Limit
    
+
    The probability of obtaining an average value \(z\) is the product of the
+probabilities of obtaining arbitrary individual mean values \(x_i\),
+but with the constraint that the average is \(z\). We can express this through
+the following expression
    
+
    
+\[
+\tilde{p}(z)=\int dx_1p(x_1)\int dx_2p(x_2)\dots\int dx_mp(x_m)
+    \delta(z-\frac{x_1+x_2+\dots+x_m}{m}),
+\]
    
+
    where the \(\delta\)-function enbodies the constraint that the mean is \(z\).
+All measurements that lead to each individual \(x_i\) are expected to
+be independent, which in turn means that we can express \(\tilde{p}\) as the
+product of individual \(p(x_i)\).  The independence assumption is important in the derivation of the central limit theorem.
    
+
    
+
    
+
    Rewriting the \(\delta\)-function
    
+
    If we use the integral expression for the \(\delta\)-function
    
+
    
+\[
+\delta(z-\frac{x_1+x_2+\dots+x_m}{m})=\frac{1}{2\pi}\int_{-\infty}^{\infty}
+   dq\exp{\left(iq(z-\frac{x_1+x_2+\dots+x_m}{m})\right)},
+\]
    
+
    and inserting \(e^{i\mu q-i\mu q}\) where \(\mu\) is the mean value
+we arrive at
    
+
    
+\[
+\tilde{p}(z)=\frac{1}{2\pi}\int_{-\infty}^{\infty}
+   dq\exp{\left(iq(z-\mu)\right)}\left[\int_{-\infty}^{\infty}
+   dxp(x)\exp{\left(iq(\mu-x)/m\right)}\right]^m,
+\]
    
+
    with the integral over \(x\) resulting in
    
+
    
+\[
+\int_{-\infty}^{\infty}dxp(x)\exp{\left(iq(\mu-x)/m\right)}=
+  \int_{-\infty}^{\infty}dxp(x)
+   \left[1+\frac{iq(\mu-x)}{m}-\frac{q^2(\mu-x)^2}{2m^2}+\dots\right].
+\]
    
+
    
+
    
+
    Identifying Terms
    
+
    The second term on the rhs disappears since this is just the mean and
+employing the definition of \(\sigma^2\) we have
    
+
    
+\[
+\int_{-\infty}^{\infty}dxp(x)e^{\left(iq(\mu-x)/m\right)}=
+  1-\frac{q^2\sigma^2}{2m^2}+\dots,
+\]
    
+
    resulting in
    
+
    
+\[
+\left[\int_{-\infty}^{\infty}dxp(x)\exp{\left(iq(\mu-x)/m\right)}\right]^m\approx
+  \left[1-\frac{q^2\sigma^2}{2m^2}+\dots \right]^m,
+\]
    
+
    and in the limit \(m\rightarrow \infty\) we obtain
    
+
    
+\[
+\tilde{p}(z)=\frac{1}{\sqrt{2\pi}(\sigma/\sqrt{m})}
+    \exp{\left(-\frac{(z-\mu)^2}{2(\sigma/\sqrt{m})^2}\right)},
+\]
    
+
    which is the normal distribution with variance
+\(\sigma^2_m=\sigma^2/m\), where \(\sigma\) is the variance of the PDF \(p(x)\)
+and \(\mu\) is also the mean of the PDF \(p(x)\).
    
+
    
+
    
+
    Wrapping it up
    
+
    Thus, the central limit theorem states that the PDF \(\tilde{p}(z)\) of
+the average of \(m\) random values corresponding to a PDF \(p(x)\)
+is a normal distribution whose mean is the
+mean value of the PDF \(p(x)\) and whose variance is the variance
+of the PDF \(p(x)\) divided by \(m\), the number of values used to compute \(z\).
    
+
    The central limit theorem leads to the well-known expression for the
+standard deviation, given by
    
+
    
+\[
+\sigma_m=
+\frac{\sigma}{\sqrt{m}}.
+\]
    
+
    The latter is true only if the average value is known exactly. This is obtained in the limit
+\(m\rightarrow \infty\)  only. Because the mean and the variance are measured quantities we obtain
+the familiar expression in statistics (the so-called Bessel correction)
    
+
    
+\[
+\sigma_m\approx 
+\frac{\sigma}{\sqrt{m-1}}.
+\]
    
+
    In many cases however the above estimate for the standard deviation,
+in particular if correlations are strong, may be too simplistic. Keep
+in mind that we have assumed that the variables \(x\) are independent
+and identically distributed. This is obviously not always the
+case. For example, the random numbers (or better pseudorandom numbers)
+we generate in various calculations do always exhibit some
+correlations.
    
+
    The theorem is satisfied by a large class of PDFs. Note however that for a
+finite \(m\), it is not always possible to find a closed form /analytic expression for
+\(\tilde{p}(x)\).
    
+
    
+
    
+
    Confidence Intervals
    
+
    Confidence intervals are used in statistics and represent a type of estimate
+computed from the observed data. This gives a range of values for an
+unknown parameter such as the parameters \(\boldsymbol{\beta}\) from linear regression.
    
+
    With the OLS expressions for the parameters \(\boldsymbol{\beta}\) we found
+\(\mathbb{E}(\boldsymbol{\beta}) = \boldsymbol{\beta}\), which means that the estimator of the regression parameters is unbiased.
    
+
    We found also that the variance of the estimate of the \(j\)-th regression coefficient is
+\(\boldsymbol{\sigma}^2 (\boldsymbol{\beta}_j ) = \boldsymbol{\sigma}^2 [(\mathbf{X}^{T} \mathbf{X})^{-1}]_{jj} \).
    
+
    This quantity will be used to
+construct a confidence interval for the estimates.
    
+
    
+
    
+
    Standard Approach based on the Normal Distribution
    
+
    We will assume that the parameters \(\beta\) follow a normal
+distribution.  We can then define the confidence interval.  Here we will be using as
+shorthands \(\mu_{\beta}\) for the above mean value and \(\sigma_{\beta}\)
+for the standard deviation. We have then a confidence interval
    
+
    
+\[
+\left(\mu_{\beta}\pm \frac{z\sigma_{\beta}}{\sqrt{n}}\right),
+\]
    
+
    where \(z\) defines the level of certainty (or confidence). For a normal
+distribution typical parameters are \(z=2.576\) which corresponds to a
+confidence of \(99\%\) while \(z=1.96\) corresponds to a confidence of
+\(95\%\).  A confidence level of \(95\%\) is commonly used and it is
+normally referred to as a two-sigmas confidence level, that is we
+approximate \(z\approx 2\).
    
+
    For more discussions of confidence intervals (and in particular linked with a discussion of the bootstrap method), see chapter 5 of the textbook by Davison on the Bootstrap Methods and their Applications
    
+
    In this text you will also find an in-depth discussion of the
+Bootstrap method, why it works and various theorems related to it.
    
+
    
+
    
+
    Resampling methods: Bootstrap background
    
+
    Since \(\widehat{\beta} = \widehat{\beta}(\boldsymbol{X})\) is a function of random variables,
+\(\widehat{\beta}\) itself must be a random variable. Thus it has
+a pdf, call this function \(p(\boldsymbol{t})\). The aim of the bootstrap is to
+estimate \(p(\boldsymbol{t})\) by the relative frequency of
+\(\widehat{\beta}\). You can think of this as using a histogram
+in the place of \(p(\boldsymbol{t})\). If the relative frequency closely
+resembles \(p(\vec{t})\), then using numerics, it is straight forward to
+estimate all the interesting parameters of \(p(\boldsymbol{t})\) using point
+estimators.
    
+
    
+
    
+
    Resampling methods: More Bootstrap background
    
+
    In the case that \(\widehat{\beta}\) has
+more than one component, and the components are independent, we use the
+same estimator on each component separately.  If the probability
+density function of \(X_i\), \(p(x)\), had been known, then it would have
+been straightforward to do this by:
    
+
      
+
    1. Drawing lots of numbers from \(p(x)\), suppose we call one such set of numbers \((X_1^*, X_2^*, \cdots, X_n^*)\).
      2. 
+
    2. Then using these numbers, we could compute a replica of \(\widehat{\beta}\) called \(\widehat{\beta}^*\).
      3. 
+
    
+
    By repeated use of the above two points, many
+estimates of \(\widehat{\beta}\) can  be obtained. The
+idea is to use the relative frequency of \(\widehat{\beta}^*\)
+(think of a histogram) as an estimate of \(p(\boldsymbol{t})\).
    
+
    
+
    
+
    Resampling methods: Bootstrap approach
    
+
    But
+unless there is enough information available about the process that
+generated \(X_1,X_2,\cdots,X_n\), \(p(x)\) is in general
+unknown. Therefore, Efron in 1979  asked the
+question: What if we replace \(p(x)\) by the relative frequency
+of the observation \(X_i\)?
    
+
    If we draw observations in accordance with
+the relative frequency of the observations, will we obtain the same
+result in some asymptotic sense? The answer is yes.
    
+
    
+
    
+
    Resampling methods: Bootstrap steps
    
+
    The independent bootstrap works like this:
    
+
      
+
    1. Draw with replacement \(n\) numbers for the observed variables \(\boldsymbol{x} = (x_1,x_2,\cdots,x_n)\).
      2. 
+
    2. Define a vector \(\boldsymbol{x}^*\) containing the values which were drawn from \(\boldsymbol{x}\).
      3. 
+
    3. Using the vector \(\boldsymbol{x}^*\) compute \(\widehat{\beta}^*\) by evaluating \(\widehat \beta\) under the observations \(\boldsymbol{x}^*\).
      4. 
+
    4. Repeat this process \(k\) times.
      5. 
+
    
+
    When you are done, you can draw a histogram of the relative frequency
+of \(\widehat \beta^*\). This is your estimate of the probability
+distribution \(p(t)\). Using this probability distribution you can
+estimate any statistics thereof. In principle you never draw the
+histogram of the relative frequency of \(\widehat{\beta}^*\). Instead
+you use the estimators corresponding to the statistic of interest. For
+example, if you are interested in estimating the variance of \(\widehat
+\beta\), apply the etsimator \(\widehat \sigma^2\) to the values
+\(\widehat \beta^*\).
    
+
    
+
    
+
    Code example for the Bootstrap method
    
+
    The following code starts with a Gaussian distribution with mean value
+\(\mu =100\) and variance \(\sigma=15\). We use this to generate the data
+used in the bootstrap analysis. The bootstrap analysis returns a data
+set after a given number of bootstrap operations (as many as we have
+data points). This data set consists of estimated mean values for each
+bootstrap operation. The histogram generated by the bootstrap method
+shows that the distribution for these mean values is also a Gaussian,
+centered around the mean value \(\mu=100\) but with standard deviation
+\(\sigma/\sqrt{n}\), where \(n\) is the number of bootstrap samples (in
+this case the same as the number of original data points). The value
+of the standard deviation is what we expect from the central limit
+theorem.
    
+
    
+
    
+
    %matplotlib inline
+
+import numpy as np
+from time import time
+from scipy.stats import norm
+import matplotlib.pyplot as plt
+
+# Returns mean of bootstrap samples 
+# Bootstrap algorithm
+def bootstrap(data, datapoints):
+    t = np.zeros(datapoints)
+    n = len(data)
+    # non-parametric bootstrap         
+    for i in range(datapoints):
+        t[i] = np.mean(data[np.random.randint(0,n,n)])
+    # analysis    
+    print("Bootstrap Statistics :")
+    print("original           bias      std. error")
+    print("%8g %8g %14g %15g" % (np.mean(data), np.std(data),np.mean(t),np.std(t)))
+    return t
+
+# We set the mean value to 100 and the standard deviation to 15
+mu, sigma = 100, 15
+datapoints = 10000
+# We generate random numbers according to the normal distribution
+x = mu + sigma*np.random.randn(datapoints)
+# bootstrap returns the data sample                                    
+t = bootstrap(x, datapoints)
+
    
+
    
+
    
+
    
+
    Bootstrap Statistics :
+original           bias      std. error
+ 100.232  14.9426        100.231        0.148895
+
    
+
    
+
    
+
    
+
    We see that our new variance and from that the standard deviation, agrees with the central limit theorem.
    
+
    
+
    
+
    Plotting the Histogram
    
+
    
+
    
+
    # the histogram of the bootstrapped data (normalized data if density = True)
+n, binsboot, patches = plt.hist(t, 50, density=True, facecolor='red', alpha=0.75)
+# add a 'best fit' line  
+y = norm.pdf(binsboot, np.mean(t), np.std(t))
+lt = plt.plot(binsboot, y, 'b', linewidth=1)
+plt.xlabel('x')
+plt.ylabel('Probability')
+plt.grid(True)
+plt.show()
+
    
+
    
+
    
+
    
+_images/week37_144_0.png
+
    
+
    
+
    
+
    
+
    The bias-variance tradeoff
    
+
    We will discuss the bias-variance tradeoff in the context of
+continuous predictions such as regression. However, many of the
+intuitions and ideas discussed here also carry over to classification
+tasks. Consider a dataset \(\mathcal{D}\) consisting of the data
+\(\mathbf{X}_\mathcal{D}=\{(y_j, \boldsymbol{x}_j), j=0\ldots n-1\}\).
    
+
    Let us assume that the true data is generated from a noisy model
    
+
    
+\[
+\boldsymbol{y}=f(\boldsymbol{x}) + \boldsymbol{\epsilon}
+\]
    
+
    where \(\epsilon\) is normally distributed with mean zero and standard deviation \(\sigma^2\).
    
+
    In our derivation of the ordinary least squares method we defined then
+an approximation to the function \(f\) in terms of the parameters
+\(\boldsymbol{\beta}\) and the design matrix \(\boldsymbol{X}\) which embody our model,
+that is \(\boldsymbol{\tilde{y}}=\boldsymbol{X}\boldsymbol{\beta}\).
    
+
    Thereafter we found the parameters \(\boldsymbol{\beta}\) by optimizing the means squared error via the so-called cost function
    
+
    
+\[
+C(\boldsymbol{X},\boldsymbol{\beta}) =\frac{1}{n}\sum_{i=0}^{n-1}(y_i-\tilde{y}_i)^2=\mathbb{E}\left[(\boldsymbol{y}-\boldsymbol{\tilde{y}})^2\right].
+\]
    
+
    We can rewrite this as
    
+
    
+\[
+\mathbb{E}\left[(\boldsymbol{y}-\boldsymbol{\tilde{y}})^2\right]=\frac{1}{n}\sum_i(f_i-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right])^2+\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right])^2+\sigma^2.
+\]
    
+
    The three terms represent the square of the bias of the learning
+method, which can be thought of as the error caused by the simplifying
+assumptions built into the method. The second term represents the
+variance of the chosen model and finally the last terms is variance of
+the error \(\boldsymbol{\epsilon}\).
    
+
    To derive this equation, we need to recall that the variance of \(\boldsymbol{y}\) and \(\boldsymbol{\epsilon}\) are both equal to \(\sigma^2\). The mean value of \(\boldsymbol{\epsilon}\) is by definition equal to zero. Furthermore, the function \(f\) is not a stochastics variable, idem for \(\boldsymbol{\tilde{y}}\).
+We use a more compact notation in terms of the expectation value
    
+
    
+\[
+\mathbb{E}\left[(\boldsymbol{y}-\boldsymbol{\tilde{y}})^2\right]=\mathbb{E}\left[(\boldsymbol{f}+\boldsymbol{\epsilon}-\boldsymbol{\tilde{y}})^2\right],
+\]
    
+
    and adding and subtracting \(\mathbb{E}\left[\boldsymbol{\tilde{y}}\right]\) we get
    
+
    
+\[
+\mathbb{E}\left[(\boldsymbol{y}-\boldsymbol{\tilde{y}})^2\right]=\mathbb{E}\left[(\boldsymbol{f}+\boldsymbol{\epsilon}-\boldsymbol{\tilde{y}}+\mathbb{E}\left[\boldsymbol{\tilde{y}}\right]-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right])^2\right],
+\]
    
+
    which, using the abovementioned expectation values can be rewritten as
    
+
    
+\[
+\mathbb{E}\left[(\boldsymbol{y}-\boldsymbol{\tilde{y}})^2\right]=\mathbb{E}\left[(\boldsymbol{y}-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right])^2\right]+\mathrm{Var}\left[\boldsymbol{\tilde{y}}\right]+\sigma^2,
+\]
    
+
    that is the rewriting in terms of the so-called bias, the variance of the model \(\boldsymbol{\tilde{y}}\) and the variance of \(\boldsymbol{\epsilon}\).
    
+
    
+
    
+
    A way to Read the Bias-Variance Tradeoff
    
+
+
+
    Figure 1: 
    
+
    
+
    
+
    Example code for Bias-Variance tradeoff
    
+
    
+
    
+
    import matplotlib.pyplot as plt
+import numpy as np
+from sklearn.linear_model import LinearRegression, Ridge, Lasso
+from sklearn.preprocessing import PolynomialFeatures
+from sklearn.model_selection import train_test_split
+from sklearn.pipeline import make_pipeline
+from sklearn.utils import resample
+
+np.random.seed(2018)
+
+n = 500
+n_boostraps = 100
+degree = 18  # A quite high value, just to show.
+noise = 0.1
+
+# Make data set.
+x = np.linspace(-1, 3, n).reshape(-1, 1)
+y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2) + np.random.normal(0, 0.1, x.shape)
+
+# Hold out some test data that is never used in training.
+x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2)
+
+# Combine x transformation and model into one operation.
+# Not neccesary, but convenient.
+model = make_pipeline(PolynomialFeatures(degree=degree), LinearRegression(fit_intercept=False))
+
+# The following (m x n_bootstraps) matrix holds the column vectors y_pred
+# for each bootstrap iteration.
+y_pred = np.empty((y_test.shape[0], n_boostraps))
+for i in range(n_boostraps):
+    x_, y_ = resample(x_train, y_train)
+
+    # Evaluate the new model on the same test data each time.
+    y_pred[:, i] = model.fit(x_, y_).predict(x_test).ravel()
+
+# Note: Expectations and variances taken w.r.t. different training
+# data sets, hence the axis=1. Subsequent means are taken across the test data
+# set in order to obtain a total value, but before this we have error/bias/variance
+# calculated per data point in the test set.
+# Note 2: The use of keepdims=True is important in the calculation of bias as this 
+# maintains the column vector form. Dropping this yields very unexpected results.
+error = np.mean( np.mean((y_test - y_pred)**2, axis=1, keepdims=True) )
+bias = np.mean( (y_test - np.mean(y_pred, axis=1, keepdims=True))**2 )
+variance = np.mean( np.var(y_pred, axis=1, keepdims=True) )
+print('Error:', error)
+print('Bias^2:', bias)
+print('Var:', variance)
+print('{} >= {} + {} = {}'.format(error, bias, variance, bias+variance))
+
+plt.plot(x[::5, :], y[::5, :], label='f(x)')
+plt.scatter(x_test, y_test, label='Data points')
+plt.scatter(x_test, np.mean(y_pred, axis=1), label='Pred')
+plt.legend()
+plt.show()
+
    
+
    
+
    
+
    
+
    Error: 0.013121574062587286
+Bias^2: 0.012073649469946107
+Var: 0.0010479245926411787
+0.013121574062587286 >= 0.012073649469946107 + 0.0010479245926411787 = 0.013121574062587286
+
    
+
    
+_images/week37_160_1.png
+
    
+
    
+
    
+
    
+
    Understanding what happens
    
+
    
+
    
+
    import matplotlib.pyplot as plt
+import numpy as np
+from sklearn.linear_model import LinearRegression, Ridge, Lasso
+from sklearn.preprocessing import PolynomialFeatures
+from sklearn.model_selection import train_test_split
+from sklearn.pipeline import make_pipeline
+from sklearn.utils import resample
+
+np.random.seed(2018)
+
+n = 40
+n_boostraps = 100
+maxdegree = 14
+
+
+# Make data set.
+x = np.linspace(-3, 3, n).reshape(-1, 1)
+y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)+ np.random.normal(0, 0.1, x.shape)
+error = np.zeros(maxdegree)
+bias = np.zeros(maxdegree)
+variance = np.zeros(maxdegree)
+polydegree = np.zeros(maxdegree)
+x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2)
+
+for degree in range(maxdegree):
+    model = make_pipeline(PolynomialFeatures(degree=degree), LinearRegression(fit_intercept=False))
+    y_pred = np.empty((y_test.shape[0], n_boostraps))
+    for i in range(n_boostraps):
+        x_, y_ = resample(x_train, y_train)
+        y_pred[:, i] = model.fit(x_, y_).predict(x_test).ravel()
+
+    polydegree[degree] = degree
+    error[degree] = np.mean( np.mean((y_test - y_pred)**2, axis=1, keepdims=True) )
+    bias[degree] = np.mean( (y_test - np.mean(y_pred, axis=1, keepdims=True))**2 )
+    variance[degree] = np.mean( np.var(y_pred, axis=1, keepdims=True) )
+    print('Polynomial degree:', degree)
+    print('Error:', error[degree])
+    print('Bias^2:', bias[degree])
+    print('Var:', variance[degree])
+    print('{} >= {} + {} = {}'.format(error[degree], bias[degree], variance[degree], bias[degree]+variance[degree]))
+
+plt.plot(polydegree, error, label='Error')
+plt.plot(polydegree, bias, label='bias')
+plt.plot(polydegree, variance, label='Variance')
+plt.legend()
+plt.show()
+
    
+
    
+
    
+
    
+
    Polynomial degree: 0
+Error: 0.32149601703519115
+Bias^2: 0.3123314713548606
+Var: 0.009164545680330616
+0.32149601703519115 >= 0.3123314713548606 + 0.009164545680330616 = 0.3214960170351912
+Polynomial degree: 1
+Error: 0.08426840630693412
+Bias^2: 0.0796891867672603
+Var: 0.004579219539673834
+0.08426840630693412 >= 0.0796891867672603 + 0.004579219539673834 = 0.08426840630693413
+Polynomial degree: 2
+Error: 0.10398646080125037
+Bias^2: 0.10077114273548984
+Var: 0.0032153180657605116
+0.10398646080125037 >= 0.10077114273548984 + 0.0032153180657605116 = 0.10398646080125036
+Polynomial degree: 3
+Error: 0.06547790180152352
+Bias^2: 0.062082386342319454
+Var: 0.0033955154592040923
+0.06547790180152352 >= 0.062082386342319454 + 0.0033955154592040923 = 0.06547790180152355
+Polynomial degree: 4
+Error: 0.06844519414009445
+Bias^2: 0.06453579006728322
+Var: 0.003909404072811221
+0.06844519414009445 >= 0.06453579006728322 + 0.003909404072811221 = 0.06844519414009444
+
    
+
    
+
    Polynomial degree: 5
+Error: 0.05227921801205679
+Bias^2: 0.04818727730430286
+Var: 0.004091940707753925
+0.05227921801205679 >= 0.04818727730430286 + 0.004091940707753925 = 0.05227921801205679
+Polynomial degree: 6
+Error: 0.03781367141738902
+Bias^2: 0.03365768507152769
+Var: 0.0041559863458613296
+0.03781367141738902 >= 0.03365768507152769 + 0.0041559863458613296 = 0.03781367141738902
+Polynomial degree: 7
+Error: 0.027609773491022394
+Bias^2: 0.022999498260366198
+Var: 0.004610275230656182
+0.027609773491022394 >= 0.022999498260366198 + 0.004610275230656182 = 0.02760977349102238
+Polynomial degree: 8
+Error: 0.017355848195593312
+Bias^2: 0.010331721306655165
+Var: 0.007024126888938144
+0.017355848195593312 >= 0.010331721306655165 + 0.007024126888938144 = 0.01735584819559331
+Polynomial degree: 9
+Error: 0.026605727637184558
+Bias^2: 0.010018312644139219
+Var: 0.016587414993045335
+0.026605727637184558 >= 0.010018312644139219 + 0.016587414993045335 = 0.026605727637184554
+Polynomial degree: 10
+Error: 0.021592704588021178
+Bias^2: 0.010516485576646504
+Var: 0.01107621901137467
+0.021592704588021178 >= 0.010516485576646504 + 0.01107621901137467 = 0.021592704588021174
+Polynomial degree: 11
+Error: 0.07160048164232538
+Bias^2: 0.014436800088896381
+Var: 0.05716368155342902
+0.07160048164232538 >= 0.014436800088896381 + 0.05716368155342902 = 0.0716004816423254
+Polynomial degree: 12
+Error: 0.11547777218876518
+Bias^2: 0.016285782696017142
+Var: 0.09919198949274803
+0.11547777218876518 >= 0.016285782696017142 + 0.09919198949274803 = 0.11547777218876518
+Polynomial degree: 13
+Error: 0.2284246870217162
+Bias^2: 0.01975416527168255
+Var: 0.20867052175003364
+0.2284246870217162 >= 0.01975416527168255 + 0.20867052175003364 = 0.2284246870217162
+
    
+
    
+_images/week37_162_2.png
+
    
+
    
+
    
+
    
+
    Summing up
    
+
    The bias-variance tradeoff summarizes the fundamental tension in
+machine learning, particularly supervised learning, between the
+complexity of a model and the amount of training data needed to train
+it.  Since data is often limited, in practice it is often useful to
+use a less-complex model with higher bias, that is  a model whose asymptotic
+performance is worse than another model because it is easier to
+train and less sensitive to sampling noise arising from having a
+finite-sized training dataset (smaller variance).
    
+
    The above equations tell us that in
+order to minimize the expected test error, we need to select a
+statistical learning method that simultaneously achieves low variance
+and low bias. Note that variance is inherently a nonnegative quantity,
+and squared bias is also nonnegative. Hence, we see that the expected
+test MSE can never lie below \(Var(\epsilon)\), the irreducible error.
    
+
    What do we mean by the variance and bias of a statistical learning
+method? The variance refers to the amount by which our model would change if we
+estimated it using a different training data set. Since the training
+data are used to fit the statistical learning method, different
+training data sets  will result in a different estimate. But ideally the
+estimate for our model should not vary too much between training
+sets. However, if a method has high variance  then small changes in
+the training data can result in large changes in the model. In general, more
+flexible statistical methods have higher variance.
    
+
    You may also find this recent article of interest.
    
+
    
+
    
+
    Another Example from Scikit-Learn’s Repository
    
+
    
+
    
+
    """
+============================
+Underfitting vs. Overfitting
+============================
+
+This example demonstrates the problems of underfitting and overfitting and
+how we can use linear regression with polynomial features to approximate
+nonlinear functions. The plot shows the function that we want to approximate,
+which is a part of the cosine function. In addition, the samples from the
+real function and the approximations of different models are displayed. The
+models have polynomial features of different degrees. We can see that a
+linear function (polynomial with degree 1) is not sufficient to fit the
+training samples. This is called **underfitting**. A polynomial of degree 4
+approximates the true function almost perfectly. However, for higher degrees
+the model will **overfit** the training data, i.e. it learns the noise of the
+training data.
+We evaluate quantitatively **overfitting** / **underfitting** by using
+cross-validation. We calculate the mean squared error (MSE) on the validation
+set, the higher, the less likely the model generalizes correctly from the
+training data.
+"""
+
+print(__doc__)
+
+import numpy as np
+import matplotlib.pyplot as plt
+from sklearn.pipeline import Pipeline
+from sklearn.preprocessing import PolynomialFeatures
+from sklearn.linear_model import LinearRegression
+from sklearn.model_selection import cross_val_score
+
+
+def true_fun(X):
+    return np.cos(1.5 * np.pi * X)
+
+np.random.seed(0)
+
+n_samples = 30
+degrees = [1, 4, 15]
+
+X = np.sort(np.random.rand(n_samples))
+y = true_fun(X) + np.random.randn(n_samples) * 0.1
+
+plt.figure(figsize=(14, 5))
+for i in range(len(degrees)):
+    ax = plt.subplot(1, len(degrees), i + 1)
+    plt.setp(ax, xticks=(), yticks=())
+
+    polynomial_features = PolynomialFeatures(degree=degrees[i],
+                                             include_bias=False)
+    linear_regression = LinearRegression()
+    pipeline = Pipeline([("polynomial_features", polynomial_features),
+                         ("linear_regression", linear_regression)])
+    pipeline.fit(X[:, np.newaxis], y)
+
+    # Evaluate the models using crossvalidation
+    scores = cross_val_score(pipeline, X[:, np.newaxis], y,
+                             scoring="neg_mean_squared_error", cv=10)
+
+    X_test = np.linspace(0, 1, 100)
+    plt.plot(X_test, pipeline.predict(X_test[:, np.newaxis]), label="Model")
+    plt.plot(X_test, true_fun(X_test), label="True function")
+    plt.scatter(X, y, edgecolor='b', s=20, label="Samples")
+    plt.xlabel("x")
+    plt.ylabel("y")
+    plt.xlim((0, 1))
+    plt.ylim((-2, 2))
+    plt.legend(loc="best")
+    plt.title("Degree {}\nMSE = {:.2e}(+/- {:.2e})".format(
+        degrees[i], -scores.mean(), scores.std()))
+plt.show()
+
    
+
    
+
    
+
    
+
    ============================
+Underfitting vs. Overfitting
+============================
+
+This example demonstrates the problems of underfitting and overfitting and
+how we can use linear regression with polynomial features to approximate
+nonlinear functions. The plot shows the function that we want to approximate,
+which is a part of the cosine function. In addition, the samples from the
+real function and the approximations of different models are displayed. The
+models have polynomial features of different degrees. We can see that a
+linear function (polynomial with degree 1) is not sufficient to fit the
+training samples. This is called **underfitting**. A polynomial of degree 4
+approximates the true function almost perfectly. However, for higher degrees
+the model will **overfit** the training data, i.e. it learns the noise of the
+training data.
+We evaluate quantitatively **overfitting** / **underfitting** by using
+cross-validation. We calculate the mean squared error (MSE) on the validation
+set, the higher, the less likely the model generalizes correctly from the
+training data.
+
    
+
    
+_images/week37_165_1.png
+
    
+
    
+
    
+
    
+
    Various steps in cross-validation
    
+
    When the repetitive splitting of the data set is done randomly,
+samples may accidently end up in a fast majority of the splits in
+either training or test set. Such samples may have an unbalanced
+influence on either model building or prediction evaluation. To avoid
+this \(k\)-fold cross-validation structures the data splitting. The
+samples are divided into \(k\) more or less equally sized exhaustive and
+mutually exclusive subsets. In turn (at each split) one of these
+subsets plays the role of the test set while the union of the
+remaining subsets constitutes the training set. Such a splitting
+warrants a balanced representation of each sample in both training and
+test set over the splits. Still the division into the \(k\) subsets
+involves a degree of randomness. This may be fully excluded when
+choosing \(k=n\). This particular case is referred to as leave-one-out
+cross-validation (LOOCV).
    
+
    
+
    
+
    Cross-validation in brief
    
+
    For the various values of \(k\)
    
+
      
+
    1. shuffle the dataset randomly.
      2. 
+
    2. Split the dataset into \(k\) groups.
      3. 
+
    3. For each unique group:
      4. 
+
    
+
    a. Decide which group to use as set for test data
    
+
    b. Take the remaining groups as a training data set
    
+
    c. Fit a model on the training set and evaluate it on the test set
    
+
    d. Retain the evaluation score and discard the model
    
+
      
+
    1. Summarize the model using the sample of model evaluation scores
      2. 
+
    
+
    
+
    
+
    Code Example for Cross-validation and \(k\)-fold Cross-validation
    
+
    The code here uses Ridge regression with cross-validation (CV)  resampling and \(k\)-fold CV in order to fit a specific polynomial.
    
+
    
+
    
+
    import numpy as np
+import matplotlib.pyplot as plt
+from sklearn.model_selection import KFold
+from sklearn.linear_model import Ridge
+from sklearn.model_selection import cross_val_score
+from sklearn.preprocessing import PolynomialFeatures
+
+# A seed just to ensure that the random numbers are the same for every run.
+# Useful for eventual debugging.
+np.random.seed(3155)
+
+# Generate the data.
+nsamples = 100
+x = np.random.randn(nsamples)
+y = 3*x**2 + np.random.randn(nsamples)
+
+## Cross-validation on Ridge regression using KFold only
+
+# Decide degree on polynomial to fit
+poly = PolynomialFeatures(degree = 6)
+
+# Decide which values of lambda to use
+nlambdas = 500
+lambdas = np.logspace(-3, 5, nlambdas)
+
+# Initialize a KFold instance
+k = 5
+kfold = KFold(n_splits = k)
+
+# Perform the cross-validation to estimate MSE
+scores_KFold = np.zeros((nlambdas, k))
+
+i = 0
+for lmb in lambdas:
+    ridge = Ridge(alpha = lmb)
+    j = 0
+    for train_inds, test_inds in kfold.split(x):
+        xtrain = x[train_inds]
+        ytrain = y[train_inds]
+
+        xtest = x[test_inds]
+        ytest = y[test_inds]
+
+        Xtrain = poly.fit_transform(xtrain[:, np.newaxis])
+        ridge.fit(Xtrain, ytrain[:, np.newaxis])
+
+        Xtest = poly.fit_transform(xtest[:, np.newaxis])
+        ypred = ridge.predict(Xtest)
+
+        scores_KFold[i,j] = np.sum((ypred - ytest[:, np.newaxis])**2)/np.size(ypred)
+
+        j += 1
+    i += 1
+
+
+estimated_mse_KFold = np.mean(scores_KFold, axis = 1)
+
+## Cross-validation using cross_val_score from sklearn along with KFold
+
+# kfold is an instance initialized above as:
+# kfold = KFold(n_splits = k)
+
+estimated_mse_sklearn = np.zeros(nlambdas)
+i = 0
+for lmb in lambdas:
+    ridge = Ridge(alpha = lmb)
+
+    X = poly.fit_transform(x[:, np.newaxis])
+    estimated_mse_folds = cross_val_score(ridge, X, y[:, np.newaxis], scoring='neg_mean_squared_error', cv=kfold)
+
+    # cross_val_score return an array containing the estimated negative mse for every fold.
+    # we have to the the mean of every array in order to get an estimate of the mse of the model
+    estimated_mse_sklearn[i] = np.mean(-estimated_mse_folds)
+
+    i += 1
+
+## Plot and compare the slightly different ways to perform cross-validation
+
+plt.figure()
+
+plt.plot(np.log10(lambdas), estimated_mse_sklearn, label = 'cross_val_score')
+plt.plot(np.log10(lambdas), estimated_mse_KFold, 'r--', label = 'KFold')
+
+plt.xlabel('log10(lambda)')
+plt.ylabel('mse')
+
+plt.legend()
+
+plt.show()
+
    
+
    
+
    
+
    
+_images/week37_169_0.png
+
    
+
    
+
    
+
    
+
    More examples on bootstrap and cross-validation and errors
    
+
    
+
    
+
    # Common imports
+import os
+import numpy as np
+import pandas as pd
+import matplotlib.pyplot as plt
+from sklearn.linear_model import LinearRegression, Ridge, Lasso
+from sklearn.model_selection import train_test_split
+from sklearn.utils import resample
+from sklearn.metrics import mean_squared_error
+# Where to save the figures and data files
+PROJECT_ROOT_DIR = "Results"
+FIGURE_ID = "Results/FigureFiles"
+DATA_ID = "DataFiles/"
+
+if not os.path.exists(PROJECT_ROOT_DIR):
+    os.mkdir(PROJECT_ROOT_DIR)
+
+if not os.path.exists(FIGURE_ID):
+    os.makedirs(FIGURE_ID)
+
+if not os.path.exists(DATA_ID):
+    os.makedirs(DATA_ID)
+
+def image_path(fig_id):
+    return os.path.join(FIGURE_ID, fig_id)
+
+def data_path(dat_id):
+    return os.path.join(DATA_ID, dat_id)
+
+def save_fig(fig_id):
+    plt.savefig(image_path(fig_id) + ".png", format='png')
+
+infile = open(data_path("EoS.csv"),'r')
+
+# Read the EoS data as  csv file and organize the data into two arrays with density and energies
+EoS = pd.read_csv(infile, names=('Density', 'Energy'))
+EoS['Energy'] = pd.to_numeric(EoS['Energy'], errors='coerce')
+EoS = EoS.dropna()
+Energies = EoS['Energy']
+Density = EoS['Density']
+#  The design matrix now as function of various polytrops
+
+Maxpolydegree = 30
+X = np.zeros((len(Density),Maxpolydegree))
+X[:,0] = 1.0
+testerror = np.zeros(Maxpolydegree)
+trainingerror = np.zeros(Maxpolydegree)
+polynomial = np.zeros(Maxpolydegree)
+
+trials = 100
+for polydegree in range(1, Maxpolydegree):
+    polynomial[polydegree] = polydegree
+    for degree in range(polydegree):
+        X[:,degree] = Density**(degree/3.0)
+
+# loop over trials in order to estimate the expectation value of the MSE
+    testerror[polydegree] = 0.0
+    trainingerror[polydegree] = 0.0
+    for samples in range(trials):
+        x_train, x_test, y_train, y_test = train_test_split(X, Energies, test_size=0.2)
+        model = LinearRegression(fit_intercept=False).fit(x_train, y_train)
+        ypred = model.predict(x_train)
+        ytilde = model.predict(x_test)
+        testerror[polydegree] += mean_squared_error(y_test, ytilde)
+        trainingerror[polydegree] += mean_squared_error(y_train, ypred) 
+
+    testerror[polydegree] /= trials
+    trainingerror[polydegree] /= trials
+    print("Degree of polynomial: %3d"% polynomial[polydegree])
+    print("Mean squared error on training data: %.8f" % trainingerror[polydegree])
+    print("Mean squared error on test data: %.8f" % testerror[polydegree])
+
+plt.plot(polynomial, np.log10(trainingerror), label='Training Error')
+plt.plot(polynomial, np.log10(testerror), label='Test Error')
+plt.xlabel('Polynomial degree')
+plt.ylabel('log10[MSE]')
+plt.legend()
+plt.show()
+
    
+
    
+
    
+
    
+
    Degree of polynomial:   1
+Mean squared error on training data: 446033.51374050
+Mean squared error on test data: 455173.80460179
+Degree of polynomial:   2
+Mean squared error on training data: 114550.54637219
+Mean squared error on test data: 129963.83146596
+Degree of polynomial:   3
+Mean squared error on training data: 9054.61775176
+Mean squared error on test data: 10572.87627342
+Degree of polynomial:   4
+Mean squared error on training data: 302.15313054
+Mean squared error on test data: 433.26292364
+Degree of polynomial:   5
+Mean squared error on training data: 3.64316192
+Mean squared error on test data: 7.23528337
+Degree of polynomial:   6
+Mean squared error on training data: 3.56589683
+Mean squared error on test data: 10.50427787
+Degree of polynomial:   7
+Mean squared error on training data: 0.47313680
+Mean squared error on test data: 1.53738247
+
    
+
    
+
    Degree of polynomial:   8
+Mean squared error on training data: 0.04926746
+Mean squared error on test data: 0.14629156
+Degree of polynomial:   9
+Mean squared error on training data: 0.02546675
+Mean squared error on test data: 0.11202337
+Degree of polynomial:  10
+Mean squared error on training data: 0.02424794
+Mean squared error on test data: 0.22467274
+Degree of polynomial:  11
+Mean squared error on training data: 0.01594452
+Mean squared error on test data: 1.07641937
+Degree of polynomial:  12
+Mean squared error on training data: 0.00805074
+Mean squared error on test data: 0.04295757
+Degree of polynomial:  13
+Mean squared error on training data: 0.00781918
+Mean squared error on test data: 0.56965674
+Degree of polynomial:  14
+Mean squared error on training data: 0.00465099
+Mean squared error on test data: 0.28443039
+
    
+
    
+
    Degree of polynomial:  15
+Mean squared error on training data: 0.00420072
+Mean squared error on test data: 568.47202442
+Degree of polynomial:  16
+Mean squared error on training data: 0.00325450
+Mean squared error on test data: 48.97690235
+Degree of polynomial:  17
+Mean squared error on training data: 0.00242954
+Mean squared error on test data: 2.52775466
+Degree of polynomial:  18
+Mean squared error on training data: 0.00219194
+Mean squared error on test data: 429.23643365
+Degree of polynomial:  19
+Mean squared error on training data: 0.00154860
+Mean squared error on test data: 238.16356503
+Degree of polynomial:  20
+Mean squared error on training data: 0.00140849
+Mean squared error on test data: 1345.68592431
+Degree of polynomial:  21
+Mean squared error on training data: 0.00119699
+Mean squared error on test data: 1836.21110005
+
    
+
    
+
    Degree of polynomial:  22
+Mean squared error on training data: 0.00092904
+Mean squared error on test data: 1182.64316482
+Degree of polynomial:  23
+Mean squared error on training data: 0.00089187
+Mean squared error on test data: 3886.35846425
+Degree of polynomial:  24
+Mean squared error on training data: 0.00083346
+Mean squared error on test data: 1346.92651068
+Degree of polynomial:  25
+Mean squared error on training data: 0.00079910
+Mean squared error on test data: 7697.35412147
+Degree of polynomial:  26
+Mean squared error on training data: 0.00075597
+Mean squared error on test data: 1078.81597834
+Degree of polynomial:  27
+Mean squared error on training data: 0.00068088
+Mean squared error on test data: 3189.20355156
+
    
+
    
+
    Degree of polynomial:  28
+Mean squared error on training data: 0.00063364
+Mean squared error on test data: 692.24085321
+Degree of polynomial:  29
+Mean squared error on training data: 0.00063862
+Mean squared error on test data: 3073.63180447
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7768/626635268.py:73: RuntimeWarning: divide by zero encountered in log10
+  plt.plot(polynomial, np.log10(trainingerror), label='Training Error')
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7768/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
+  plt.plot(polynomial, np.log10(testerror), label='Test Error')
+
    
+
    
+_images/week37_171_6.png
+
    
+
    
+
    Note that we kept the intercept column in the fitting here. This means that we need to set the intercept in the call to the Scikit-Learn function as False. Alternatively, we could have set up the design matrix \(X\) without the first column of ones.
    
+
    
+
    
+
    The same example but now with cross-validation
    
+
    In this example we keep the intercept column again but add cross-validation in order to estimate the best possible value of the means squared error.
    
+
    
+
    
+
    # Common imports
+import os
+import numpy as np
+import pandas as pd
+import matplotlib.pyplot as plt
+from sklearn.linear_model import LinearRegression, Ridge, Lasso
+from sklearn.metrics import mean_squared_error
+from sklearn.model_selection import KFold
+from sklearn.model_selection import cross_val_score
+
+
+# Where to save the figures and data files
+PROJECT_ROOT_DIR = "Results"
+FIGURE_ID = "Results/FigureFiles"
+DATA_ID = "DataFiles/"
+
+if not os.path.exists(PROJECT_ROOT_DIR):
+    os.mkdir(PROJECT_ROOT_DIR)
+
+if not os.path.exists(FIGURE_ID):
+    os.makedirs(FIGURE_ID)
+
+if not os.path.exists(DATA_ID):
+    os.makedirs(DATA_ID)
+
+def image_path(fig_id):
+    return os.path.join(FIGURE_ID, fig_id)
+
+def data_path(dat_id):
+    return os.path.join(DATA_ID, dat_id)
+
+def save_fig(fig_id):
+    plt.savefig(image_path(fig_id) + ".png", format='png')
+
+infile = open(data_path("EoS.csv"),'r')
+
+# Read the EoS data as  csv file and organize the data into two arrays with density and energies
+EoS = pd.read_csv(infile, names=('Density', 'Energy'))
+EoS['Energy'] = pd.to_numeric(EoS['Energy'], errors='coerce')
+EoS = EoS.dropna()
+Energies = EoS['Energy']
+Density = EoS['Density']
+#  The design matrix now as function of various polytrops
+
+Maxpolydegree = 30
+X = np.zeros((len(Density),Maxpolydegree))
+X[:,0] = 1.0
+estimated_mse_sklearn = np.zeros(Maxpolydegree)
+polynomial = np.zeros(Maxpolydegree)
+k =5
+kfold = KFold(n_splits = k)
+
+for polydegree in range(1, Maxpolydegree):
+    polynomial[polydegree] = polydegree
+    for degree in range(polydegree):
+        X[:,degree] = Density**(degree/3.0)
+        OLS = LinearRegression(fit_intercept=False)
+# loop over trials in order to estimate the expectation value of the MSE
+    estimated_mse_folds = cross_val_score(OLS, X, Energies, scoring='neg_mean_squared_error', cv=kfold)
+#[:, np.newaxis]
+    estimated_mse_sklearn[polydegree] = np.mean(-estimated_mse_folds)
+
+plt.plot(polynomial, np.log10(estimated_mse_sklearn), label='Test Error')
+plt.xlabel('Polynomial degree')
+plt.ylabel('log10[MSE]')
+plt.legend()
+plt.show()
+
    
+
    
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7768/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10
+  plt.plot(polynomial, np.log10(estimated_mse_sklearn), label='Test Error')
+
    
+
    
+_images/week37_174_1.png
+
    
+
    
+
    
+
    
+
+    
+    
+
+              
    
+              
+            
+                
+
     
+    
+        
+        
    
+            
    previous
    
+            
    Exercises week 37
    
+        
    
+        
+    
+    
    
+        
    next
    
+        
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
    
+    
    
+    
+        
+
    
+            
+        
    
+    
    
+    
    
+  
    
+    
+      By Morten Hjorth-Jensen
    
+    
+        © Copyright 2021.
    
+  
    
+
    
+
    
+
+
+      
    
+    
    
+  
+  
+
+  
+
\ No newline at end of file
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter1.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter1.ipynb
index 5af78146a..f470b9c6d 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter1.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter1.ipynb
@@ -343,7 +343,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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P8+fPV+fOnfXMM8/o3nvvVZMmTQJ6/F//+tdq166dZs2apRtvvFHHjh1Tq1at1LNnz7J6M8nJyerbt6/+8Y9/aOfOnTp16pTatWune+65R3fffbck6ayzzlKTJk00a9Ys/fjjj6pXr57OPvtsLViwQBMmTKjy8Vu2bKk1a9Zo2rRpmjZtmgoLC9WxY0fNmjVLU6ZMCfnvCtiNysOAzdxQ/RdmXZzOnTtr+vTp+v3vf293c4C4RY8NAATp888/16JFizRgwAClpKTom2++0axZs5SSkqLrr7/e7uYBcY3ABgCC1LBhQ23YsEEvvPCCjh49qtTUVGVnZ+vhhx+ucso3gOhgKAoAALiG7QX6ZsyYIY/HY/nxV6wMAACgJo4YiurWrZtlpdryZbsBAAAC5YjApm7duvTSAACAWnNEYOOt25GUlKS+ffvqT3/6kzp27Oj32KKiIkuZ9dOnT+vIkSNq3rx50GXWAQCAPQzD0LFjx5Senh5QYctA2Z48/Pbbb+vEiRPq1KmTDhw4oIceekhff/21tmzZ4neNnBkzZkSsYBcAAIiu3bt3KyMjI2z3Z3tgU9Hx48d1xhln6O677/Zb/bJij01BQYHatWun3bt3KyUlJZpNBQAAISosLFRmZmZZyYRwccRQVHkNGzbUueeeW+X6MElJSX5X3k1JSSGwAQAgxoQ7jcT26d4VFRUV6auvvvK72jIAAEB1bA9s7rrrLq1atUo7duzQp59+qrFjx6qwsLDaxdsAAAD8sX0oas+ePfrlL3+p/Px8tWzZUv369dPatWvVvn17u5sGAABijO2BzeLFi+1uAgAAcAnbh6IAAADChcAGAAC4BoENAABwDQIbAADgGgQ2AADANQhsAACAaxDYAAAA1yCwAQAArkFgAwAAXIPABgAAuAaBDQAAcA0CGwAA4BoENgAAwDUIbAAAgGsQ2AAAANcgsAEAAK5BYAMAAFyDwAYAALgGgQ0AAHANAhsAAOAaBDYAAMA1CGwAAIBrENgAAADXILABAACuQWADAABcg8AGAAC4BoENAABwDQIbAADgGgQ2AADANQhsAACAaxDYAAAA1yCwAQAArkFgAwAAXIPABgAAuAaBDQAAcA0CGwAA4BoENgAAwDUIbAAAgGsQ2AAAANcgsAEAAK5BYAMAAFyDwAYAALhGXbsbAACA45SWSnl50r59UlqaNGiQlJBgd6sQAAIbAADKW7JEmjRJ2rPHty0jQ3rySWnMGPvahYAwFAUAgNeSJdLYsdagRpL27jW3L1liT7sQMAIbAAAkc/hp0iTJMCrv826bPNk8Do5FYAMAgGTm1FTsqSnPMKTdu83j4FgENgAASGaicDiPgy0IbAAAkMzZT+E8DrYgsAEAQDKndGdkSB6P//0ej5SZaR4HxyKwAQBAMuvUPPmk+f+KwY3399mzqWfjcAQ2AAB4jRkjvfaa1LatdXtGhrmdOjaOR4E+AADKGzNGGjWKysMxisAGAICKEhKk7Gy7W4EQMBQFAABcg8AGAAC4BoENAABwDQIbAADgGgQ2AADANQhsAACAaxDYAAAA1yCwAQAArkFgAwAAXMNRgc3MmTPl8Xg0efJku5sCAABikGMCm/Xr1+u5555T9+7d7W4KAACIUY4IbH766Sf96le/0l//+lc1bdrU7uYAAIAY5YjA5tZbb1VOTo6GDh1a47FFRUUqLCy0/AAAAEgOWN178eLF2rhxo9avXx/Q8TNnztQDDzwQ4VYBAIBYZGuPze7duzVp0iS99NJLSk5ODug206ZNU0FBQdnP7t27I9xKAAAQKzyGYRh2Pfgbb7yh0aNHKyEhoWxbaWmpPB6P6tSpo6KiIss+fwoLC5WamqqCggKlpKREuskAACAMInX9tnUo6pJLLtGXX35p2TZx4kR17txZ99xzT41BDQAAQHm2BjaNGzfWOeecY9nWsGFDNW/evNJ2AACAmjhiVhQAAEA42D4rqqLc3Fy7mwAAAGIUPTYAAMA1CGwAAIBrENgAAADXILABAACuQWADAABcg8AGAAC4BoENAABwDQIbAADgGgQ2AADANQhsAACAazhuSQUAAOJeaamUlyft2yelpUmDBkkJCXa3KiYQ2AAA4CRLlkiTJkl79vi2ZWRITz4pjRljX7tiBENRAAA4xZIl0tix1qBGkvbuNbcvWWJPu2IIgQ0AAE5QWmr21BhG5X3ebZMnm8ehSgQ2AAA4QV5e5Z6a8gxD2r3bPA5VIrABAMAJ9u0L73FxisAGAAAnSEsL73FxisAGAAAnGDTInP3k8fjf7/FImZnmcagSgQ0AAE6QkGBO6ZYqBzfe32fPpp5NDQhsAABwijFjpNdek9q2tW7PyDC3U8emRhToAwDAScaMkUaNovJwiAhsAABwmoQEKTvb7lbEJIaiAACAaxDYAAAA1yCwAQAArkFgAwAAXIPABgAAuAaBDQAAcA0CGwAA4BoENgAAwDUIbAAAgGsQ2AAAANcgsAEAAK5BYAMAAFyDwAYAALgGgQ0AAHANAhsAAOAaBDYAAMA1CGwAAIBrENgAAADXILABAACuQWADAABcg8AGAAC4BoENAABwDQIbAADgGgQ2AADANQhsAACAaxDYAAAA1yCwAQAArkFgAwAAXIPABgAAuAaBDQAAcA0CGwAA4BoENgAAwDUIbAAAgGsQ2AAAANcgsAEAAK5BYAMAAFyDwAYAALgGgQ0AAHANAhsAAOAaBDYAAMA1CGwAAIBr2B7YPPPMM+revbtSUlKUkpKi/v376+2337a7WQAAIAbZHthkZGTokUce0YYNG7RhwwZdfPHFGjVqlLZs2WJ30wAAQIzxGIZh2N2Iipo1a6Y///nPuv7662s8trCwUKmpqSooKFBKSkoUWgcAAGorUtfvumG7pzAoLS3Vq6++quPHj6t///5+jykqKlJRUVHZ74WFhdFqHgAAcDjbh6Ik6csvv1SjRo2UlJSkm266SUuXLlXXrl39Hjtz5kylpqaW/WRmZka5tQAAwKkcMRRVXFysXbt26ejRo3r99df1/PPPa9WqVX6DG389NpmZmQxFAQAQQyI1FOWIwKaioUOH6owzztCzzz5b47Hk2AAAEHsidf12xFBURYZhWHplAAAAAmF78vDvf/97XX755crMzNSxY8e0ePFi5ebm6p133rG7aYB7lJZKeXnSvn1SWpo0aJCUkGB3qwAg7GwPbA4cOKDx48dr3759Sk1NVffu3fXOO+9o2LBhdjcNcIclS6RJk6Q9e3zbMjKkJ5+Uxoyxr10AEAGOzLEJBjk2QDWWLJHGjpUqvs09HvPf114juAFgi7jKsQEQBqWlZk+Nv+8u3m2TJ5vHAYBLENgAbpWXZx1+qsgwpN27zeMAwCUIbAC32rcvvMcBQAywPXkYQISkpYX3OMBNmCnoWvTYAG41aJA5+8mbKFyRxyNlZprHAfFkyRIpK0saMkQaN878NyvL3I6YR2ADuFVCgjmlW6oc3Hh/nz2bb6mIL96ZghXzz/buNbcT3MQ8AhvAzcaMMad0t21r3Z6RwVRvxB9mCsYFcmwAtxszRho1inwCIJiZgtnZUWsWwovABogHCQl8UAPMFIwLDEUBAOIDMwXjAoENACA+MFMwLhDYAADiAzMF4wKBDQAgfjBT0PVIHgYAxBdmCroagQ0AIP4wU9C1GIoCAACuQY8NAISKhRQBxyGwAYBQLFlilucvX8k2I8OcdUMCKmAbhqIAIFgspAg4FoENAASDhRQBRyOwAYBgBLOQIoCoI8cGAIIR6AKJe/eGdv8kJAO1Qo8NAAQj0AUSJ08OPtdmyRIpK0saMkQaN878NyuLnB0gCAQ2ABCMmhZS9MrPDy6RmIRkICwIbAAgGNUtpOhPIInEJCQDYUNgAwDB8i6k2KJF9ccFmkhMQjIQNkEFNrt3745UOwAgtowZIz3xRGDH1pRwHGhCcqDHAXEsqMCmc+fOuu+++3T8+PFItQcAYkfbtoEdV1PCcaAJyYEeB8SxoAKbFStW6L333tNZZ52l+fPnR6pNABAbakok9nikzEzzuGjcD9yptFTKzZUWLTL/JdeqWkEFNgMGDNCnn36qRx55RPfff7/OO+885ebmRqhpAOBw1SUSe3+fPbvmOjThup9o4UIbPZQACFpIycPXXnuttm3bpiuuuEI5OTkaPXq0vvvuu3C3DQCcz5tIXHFYKiPD3B7ogpjhup9I40IbPZQACInHMPzNL6zZiRMntHHjRr3++ut66qmnlJiYqFtvvVUzZsxQ48aNw93OKhUWFio1NVUFBQVKSUmJ2uMCgEW4KgY7ufKw90Jb8bLh7VVyUgAW60pLzYCxqtlyHo8Z9O7Y4ZzXR5Aidf0OKrCZN2+e1q9fr/Xr1+urr75SQkKCunfvrn79+qlnz556+eWXtW3bNi1dulS9e/cOWyOrQ2ADAFEQBxdaR8nNNXvDarJypZSdbf7fyUGxH5G6fge1VtTDDz+sfv36acKECerXr5969+6tpKSksv2/+c1v9Kc//UnXXXed/vWvf4WtkQAAmwVTa8d7oUXogi0BsGSJWeSx/DnKyDBzt+KsFy2owCaQOjbXX3+97rvvvpAbBABwIGrtRFcwJQCqGiL05uLE2RBh2CsPt2rVSh9++GG47xYAYCdq7URXoCUABgxgOY4Kwh7YeDweDR48ONx3CwCwE7V2oivQEgBr1rAcRwWsFQUAqFms1dpxg0BKADBEWAmBDQAgMLFSa8dNxoyRdu40Zz8tXGj+u2OH72/NEGElIdexcQqmewNAlMXYtGJX807D37vXf56Nx2OuQv/EE2ZA6qBz5Yg6Nk5EYAMAiGveWVGS/+CmPAdNAY/U9ZuhKAAAYllVQ4T+xMFyDAQ2AADEuvK5OC+9ZA4/+RMHU8AJbAC4D6tPIx4lJJhVn9u2lfLzqz7O5VPAg6o8DACOV5vS8iTFwg3ifAo4PTYA3MObRFmxYFkgeQVLlpizS4YMkcaNM//NynJ1LgJcKs6ngDMrCoA71Gb16arW2vEWnqNGC2JJIFPAHbASO7OiAKA6waw+XV5pKWvtwF3ivEo0gQ0Adwg1ryDUgAhwsuqqRL/yitSsmWuT60keBuAOoeYVxHmiJVxszBhp1ChrQnx+vnTHHaEl18cIemwAuEOoq0/HeaIlXM47BfyXv5SOHJGuvjq05PoYQmADwB1CzSsINSCCPahRFJo4yiUjsAHgHqGsPh3niZYxhSn5oYujXDICGwDuUr60/MKF5r87dlSfPxBKQISahbN3pTY1ihBXuWTUsQEAr1ArD1OxuLLaVICuqDY1imDKzTV7uGqycqWZkxMFkbp+E9gAQG2E8wIeTnYGW+EueOjAi3LMcWDRPgr0AYDTOHV4xM5clEgkqcbRMErExFEuGYENAITCqbNM7A62IpGkypT88IiTXDICGwAIhRNnmTgh2IpE7wpT8sMnlOT6GEPlYQAIhROHR4IJtiKVixKJ3hXvMMrYsWYQUz5wc9kwSlR4i/a5FD02ABAKJw6POCHYilTvSpwMo6D26LEBgFB4L+A1zTKJ5vCIE4KtSPau+Fv7iKn1qIAeGwAIhRNnmTglFyWSvSvl1z7Kzrb+fVluAXJAYDNz5kxdcMEFaty4sVq1aqWrrrpK33zzjd3NAoCaOW14xEnBVrSTVFluAf9he4G+yy67TP/93/+tCy64QCUlJbr33nv15ZdfauvWrWrYsGGNt6dAHwDbOa3ysL+igZmZZlDjxlyUcBcERFTETeXhQ4cOqVWrVlq1apUuuuiiGo8nsAEAP5wWbEUKyy3ErMLDh5XaokXYr9+OSx4uKCiQJDVr1szv/qKiIhUVFZX9XlhYGJV2AUBMcfmU3jJOmOKOwOXnS2+/LS1bJr3zTkQewlGBjWEYmjJlii688EKdc845fo+ZOXOmHnjggSi3DADgSE6Y4o6qGYb05ZdmILNsmbR2rf9ZhGHkqMDmtttu0xdffKGPPvqoymOmTZumKVOmlP1eWFiozMzMaDQPAOA0TpjiDquff5Y+/FBavtwMZnbvtu7v2VMaOdLsQRs6NOwP75jA5ne/+53efPNNrV69WhkZGVUel5SUpKSkpCi2DADgWE6sJxSP9uzxBTIffGAGN17165sBTE6O+eO9xkcolcT2wMYwDP3ud7/T0qVLlZubqw4dOtjdJABwpnhJCA4Gyy3Yo7RUWr/eDGSWL5c2b7buz8w0e2VGjjSn3tevH7Wm2R7Y3HrrrVq4cKH++c9/qnHjxtq/f78kKTU1VfWj+IcAAEfzN4U7I8O8qMf7VGZvPSF/fx+3TnG3Q2Gh9N57ZjDz1lvSoUO+fR6P1L+/L5g555yqC0VGmO3TvT1VPPH58+fruuuuq/H2TPcG4HrUaQkMPVrh9+23vsTf1aulkhLfvtRU6bLLzOGlyy+XWrQI6q7jpo5NsAhsALgadVrsE4+BUnGx9NFHviGmbdus+88+29crM3CglJgY8kNF6vpt+1AUAAeIxw/wWEGdFnvE09DfoUO+2jLvvmtN6k1MlAYPNgOZnBzpzDPta2eACGyAeBdPH+CxiDot0VfV0N/eveb2WB/6Mwzpiy98Q0yffmp9rq1aSSNGmMHMsGFSjI2GENgA8cztH+BuQJ2W6CotNQN9f1kahmEO/U2eLI0aFVu9midOmLVlvENMFXsBzzvPN8TUu7dUx/Y1skNGjg0Qr8jdiA3e81RTnRbOU3jk5prTk2uycqXzh/5277bWljl50revfn2zN2bkSLN3puIK9VFAjg2A8Ao0dyM317xgkn9jD+q0RFcsD/2Vlkrr1vmGmL74wrq/XTtfr0x2dlRry0QTgQ0QrwL9YL76aunIEd/v5N9EH3VaoifWhv4KCsyE32XLzATg/Hzfvjp1rLVlunWzrbZMNDEUBcSrQLvcK6J2in2YvRZ5sTD0t22br1cmL69ybZnLLzcDmcsuk5o3r/3jReh1Rx2bKhDYACGq6QO8Ok74cAcixZtUL/kf+ot2UF9cbAYW3mDmu++s+7t0MadijxwpDRhQq9oylYRj1mQVgRGBTRUIbIBaqOoDPFCxkEAJhMLfBT0zM3pDfwcPmssWLFtmLmNw7JhvX2Ki+b7z1pY544zItCEcFa+rCYwKhw4lsPGHwAaoJX8fPM2aWfNqqrJwofTLX0aubYCdojn0ZxjmQpLeWUzr1lkDitatfatjDxsmNW4cmXZ4hWPWZA2BUeGLLyp1/HgCm4oIbIAwqPgBXloqDR1a8+3osQFCd+KEOQ3bW1tm717r/l69fIm/558f3doytZ32HkBgVJiertS9e5nuDSACEhKsH06lpea3sZoSKAcNiloTAVf44QcziFm+3CyYV762TIMG1toy6en2tbO2094DKSdRMZALEwIbAJVROwUIj9JSc8kCb+Lvl19a97dvL11xhTnElJ0tJSfb0sxKajvt3cY6PwQ2APyjdgoQmqNHrbVlDh/27atTx5y55B1i6trVmbVlBg2qXa+tjXV+yLEBUD2n1E5xSjuAigxD+uYbX65MXp75evVq0sRXW+bSS8NTWyYaajPtPYB6QJHKsSGwAeB8rEAOpykullav9g0xbd9u3d+1q7W2TN0YHSCpzbT3GgIjZkVVgcDGIfg2jUgJRy0NIBwOHLDWlvnpJ9++evWstWU6drStmWFXm8/3agIj6thUgcDGAfg2jUhhBXLYyTCkTZt8Q0zr1ln3t2nj65UZOlRq1MiedjpdlCsPx2jfGByjqm/Te/ea2/k2jdoIdAXyvDzq6SA8jh+31pb58Ufr/t69fcFMr17RrS0TqyqWk4gwAhuErrTU7Knx1+lnGOa36cmTpVGj+DaN0NS2lgYQiJ07fRV/V66Uiop8+xo2tNaWccqq3qgSgQ1Cx7dpRFpta2kA/pSUSGvX+oKZf/3Luj8ry6wtM3KkNHiwlJRkSzMRGgIbhI5v04i02tbSALz+/W9rbZnya6ElJEgDB/qGmLp0cWZtGQSEwAah49s0Io0KyAiVYUhff+2bjv3xx9baMk2bWmvLNGtmX1sRVgQ2CJ3323R1w1GSlJ8fnfbAnaiAjEAVFUmrVvmGmL7/3rq/WzffdOz+/WO3tgyqxXRv1M6rr0pXX139MZmZTMdF7cVDraR4eI7htn+/tbbM8eO+ffXqmStUe4OZDh3saycqYbo3nKlly5qPIYEY4RDlKaNRRz2owJw+ba0ts369dX9ami9X5pJLqC0ThwhsUDskEAO1Rz2o6v30k7W2TMXPkwsu8PXKnHcetWXiHIENfELpBieBODIYkogf1IPyb8cOa22Z4mLfvkaNrLVl2rSxr51wHAIbr3i/kITaDc503PAL9lzE+2s31lEPylRSIn3yia9XZssW6/4OHXy1ZS66iNoyqBKBjcTYdm26wZmOG17Bnot4f+26QTwP5x45Yq0t8+9/+/YlJEgXXujLl+ncmdoyCAizouJ95eBwLTJYm6XtYQr2XMT7a9ctcnPNmTs1Wbky9ntsDEP66itrbZnTp337mzWz1pZp2tS+tiLiIjUrKr4DG7etHBzKkEQ4P1QZEqmdYM7FoEHueu3WViy/9ryfQzUN58bquTx50qwt4x1i2rHDuv+cc8xAZuRIqW9fasvUVgy9F5juHQluGtsOdUginN3gbp+OG2nBnAs3vXZrK9aH49w4nLtvn6+2zIoV1toySUnSxRebQ0w5OWZQh/CI9fdCmMR3YOOWse3a5Mgwq8k5gjkXbnnt1pZbpknHenXl06eljRt9Q0yffWbdn5bm65W55BJzxexAxVAPhK3c8l4Ig/geinLD2HZth9Pc3g0eS4I5F3l5sf/arS23DSVLsXURP3ZMev99M5B56y2zAnB5ffpYa8uEkvhLD0RgYvS9ELGVA4wYV1BQYEgyCgoKgr9xSYlhZGQYhsdjGOalxPrj8RhGZqZ5nFOtXOm/7RV/Vq6s+j5ef918rhX/Dt5tr78erWfjHiUl5t984ULz30BfQ4GeCze8dmsrHK99BGf7dsN46inDGD7cMOrVs/6dGzUyjDFjDONvfzOMfftq/1je94K/1zafS1Yx+l6o1fW7GvFdntE7ti1V/jYRK2Pb4RiS8HaDt21r3Z6REVfdl2GzZIn57WnIEGncOPPfrCxze00CPRdueO3WltOH40pLzV7hRYvMf8uvLB0rSkqk1aulu++WunaVzjhDuv12c02m4mKpY0ezR2XFCnOx29dflyZOrH3BvJqKFkpm0cLSUnf8nWvLKe8Fp5yLsIZJNghLxPf66+a33/KRbWZmbHwjCGekHmovA3zC9S0z0HMRy6/d2nLyt1R/5yUjIzbOS36+Ybz0kmH88peG0aSJ9TkkJBhGdrZh/OUvhvHVV4Zx+nRk2hDouZ04MXb/zuHkhPdCCK/5SPXYxHeOTXmxNLZdHjkyzmHXOHesvnZry6mv/VirL2QYZpVf7/IFa9ZYa8s0b26tLdOkSeTbtGiR2dsZCqf+nYMVzPva7vdCiK95cmyqEKmIL6aQI+MMTvjWFG+c9tr35j5Vde6dkvv088+G8fbbhnHrrYbRvn3ldp57rmFMm2YYH39sT1sDfS85/e8cqlB6/Ox6L9TiNR+p6zeBjVvE85CEUyxcGNiH7sKFdrfUXZz02ndycLt3r2E895xhjBplGA0aWNuTlGQYI0YYxpw5hrFzZ/TbVlFNyfGB/sTil4jaDGfb8V6oxWs+Utfv+K5j4yZjxpir/8bjkIRTUBPIHk567TsliVMyh5M++8xXW2bjRuv+9HRfbZmLLw6utkykVVe0MBixVseptiu92/FecNJr/j8IbNyEyr/2YqVz+zjltW93cHvsmDlDyVtb5sAB3z6Px1dbZuRIqUcPZy8q6Z0heNNN0qFDod1HrH2JCEdF8Wi/F+x+zftBYAOEixtL4yM4dgS327f7En9zc6VTp3z7Gjc2E35zcswE4Natw/e40TBmjPTzz9Kvfx3c7WL1S4QDez9q5MAvdAQ2QDjFeml81E40gttTp8yZS94hpq+/tu4/80xfr8ygQVK9eqE/lhNUrOlUk1j+EuHA3o8aOfALHdO9gUiI1ynYMPlbCiAzM/Tg9vBh6e23zUDmnXekggLfvrp1zdeXN5jp1KnWzXeUmsooVFSbv7Pd7J62XRshvOYjdf0msAGASKhNcGsY0r/+5Rti+uQTa22ZFi18tWWGD49ObRk7VVUnxeuaa8ykWTd8ifA+V8l/74eT6/ME+ZonsKkCgQ2CQk8KnOrkSXPRUu8Q065d1v3du/t6Zfr0ib/Xrb8egZYtpTlzpP/6L/vaFQnh7vFzKAKbKhDYxIFwBSOsFAyn2bvX1yvzwQfSiRO+fcnJ0iWXmIHMiBFSu3b2tdMp4umLSRw8VwKbKhDYuFy4gpFYK3MPdzp9Wtqwwdcrs2mTdX9GhjmDyVtbpkEDe9oJRAGBTRUIbFwsXMGIXWs4AZJUWGitLXPwoG+fxyP17esbYure3dm1ZYAwitT1m+necKbaVuAsLxxFr4BgfPedr1dm9WprbZmUFLO2zMiRZgJwy5b2tRNwIQIbOFM4g5FYLHqF2HLqlPTRR758mW++se7v1Mk3xHThhbFfWwZwMAIbOFM4g5FYLHoF58vP99WWeffdyrVlLrrIDGRyctxXWwZwMAIbOFM4gxEHlvxGDDIM6csvzUBm+XKztkz511OLFmYQk5Nj1pZJTbWvrbURB7Nx4G4ENrCfvw/ScAYjDiz5jRjx88/W2jK7d1v39+jhS/y94ILYfw1REgEuwKwo2Ku6D1IpvBU446ToFWqhtNR8nbz7rrRli7R5s1k4zys5WRo61FdbJjPTtqaGHSUREGVM964CgU0MC+SDVApvMEI3OyoqLZXWr5f+8hfpzTetM5gkqXlz6eqrzSGmIUPcWVuGkgixKRyfZzZ+JhLYVIHAJkYF80EqEYwgvAoLpffe89WWOXTI/3Hx0luRm2sGbTVZuZKSCE4RjmFDm4ceqWMDdwl2Ojcfpqitb7+11pYpKfHtq5h75RVszaRYRUmE2FJVb/feveb2QALxcNyHQ9WxuwGIU3yQItKKi6UPP5TuvFM6+2xzyvWUKea2khJz2513So8/XvWq0ZI1yHYrSiLEjpqKl0pmIF5aGtn7cDB6bGAPPkgRCYcOWWvLFBb69tWtKw0e7Kstc9ZZ5vZFiwK7bzcH2ZREiB3hKF7q8mrsBDawBx+kCAfDkL74wjfE9Omn1tdTy5a+ir/DhpnLGVREkE1JhFgSjt5ul/eY2z4UtXr1al1xxRVKT0+Xx+PRG2+8YXeTEA3eD1Kp8qJ/fJCiOidOmEHMTTdJ7dpJPXtKf/iDtHateUE+7zzf7/v3S/PnS7/4hf+gRvIF2VUtPunxmDPx3B5kjxlj5lW0bWvdnpER0/kWrhOOQNzlwbztPTbHjx9Xjx49NHHiRP3iF7+wuzmIJu8Hqb+sfGrLoLzdu33rMH3wgbW2TP361toyGRnB3Te9FT5jxphJ0sxCdK5w9Ha7vMfcUdO9PR6Pli5dqquuuirg2zDd2wWoLYOKSkuldet8Q0xffGHd366dr+JvdrYZ3NQWBRyDx3vXHt4ZTVLoxUvDcR+1xHTv/ygqKlJRUVHZ74XlkwMRmxISYjJBrVp84AevoMBM+F2+3Kwtk5/v21enjtS/vy9f5pxzqh46ChW9FcFh+QX7hKO328U95jHXYzNjxgw98MADlbbTYwPH4AM/cNu2+Xpl8vKstWVSU6XLLjMDmcsuMxeZhDOw/IIzUHnYr5gLbPz12GRmZhLYwBnc/oFf2w/B4mLz9t5g5rvvrPs7d/ZNxx44UEpMDG/7UXssv4AwYSjqP5KSkpSUlGR3M4DKF/kBA6ovehXrFWxD7Yk6eNAcWlq+3BxqOnbMty8x0Vpb5swzI9d+hIcTa6Aw9ItyYi6wARzB30W+Zcuq1xySYrvoVTDl1w1D+vxzX6/MunXW27VqZa0t07hx9J4Has9pNVAY+kUFtgc2P/30k74r1x29Y8cObd68Wc2aNVO7du1sbBlQhaou8tUFNeXFWtGrmsqvezzm/jp1zKq/y5ebAU95vXr5emV69zaPRWxyUg0UF693hNDZnmOTm5urIX5WlZ0wYYIWLFhQ4+2Z7o2oqim/IBCxtkJyoCs/l9eggbW2TMWibwiNE4ZcvO+BmmqgRDrHhlyfmOfaHJvs7Gw5KH8ZqF5N+QXVidWiV4H2MLVoIV1zja+2THJyRJsVd5wy5OKUgoZOzPWBI9AfDAQj1GGkWK1ge/So9NVXgR37//6f9L//a07NJqgJL++QS8ULuXfIZcmS6LbHCcsvOC3XB45he48NEFMCzRto0cJaYC5Wil4ZhvTNN77lC/LyzC7/6nh7oi66KDptjDeB5DjZMdvO7oKGTsr1gaMQ2CB+hCM/IdA1Vr77TlqzJrof+KE+v+JiafVq3yym7dut+7t0kTp1kv75T9ZSsoOTh1zsrBru8vWOEDoCG8SHcOUnBJpfUK9edD/wg31+Bw6YtWWWLZNWrLDWlvG2PSfH/DnjjOofIxZ6omIZQy7+OSXXB45j+6yo2mJWFGoUiWrATlowMZDnN3q0tHmztbZMea1b+2rLDB1adW0ZJ8zKiTeBzkqLtdl24eKk9yKCEhdLKoSCwAbViuSUUCdc5AOZft6woZSSUvkb/fnn+1bI7tWL2jJO5ZTp1U7mhPciqlbF+XHtdG8goiKZn+CEVckDmX5+/Lj507ChWek3J8esLZOeHp02onYYcqmZE96L8K+6YfKhQyPykAQ2TsM3j/Bye35CoDV17rlHmjGDadixyju9mhwnxJKaKkO/+GJEHpbAxkmcUoDLTdw4JfTf/zYXk1y2THrzzcBuQ22Z2Gf39GogGIGUKZg6NSIPTY6NU0QiwRXuyE8wDOnrr81AZvly6aOPrLVlKg5PlBcLzw+A+wSQ9F4oKVUix8aVnFqAyw1iNT+hqMhaW+b77637u3b1Jf7u328uZSDFzvMD4G42Du8T2DiBkwtwuUGs5Cfs32+tLfPTT7599eqZ3368K2R36GC9bUKC858fgPhh4/A+gY0TuD3B1QmcmJ9w+rS0aZNv+YL1663727Sx1pZp1Kjq+3Li8wMQOLdNHAmkMnR6urk/zAhsnMCNCa5O5IQpoT/9JH3wgS9fpmKw2ru3b4jpvPOCqy3jhOcHIHhunDgSSBrAI49I48eH/aFJHq7IjqjZDQmuqNrOnb5cmZUrzbWZvBo2lIYPNwOZyy8neAXijdsnjlRTGbpw6FAqD/sT1sDGzqjZ++KW/Ee2sf7ijiclJdInn/iGmLZsse7v0MHXKzN4sJSUZE87AdgrkpXRnSTKlYcJbLycEDWz5knsOnLEV1vm7bfNWjNeCQnSwIG+YKZzZ9/rCkD8ivN1wFhSIZKcMt2aBNDYYRjSV1/5hpg+/thMBvZq2tRctmDkSOnSS83fAaA8Jo5EBIGNFJ7p1uHKzSEB1LlOnpRWrfIl/u7YYd3frZuvV6ZfP6kuby8A1WDiSETExydvTUFHbaNmN2a0w7Rvn7W2zPHjvn316kkXX+yrLZOVZVszAcSgQKZEZ2SYxyFg7g9sAgk6ahM117TIF0m/seX0aWnjRt8Q02efWfenpfkCmUsuqb62DABUJ1Yrozucu5OHA00IDnW6dbxktLvdTz+ZvTHLl5s/+/db919wgbW2DIm/AMIpTieOMCuqClX+YYINOkKZbh3nGe0x7fvvfdOxc3OttWUaNbLWlmnTxrZmAogTbqs8HABmRQUr2ITgUNYTIqPdOWr6UCgpkdas8Q0xffWV9fYdO0pXXGEOMV10EbVlAEQXE0fCxr2BTShBR7DTrZ2Q0R6HUX4lVeVRPfSQOTNp+XKztszRo779CQnShRf6hpjOPpshJgBwAfcGNqEGHcFEzXZntDMbq+o8qj17pOuus25r1sxXW2b4cGrLAIALuT/HJtLrL9m1FIITKiXbrbRUat+++tVhExOlO+6QrrzSrC1T3bmm9wsAoiZSOTZBLB0cY7zT6KTKQwzhnEbnzc1p29a6PSMjcsFFTZWSJbNScmlp+B/bCX78UXr+eXOdpZqWvD91ykwAHjiw8oy23Fxp0SLz31dfNQPhIUOkcePMf7OyzAASABAz3Ntj4xWtaXTR/LYfb7OxTp8268l4E383bgzu9gsXSr/8pe93f68Jf+Kp9wsAooxZUaGK1vpL0cxoj4fZWMeOmbVlli0zK/8eOODb5/FIffpIXbtK8+fXfF/l86iqGsLzJ5rrhAEAwsL9gY3kvml0TpiNFQnbt1try5w65dvXqJG5mKS3tkzr1mYv2YoVgSdvVzeEV5VA1gkDADhGfAQ2bmP3bKxwOXXKWlvm66+t+884w6wtM3Kk+Vzq1bPuD7YceU21jaoTy71fiG8kxSPOENjEolheX+TwYbOmzLJl0rvvWmvL1K1rrS3TqVPNtWWCKaxYm+Ak1nq/AImSEIhL7k8edrNYWF/EMKQtW3y9Mp98YiYDezVvbq0t06RJaI8TyLfSQJOuy2O9L8QqSkLEpxjqoWOtqCrEdWAjOfNFfPKkOSPLG8zs2mXd3727b4Xsvn2j196aahtVxAUAsYoFeuNTjPXQEdhUwTWBjRMDlGDs3etbHfv996UTJ3z7kpOliy/2BTPt2tnXzqoKKvrjtN4vIFDxVhICMdlDx3RvN4uxKFuSOZy0YYOvV2bTJuv+tm19uTIXXyw1aGBPOyuqKicnM1N6/HGpRYvYDS4Br3goCQGfmoq2xlnZCgIbu1UVZe/da253UpRdWGitLXPwoG+fx2MOK3l7ZXr0cO6iktGqbRQvYr230Y3cWhIC/tU04zPOylYQ2NgpFqLs774zA5nly6VVq6y1ZRo3ttaWadXKnjaGIpy1jeL5wh6LvY3xwC0lIRAYeugsCGzs5MQo+9Qp6eOPfUNM33xj3X/mmb7aMhdeWLm2TLyJ5wt7LPU2xptYLgmB4NFDZ0FgYyenRNn5+dbaMgUFvn1160oXXWQOL3lry8AUzxf2WOhtjHfB1HhCbKOHzoLAxk52RdmGIX35pW/5gk8+sb4ZWrSw1pZJTQ3v47tBvF/YndjbGO/8DYnGSz5ZPA8HS/TQVUBgY6doRtk//2ytLbN7t3V/jx6+WUwXXBA3b4CQReLCHksfzk7pbYSppiFRNweX8TwcXB49dGUIbOwU6Sh7zx5fr8wHH5jBjVdysjR0qDnElJNjTndG4MJ9YY+1D2fG9J0jnodE4/m5+xMvPXQ1oECfE4RraYTSUmn9et8sps2brfszMny9MkOGOKe2TCwKZwG0GCysVWMVZyrbRkc8VxiO5+fuElQeroIrAhsp9GGIwkLpvfd8tWUOHfLt83ikfv18wcy55zq3tkysCdeFPZY/nKuq4uzkgMxt4rnCcDw/d5eg8rDbBVNX5dtvfbkyq1dLJSW+fSkp0mWXmcNLl18utWwZkebGvXANI8ZyEi5j+vaL51yneH7uqBaBTSwoLpY++siXL7Ntm3V/p06+XpkLL5QSE+1pZ7wJx4U91j+cGdO3VzznOsXzc0e1CGyc6tAha22ZwkLfvrp1pcGDfcsXnHWWfe2Md7W9sLvhwzmcVZwRnHiuXxLPzx3VIrBxCsOQvvjCN8T06afWN2vLlr7aMsOGUVvGSWpzYefDGbURz/VL4vm5o1oENnY6cUL68EPfEFPFXIuePa21ZerUsaWZiCA+nFFb8ZzrFM/PHVViVlS07d5trS1z8qRvX/361toyGRn2tRPRFa4p/4hfsVTgMdzi+bnHMKZ7V6HKP4xTXuilpdK6db4hpi++sO7PzLTWlqlfP/pthDM45TULAFHAdO9g2F3FtaDATPhdvtysLZOf79vn8Uj9+/uCmXPOobYMTCThAkCtuS+wsavE9rZtvl6ZvDxrbZnUVGttmRYtwv/4AADAZUNRDRtGr4prcbEZwHiXL/j2W+v+s8/29coMHEhtGQAAymEoKhCRruJ68KC1tsyxY759iYnW2jJnnhn8/TsVuR8AgBjhrsAm3FVcDUP6/HPfENO6ddYhrlatrLVlYmFWVrDszleyG0EdAMQUdwU24ajieuKEOQ3bO8S0d691/3nn+YaYevd2d20Zu/KVnCLegzoAiEHuzLEJdsXlXbt8tWU+/LBybZlhw8xAZsQIqW3biD8nR4jlVafDoaqgjpWrASAsyLEJRKBVXCVpzRrfENOXX1rvp107X69MdnZ81pZxyqrTdgwFlZaaPTX+gmPDMF9Lkyeba0S5MagDgBjmrsBGqrrEdnq6dM010tKl0m9/Kx0+7NtXp461tky3btSWccKq03YNBTklqAMABM0RCSJz585Vhw4dlJycrPPPP195eXm1u8MxY8whkr//XfrVr6QePcwL8OOPSy+9ZAY1qanSf/+3+fvBg9JHH0lTp1Iwz8vuVae9Q0EVAwxvfs+SJZF5XMkZQR0AICS299i88sormjx5subOnauBAwfq2Wef1eWXX66tW7eqXbt2wd1ZcbG0erVviGn7duv+Ll3MqdgjR0oDBlBbpjp2rjpt91CQ3UEdACBkticP9+3bV7169dIzzzxTtq1Lly666qqrNHPmzBpvX5Z8dOWVSlm5snJtmexsM5C57DLpxx+ZthsMb6+J5D9fKVIJtLm55rpZNVm5MjJDQd7E6WCT0AEAAYtU8rCtQ1HFxcX67LPPNHz4cMv24cOHa82aNcHd2ZtvmkFN69bSb34jvf66OeT03nvmReiSS8yL5bhx5r9ZWZEdznADb75SxZlgGRmRnRVk91CQNwldqjwsWT4JPVaCmtJSM1hctMj8t7TU7hYBQMTYOhSVn5+v0tJStW7d2rK9devW2r9/v9/bFBUVqaioqOz3goICSVLh5MnSlVeadWa8tWUMw8yhGT++8h3t2SP94hfSP/5h3g7+DR1qrki+Zo20f7/Upo05jJeQIBUWRuYxA43cU1Ii14ahQ6UXX5Tuucfs6fNKT5ceecTcH6nHDqc33/T/HB59lNc9AFsV/uczNOwDR4aN9u7da0gy1qxZY9n+0EMPGWeffbbf20yfPt2QxA8//PDDDz/8uOBn+/btYY0tbO2xadGihRISEir1zhw8eLBSL47XtGnTNGXKlLLfjx49qvbt22vXrl1KTU2NaHtRvcLCQmVmZmr37t1hHS9FaDgfzsG5cA7OhXMUFBSoXbt2atasWVjv19bApl69ejr//PO1YsUKjR49umz7ihUrNGrUKL+3SUpKUlJSUqXtqampvEgdIiUlhXPhIJwP5+BcOAfnwjnqhHlpItune0+ZMkXjx49X79691b9/fz333HPatWuXbrrpJrubBgAAYoztgc0111yjw4cP68EHH9S+fft0zjnn6K233lL79u3tbhoAAIgxtgc2knTLLbfolltuCem2SUlJmj59ut/hKUQX58JZOB/OwblwDs6Fc0TqXNheoA8AACBcHLFWFAAAQDgQ2AAAANcgsAEAAK5BYAMAAFwjJgKbuXPnqkOHDkpOTtb555+vvLy8ao9ftWqVzj//fCUnJ6tjx46aN29elFrqfsGciyVLlmjYsGFq2bKlUlJS1L9/f7377rtRbK27Bfu+8Pr4449Vt25d9ezZM7INjDPBno+ioiLde++9at++vZKSknTGGWfob3/7W5Ra627BnouXX35ZPXr0UIMGDZSWlqaJEyfq8OHDUWqte61evVpXXHGF0tPT5fF49MYbb9R4m7Bcv8O6QEMELF682EhMTDT++te/Glu3bjUmTZpkNGzY0Pjhhx/8Hv/9998bDRo0MCZNmmRs3brV+Otf/2okJiYar732WpRb7j7BnotJkyYZjz76qLFu3Tpj27ZtxrRp04zExERj48aNUW65+wR7LryOHj1qdOzY0Rg+fLjRo0eP6DQ2DoRyPq688kqjb9++xooVK4wdO3YYn376qfHxxx9HsdXuFOy5yMvLM+rUqWM8+eSTxvfff2/k5eUZ3bp1M6666qoot9x93nrrLePee+81Xn/9dUOSsXTp0mqPD9f12/GBTZ8+fYybbrrJsq1z587G1KlT/R5/9913G507d7Zsu/HGG41+/fpFrI3xIthz4U/Xrl2NBx54INxNizuhnotrrrnG+MMf/mBMnz6dwCaMgj0fb7/9tpGammocPnw4Gs2LK8Geiz//+c9Gx44dLdueeuopIyMjI2JtjEeBBDbhun47eiiquLhYn332mYYPH27ZPnz4cK1Zs8bvbT755JNKx1966aXasGGDTp06FbG2ul0o56Ki06dP69ixY2Ff8CzehHou5s+fr+3bt2v69OmRbmJcCeV8vPnmm+rdu7dmzZqltm3bqlOnTrrrrrv0888/R6PJrhXKuRgwYID27Nmjt956S4Zh6MCBA3rttdeUk5MTjSajnHBdvx1Rebgq+fn5Ki0trbTSd+vWrSutCO61f/9+v8eXlJQoPz9faWlpEWuvm4VyLip67LHHdPz4cV199dWRaGLcCOVcfPvtt5o6dary8vJUt66j3/YxJ5Tz8f333+ujjz5ScnKyli5dqvz8fN1yyy06cuQIeTa1EMq5GDBggF5++WVdc801OnnypEpKSnTllVfq6aefjkaTUU64rt+O7rHx8ng8lt8Nw6i0rabj/W1H8II9F16LFi3SjBkz9Morr6hVq1aRal5cCfRclJaWaty4cXrggQfUqVOnaDUv7gTz3jh9+rQ8Ho9efvll9enTRyNGjNDjjz+uBQsW0GsTBsGci61bt+r222/X/fffr88++0zvvPOOduzYwULMNgnH9dvRX91atGihhISESpH2wYMHK0V1Xm3atPF7fN26ddW8efOItdXtQjkXXq+88oquv/56vfrqqxo6dGgkmxkXgj0Xx44d04YNG7Rp0ybddtttkswLq2EYqlu3rt577z1dfPHFUWm7G4Xy3khLS1Pbtm2Vmppatq1Lly4yDEN79uzRWWedFdE2u1Uo52LmzJkaOHCg/ud//keS1L17dzVs2FCDBg3SQw89RC9/FIXr+u3oHpt69erp/PPP14oVKyzbV6xYoQEDBvi9Tf/+/Ssd/95776l3795KTEyMWFvdLpRzIZk9Ndddd50WLlzImHWYBHsuUlJS9OWXX2rz5s1lPzfddJPOPvtsbd68WX379o1W010plPfGwIED9eOPP+qnn34q27Zt2zbVqVNHGRkZEW2vm4VyLk6cOKE6dayXwoSEBEm+3gJER9iu30GlGtvAO3XvhRdeMLZu3WpMnjzZaNiwobFz507DMAxj6tSpxvjx48uO904Xu+OOO4ytW7caL7zwAtO9wyTYc7Fw4UKjbt26xpw5c4x9+/aV/Rw9etSup+AawZ6LipgVFV7Bno9jx44ZGRkZxtixY40tW7YYq1atMs466yzjhhtusOspuEaw52L+/PlG3bp1jblz5xrbt283PvroI6N3795Gnz597HoKrnHs2DFj06ZNxqZNmwxJxuOPP25s2rSpbOp9pK7fjg9sDMMw5syZY7Rv396oV6+e0atXL2PVqlVl+yZMmGAMHjzYcnxubq5x3nnnGfXq1TOysrKMZ555Jsotdq9gzsXgwYMNSZV+JkyYEP2Gu1Cw74vyCGzCL9jz8dVXXxlDhw416tevb2RkZBhTpkwxTpw4EeVWu1Ow5+Kpp54yunbtatSvX99IS0szfvWrXxl79uyJcqvdZ+XKldVeAyJ1/fYYBn1tAADAHRydYwMAABAMAhsAAOAaBDYAAMA1CGwAAIBrENgAAADXILABAACuQWADAABcg8AGAAC4BoENAABwDQIbAADgGgQ2ABxn0aJFSk5O1t69e8u23XDDDerevbsKCgpsbBkAp2OtKACOYxiGevbsqUGDBul///d/9cADD+j555/X2rVr1bZtW7ubB8DB6trdAACoyOPx6OGHH9bYsWOVnp6uJ598Unl5eQQ1AGpEjw0Ax+rVq5e2bNmi9957T4MHD7a7OQBiADk2ABzp3Xff1ddff63S0lK1bt3a7uYAiBH02ABwnI0bNyo7O1tz5szR4sWL1aBBA7366qt2NwtADCDHBoCj7Ny5Uzk5OZo6darGjx+vrl276oILLtBnn32m888/3+7mAXA4emwAOMaRI0c0cOBAXXTRRXr22WfLto8aNUpFRUV65513bGwdgFhAYAMAAFyD5GEAAOAaBDYAAMA1CGwAAIBrENgAAADXILABAACuQWADAABcg8AGAAC4BoENAABwDQIbAADgGgQ2AADANQhsAACAaxDYAAAA1/j/XISwC+Z68BUAAAAASUVORK5CYII=\n",
       "text/plain": [
        "
    "
       ]
@@ -515,7 +515,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "
    "
       ]
@@ -583,18 +583,18 @@
      "output_type": "stream",
      "text": [
       "The intercept alpha: \n",
-      " [2.05177695]\n",
+      " [1.89563529]\n",
       "Coefficient beta : \n",
-      " [[5.05971574]]\n",
-      "Mean squared error: 0.28\n",
-      "Variance score: 0.88\n",
+      " [[5.26512016]]\n",
+      "Mean squared error: 0.27\n",
+      "Variance score: 0.87\n",
       "Mean squared log error: 0.01\n",
-      "Mean absolute error: 0.45\n"
+      "Mean absolute error: 0.41\n"
      ]
     },
     {
      "data": {
-      "image/png": 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\n",
+      "image/png": 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\n",
       "text/plain": [
        "
    "
       ]
@@ -822,7 +822,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "
    "
       ]
@@ -838,7 +838,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0.004999999999999997\n"
+      "0.0049999999999999845\n"
      ]
     }
    ],
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter10.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter10.ipynb
index bc64986ba..3d8c9ceb8 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter10.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter10.ipynb
@@ -1077,7 +1077,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -1655,7 +1655,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -1673,7 +1673,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -1691,7 +1691,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -1709,7 +1709,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -1727,7 +1727,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -1745,7 +1745,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -1763,7 +1763,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -1781,11 +1781,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -1803,11 +1803,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -1825,11 +1825,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -1847,11 +1847,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -1869,11 +1869,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -1891,7 +1891,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -1909,11 +1909,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -1931,11 +1931,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -1953,11 +1953,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -1975,11 +1975,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -1997,11 +1997,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -2019,11 +2019,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -2041,11 +2041,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -2063,11 +2063,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -2128,15 +2128,15 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16145/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -2755,10 +2755,6 @@
       "Learning rate  =  1.0\n",
       "Lambda =  0.1\n",
       "Accuracy score on test set:  0.08333333333333333\n",
-      "\n",
-      "Learning rate  =  1.0\n",
-      "Lambda =  1.0\n",
-      "Accuracy score on test set:  0.08888888888888889\n",
       "\n"
      ]
     },
@@ -2766,6 +2762,10 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
+      "Learning rate  =  1.0\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on test set:  0.08888888888888889\n",
+      "\n",
       "Learning rate  =  1.0\n",
       "Lambda =  10.0\n",
       "Accuracy score on test set:  0.09444444444444444\n",
@@ -2773,10 +2773,6 @@
       "Learning rate  =  10.0\n",
       "Lambda =  1e-05\n",
       "Accuracy score on test set:  0.17222222222222222\n",
-      "\n",
-      "Learning rate  =  10.0\n",
-      "Lambda =  0.0001\n",
-      "Accuracy score on test set:  0.11666666666666667\n",
       "\n"
      ]
     },
@@ -2784,6 +2780,10 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
+      "Learning rate  =  10.0\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on test set:  0.11666666666666667\n",
+      "\n",
       "Learning rate  =  10.0\n",
       "Lambda =  0.001\n",
       "Accuracy score on test set:  0.10555555555555556\n",
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter11.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter11.ipynb
index 0f5b522f8..9115e9414 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter11.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter11.ipynb
@@ -3034,13 +3034,15 @@
       "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_wrapper.py:88\u001b[0m, in \u001b[0;36m\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m     83\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mstack\u001b[39m(arrays, axis\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0\u001b[39m):\n\u001b[1;32m     84\u001b[0m     \u001b[38;5;66;03m# this code is basically copied from numpy/core/shape_base.py's stack\u001b[39;00m\n\u001b[1;32m     85\u001b[0m     \u001b[38;5;66;03m# we need it here because we want to re-implement stack in terms of the\u001b[39;00m\n\u001b[1;32m     86\u001b[0m     \u001b[38;5;66;03m# primitives defined in this file\u001b[39;00m\n\u001b[0;32m---> 88\u001b[0m     arrays \u001b[38;5;241m=\u001b[39m [array(arr) \u001b[38;5;28;01mfor\u001b[39;00m arr \u001b[38;5;129;01min\u001b[39;00m arrays]\n\u001b[1;32m     89\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m arrays:\n\u001b[1;32m     90\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mneed at least one array to stack\u001b[39m\u001b[38;5;124m'\u001b[39m)\n",
       "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:14\u001b[0m, in \u001b[0;36mmake_vjp..vjp\u001b[0;34m(g)\u001b[0m\n\u001b[0;32m---> 14\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mvjp\u001b[39m(g): \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mbackward_pass\u001b[49m\u001b[43m(\u001b[49m\u001b[43mg\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mend_node\u001b[49m\u001b[43m)\u001b[49m\n",
       "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:21\u001b[0m, in \u001b[0;36mbackward_pass\u001b[0;34m(g, end_node)\u001b[0m\n\u001b[1;32m     19\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m node \u001b[38;5;129;01min\u001b[39;00m toposort(end_node):\n\u001b[1;32m     20\u001b[0m     outgrad \u001b[38;5;241m=\u001b[39m outgrads\u001b[38;5;241m.\u001b[39mpop(node)\n\u001b[0;32m---> 21\u001b[0m     ingrads \u001b[38;5;241m=\u001b[39m \u001b[43mnode\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mvjp\u001b[49m\u001b[43m(\u001b[49m\u001b[43moutgrad\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     22\u001b[0m     \u001b[38;5;28;01mfor\u001b[39;00m parent, ingrad \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mzip\u001b[39m(node\u001b[38;5;241m.\u001b[39mparents, ingrads):\n\u001b[1;32m     23\u001b[0m         outgrads[parent] \u001b[38;5;241m=\u001b[39m add_outgrads(outgrads\u001b[38;5;241m.\u001b[39mget(parent), ingrad)\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:78\u001b[0m, in \u001b[0;36mdefvjp..vjp_argnums..\u001b[0;34m(g)\u001b[0m\n\u001b[1;32m     76\u001b[0m     vjp_0 \u001b[38;5;241m=\u001b[39m vjp_0_fun(ans, \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[1;32m     77\u001b[0m     vjp_1 \u001b[38;5;241m=\u001b[39m vjp_1_fun(ans, \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[0;32m---> 78\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;01mlambda\u001b[39;00m g: (vjp_0(g), \u001b[43mvjp_1\u001b[49m\u001b[43m(\u001b[49m\u001b[43mg\u001b[49m\u001b[43m)\u001b[49m)\n\u001b[1;32m     79\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m     80\u001b[0m     vjps \u001b[38;5;241m=\u001b[39m [vjps_dict[argnum](ans, \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs) \u001b[38;5;28;01mfor\u001b[39;00m argnum \u001b[38;5;129;01min\u001b[39;00m argnums]\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:660\u001b[0m, in \u001b[0;36munbroadcast_f..\u001b[0;34m(g)\u001b[0m\n\u001b[1;32m    658\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21munbroadcast_f\u001b[39m(target, f):\n\u001b[1;32m    659\u001b[0m     target_meta \u001b[38;5;241m=\u001b[39m anp\u001b[38;5;241m.\u001b[39mmetadata(target)\n\u001b[0;32m--> 660\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;01mlambda\u001b[39;00m g: unbroadcast(\u001b[43mf\u001b[49m\u001b[43m(\u001b[49m\u001b[43mg\u001b[49m\u001b[43m)\u001b[49m, target_meta)\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:35\u001b[0m, in \u001b[0;36m\u001b[0;34m(g)\u001b[0m\n\u001b[1;32m     30\u001b[0m \u001b[38;5;66;03m# ----- Binary ufuncs -----\u001b[39;00m\n\u001b[1;32m     32\u001b[0m defvjp(anp\u001b[38;5;241m.\u001b[39madd,         \u001b[38;5;28;01mlambda\u001b[39;00m ans, x, y : unbroadcast_f(x, \u001b[38;5;28;01mlambda\u001b[39;00m g: g),\n\u001b[1;32m     33\u001b[0m                         \u001b[38;5;28;01mlambda\u001b[39;00m ans, x, y : unbroadcast_f(y, \u001b[38;5;28;01mlambda\u001b[39;00m g: g))\n\u001b[1;32m     34\u001b[0m defvjp(anp\u001b[38;5;241m.\u001b[39mmultiply,    \u001b[38;5;28;01mlambda\u001b[39;00m ans, x, y : unbroadcast_f(x, \u001b[38;5;28;01mlambda\u001b[39;00m g: y \u001b[38;5;241m*\u001b[39m g),\n\u001b[0;32m---> 35\u001b[0m                         \u001b[38;5;28;01mlambda\u001b[39;00m ans, x, y : unbroadcast_f(y, \u001b[38;5;28;01mlambda\u001b[39;00m g: \u001b[43mx\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43m \u001b[49m\u001b[43mg\u001b[49m))\n\u001b[1;32m     36\u001b[0m defvjp(anp\u001b[38;5;241m.\u001b[39msubtract,    \u001b[38;5;28;01mlambda\u001b[39;00m ans, x, y : unbroadcast_f(x, \u001b[38;5;28;01mlambda\u001b[39;00m g: g),\n\u001b[1;32m     37\u001b[0m                         \u001b[38;5;28;01mlambda\u001b[39;00m ans, x, y : unbroadcast_f(y, \u001b[38;5;28;01mlambda\u001b[39;00m g: \u001b[38;5;241m-\u001b[39mg))\n\u001b[1;32m     38\u001b[0m defvjp(anp\u001b[38;5;241m.\u001b[39mdivide,      \u001b[38;5;28;01mlambda\u001b[39;00m ans, x, y : unbroadcast_f(x, \u001b[38;5;28;01mlambda\u001b[39;00m g:   g \u001b[38;5;241m/\u001b[39m y),\n\u001b[1;32m     39\u001b[0m                         \u001b[38;5;28;01mlambda\u001b[39;00m ans, x, y : unbroadcast_f(y, \u001b[38;5;28;01mlambda\u001b[39;00m g: \u001b[38;5;241m-\u001b[39m g \u001b[38;5;241m*\u001b[39m x \u001b[38;5;241m/\u001b[39m y\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m2\u001b[39m))\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_boxes.py:35\u001b[0m, in \u001b[0;36mArrayBox.__rmul__\u001b[0;34m(self, other)\u001b[0m\n\u001b[0;32m---> 35\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21m__rmul__\u001b[39m(\u001b[38;5;28mself\u001b[39m, other): \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43manp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mmultiply\u001b[49m\u001b[43m(\u001b[49m\u001b[43mother\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m)\u001b[49m\n",
+      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:67\u001b[0m, in \u001b[0;36mdefvjp..vjp_argnums..\u001b[0;34m(g)\u001b[0m\n\u001b[1;32m     64\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mNotImplementedError\u001b[39;00m(\n\u001b[1;32m     65\u001b[0m             \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mVJP of \u001b[39m\u001b[38;5;132;01m{}\u001b[39;00m\u001b[38;5;124m wrt argnum 0 not defined\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;241m.\u001b[39mformat(fun\u001b[38;5;241m.\u001b[39m\u001b[38;5;18m__name__\u001b[39m))\n\u001b[1;32m     66\u001b[0m     vjp \u001b[38;5;241m=\u001b[39m vjpfun(ans, \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[0;32m---> 67\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;01mlambda\u001b[39;00m g: (\u001b[43mvjp\u001b[49m\u001b[43m(\u001b[49m\u001b[43mg\u001b[49m\u001b[43m)\u001b[49m,)\n\u001b[1;32m     68\u001b[0m \u001b[38;5;28;01melif\u001b[39;00m L \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m2\u001b[39m:\n\u001b[1;32m     69\u001b[0m     argnum_0, argnum_1 \u001b[38;5;241m=\u001b[39m argnums\n",
+      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:423\u001b[0m, in \u001b[0;36mmatmul_vjp_1..\u001b[0;34m(g)\u001b[0m\n\u001b[1;32m    421\u001b[0m A_ndim \u001b[38;5;241m=\u001b[39m anp\u001b[38;5;241m.\u001b[39mndim(A)\n\u001b[1;32m    422\u001b[0m B_meta \u001b[38;5;241m=\u001b[39m anp\u001b[38;5;241m.\u001b[39mmetadata(B)\n\u001b[0;32m--> 423\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;01mlambda\u001b[39;00m g: \u001b[43mmatmul_adjoint_1\u001b[49m\u001b[43m(\u001b[49m\u001b[43mA\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mg\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mA_ndim\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mB_meta\u001b[49m\u001b[43m)\u001b[49m\n",
+      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:410\u001b[0m, in \u001b[0;36mmatmul_adjoint_1\u001b[0;34m(A, G, A_ndim, B_meta)\u001b[0m\n\u001b[1;32m    408\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:  \u001b[38;5;66;03m# We need to swap the last two axes of A\u001b[39;00m\n\u001b[1;32m    409\u001b[0m     A \u001b[38;5;241m=\u001b[39m anp\u001b[38;5;241m.\u001b[39mswapaxes(A, A_ndim \u001b[38;5;241m-\u001b[39m \u001b[38;5;241m2\u001b[39m, A_ndim \u001b[38;5;241m-\u001b[39m \u001b[38;5;241m1\u001b[39m)\n\u001b[0;32m--> 410\u001b[0m result \u001b[38;5;241m=\u001b[39m \u001b[43manp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mmatmul\u001b[49m\u001b[43m(\u001b[49m\u001b[43mA\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mG\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    411\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m B_is_vec:\n\u001b[1;32m    412\u001b[0m     result \u001b[38;5;241m=\u001b[39m anp\u001b[38;5;241m.\u001b[39msqueeze(result, anp\u001b[38;5;241m.\u001b[39mndim(G) \u001b[38;5;241m-\u001b[39m \u001b[38;5;241m1\u001b[39m)\n",
       "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:45\u001b[0m, in \u001b[0;36mprimitive..f_wrapped\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m     43\u001b[0m     argnums \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mtuple\u001b[39m(argnum    \u001b[38;5;28;01mfor\u001b[39;00m argnum, _   \u001b[38;5;129;01min\u001b[39;00m boxed_args)\n\u001b[1;32m     44\u001b[0m     ans \u001b[38;5;241m=\u001b[39m f_wrapped(\u001b[38;5;241m*\u001b[39margvals, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[0;32m---> 45\u001b[0m     node \u001b[38;5;241m=\u001b[39m \u001b[43mnode_constructor\u001b[49m\u001b[43m(\u001b[49m\u001b[43mans\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mf_wrapped\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43margvals\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mkwargs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43margnums\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mparents\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     46\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m new_box(ans, trace, node)\n\u001b[1;32m     47\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n",
       "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:36\u001b[0m, in \u001b[0;36mVJPNode.__init__\u001b[0;34m(self, value, fun, args, kwargs, parent_argnums, parents)\u001b[0m\n\u001b[1;32m     33\u001b[0m     fun_name \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mgetattr\u001b[39m(fun, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124m__name__\u001b[39m\u001b[38;5;124m'\u001b[39m, fun)\n\u001b[1;32m     34\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mNotImplementedError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mVJP of \u001b[39m\u001b[38;5;132;01m{}\u001b[39;00m\u001b[38;5;124m wrt argnums \u001b[39m\u001b[38;5;132;01m{}\u001b[39;00m\u001b[38;5;124m not defined\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m     35\u001b[0m                               \u001b[38;5;241m.\u001b[39mformat(fun_name, parent_argnums))\n\u001b[0;32m---> 36\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mvjp \u001b[38;5;241m=\u001b[39m \u001b[43mvjpmaker\u001b[49m\u001b[43m(\u001b[49m\u001b[43mparent_argnums\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mvalue\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:56\u001b[0m, in \u001b[0;36mdefvjp..vjp_argnums\u001b[0;34m(argnums, ans, args, kwargs)\u001b[0m\n\u001b[1;32m     53\u001b[0m argnums \u001b[38;5;241m=\u001b[39m kwargs\u001b[38;5;241m.\u001b[39mget(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124margnums\u001b[39m\u001b[38;5;124m'\u001b[39m, count())\n\u001b[1;32m     54\u001b[0m vjps_dict \u001b[38;5;241m=\u001b[39m {argnum : translate_vjp(vjpmaker, fun, argnum)\n\u001b[1;32m     55\u001b[0m              \u001b[38;5;28;01mfor\u001b[39;00m argnum, vjpmaker \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mzip\u001b[39m(argnums, vjpmakers)}\n\u001b[0;32m---> 56\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mvjp_argnums\u001b[39m(argnums, ans, args, kwargs):\n\u001b[1;32m     57\u001b[0m     L \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mlen\u001b[39m(argnums)\n\u001b[1;32m     58\u001b[0m     \u001b[38;5;66;03m# These first two cases are just optimizations\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:77\u001b[0m, in \u001b[0;36mdefvjp..vjp_argnums\u001b[0;34m(argnums, ans, args, kwargs)\u001b[0m\n\u001b[1;32m     74\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mNotImplementedError\u001b[39;00m(\n\u001b[1;32m     75\u001b[0m             \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mVJP of \u001b[39m\u001b[38;5;132;01m{}\u001b[39;00m\u001b[38;5;124m wrt argnums 0, 1 not defined\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;241m.\u001b[39mformat(fun\u001b[38;5;241m.\u001b[39m\u001b[38;5;18m__name__\u001b[39m))\n\u001b[1;32m     76\u001b[0m     vjp_0 \u001b[38;5;241m=\u001b[39m vjp_0_fun(ans, \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[0;32m---> 77\u001b[0m     vjp_1 \u001b[38;5;241m=\u001b[39m \u001b[43mvjp_1_fun\u001b[49m\u001b[43m(\u001b[49m\u001b[43mans\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     78\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;01mlambda\u001b[39;00m g: (vjp_0(g), vjp_1(g))\n\u001b[1;32m     79\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n",
+      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:422\u001b[0m, in \u001b[0;36mmatmul_vjp_1\u001b[0;34m(ans, A, B)\u001b[0m\n\u001b[1;32m    420\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mmatmul_vjp_1\u001b[39m(ans, A, B):\n\u001b[1;32m    421\u001b[0m     A_ndim \u001b[38;5;241m=\u001b[39m anp\u001b[38;5;241m.\u001b[39mndim(A)\n\u001b[0;32m--> 422\u001b[0m     B_meta \u001b[38;5;241m=\u001b[39m \u001b[43manp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mmetadata\u001b[49m\u001b[43m(\u001b[49m\u001b[43mB\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    423\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;01mlambda\u001b[39;00m g: matmul_adjoint_1(A, g, A_ndim, B_meta)\n",
+      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:61\u001b[0m, in \u001b[0;36mnotrace_primitive..f_wrapped\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m     58\u001b[0m \u001b[38;5;129m@wraps\u001b[39m(f_raw)\n\u001b[1;32m     59\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mf_wrapped\u001b[39m(\u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs):\n\u001b[1;32m     60\u001b[0m     argvals \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mmap\u001b[39m(getval, args)\n\u001b[0;32m---> 61\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mf_raw\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margvals\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
+      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_wrapper.py:148\u001b[0m, in \u001b[0;36mmetadata\u001b[0;34m(A)\u001b[0m\n\u001b[1;32m    146\u001b[0m \u001b[38;5;129m@notrace_primitive\u001b[39m\n\u001b[1;32m    147\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mmetadata\u001b[39m(A):\n\u001b[0;32m--> 148\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m _np\u001b[38;5;241m.\u001b[39mshape(A), _np\u001b[38;5;241m.\u001b[39mndim(A), _np\u001b[38;5;241m.\u001b[39mresult_type(A), _np\u001b[38;5;241m.\u001b[39miscomplexobj(A)\n",
       "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
      ]
     }
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter1_144_0.png b/doc/LectureNotes/_build/jupyter_execute/chapter1_144_0.png
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diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter2.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter2.ipynb
index f2170c67a..38a0fb505 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter2.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter2.ipynb
@@ -1798,10 +1798,10 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0.01354598394614281\n",
-      "4.037503978471253\n",
-      "[[0.95927495 2.85834701]\n",
-      " [2.85834701 9.70233292]]\n"
+      "0.003788445263115483\n",
+      "3.859628021353642\n",
+      "[[0.93725291 2.8143782 ]\n",
+      " [2.8143782  9.64008343]]\n"
      ]
     }
    ],
@@ -1845,10 +1845,10 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0.09309965420717024\n",
-      "1.6546329613199204\n",
-      "[[1.         0.57867898]\n",
-      " [0.57867898 1.        ]]\n"
+      "0.07783152589039466\n",
+      "2.06282378894371\n",
+      "[[1.         0.66124684]\n",
+      " [0.66124684 1.        ]]\n"
      ]
     }
    ],
@@ -1905,30 +1905,30 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[[-0.49352496 -2.38394242]\n",
-      " [ 0.18849928  0.73454039]\n",
-      " [-1.58104393 -5.16350368]\n",
-      " [ 0.34695383  0.23472346]\n",
-      " [ 0.95953339  2.95819409]\n",
-      " [ 1.31331481  3.59914165]\n",
-      " [ 0.14846308  1.1180677 ]\n",
-      " [ 0.26022531  0.23496851]\n",
-      " [-0.12178678 -0.11868087]\n",
-      " [-1.02063403 -1.21350883]]\n",
+      "[[-0.15499979 -0.6924788 ]\n",
+      " [-0.50456256 -2.98248681]\n",
+      " [ 1.97264311  4.4533029 ]\n",
+      " [ 0.03286166 -0.27108228]\n",
+      " [-0.97421755 -3.08891672]\n",
+      " [-0.3744637   0.62223681]\n",
+      " [ 1.18655084  4.67392051]\n",
+      " [-0.51719273 -1.14648903]\n",
+      " [-0.51793145 -1.51975002]\n",
+      " [-0.14868784 -0.04825655]]\n",
       "          0         1\n",
-      "0 -0.493525 -2.383942\n",
-      "1  0.188499  0.734540\n",
-      "2 -1.581044 -5.163504\n",
-      "3  0.346954  0.234723\n",
-      "4  0.959533  2.958194\n",
-      "5  1.313315  3.599142\n",
-      "6  0.148463  1.118068\n",
-      "7  0.260225  0.234969\n",
-      "8 -0.121787 -0.118681\n",
-      "9 -1.020634 -1.213509\n",
+      "0 -0.155000 -0.692479\n",
+      "1 -0.504563 -2.982487\n",
+      "2  1.972643  4.453303\n",
+      "3  0.032862 -0.271082\n",
+      "4 -0.974218 -3.088917\n",
+      "5 -0.374464  0.622237\n",
+      "6  1.186551  4.673921\n",
+      "7 -0.517193 -1.146489\n",
+      "8 -0.517931 -1.519750\n",
+      "9 -0.148688 -0.048257\n",
       "          0         1\n",
-      "0  1.000000  0.949087\n",
-      "1  0.949087  1.000000\n"
+      "0  1.000000  0.929612\n",
+      "1  0.929612  1.000000\n"
      ]
     }
    ],
@@ -1974,37 +1974,37 @@
      "text": [
       "     0         1         2         3         4         5         6         7   \\\n",
       "0   0.0  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000   \n",
-      "1   0.0  0.072254  0.074732  0.075050  0.075400  0.075727  0.068297  0.068215   \n",
-      "2   0.0  0.074732  0.078265  0.076259  0.077107  0.077954  0.068418  0.068622   \n",
-      "3   0.0  0.075050  0.076259  0.082604  0.082322  0.081988  0.078133  0.077663   \n",
-      "4   0.0  0.075400  0.077107  0.082322  0.082315  0.082269  0.077387  0.077091   \n",
-      "5   0.0  0.075727  0.077954  0.081988  0.082269  0.082525  0.076570  0.076454   \n",
-      "6   0.0  0.068297  0.068418  0.078133  0.077387  0.076570  0.075952  0.075224   \n",
-      "7   0.0  0.068215  0.068622  0.077663  0.077091  0.076454  0.075224  0.074613   \n",
-      "8   0.0  0.068168  0.068876  0.077210  0.076818  0.076371  0.074495  0.074004   \n",
-      "9   0.0  0.068163  0.069190  0.076775  0.076573  0.076324  0.073764  0.073398   \n",
-      "10  0.0  0.060924  0.060401  0.071600  0.070601  0.069522  0.071006  0.070141   \n",
-      "11  0.0  0.060711  0.060369  0.071122  0.070241  0.069283  0.070364  0.069583   \n",
-      "12  0.0  0.060534  0.060381  0.070671  0.069911  0.069080  0.069738  0.069042   \n",
-      "13  0.0  0.060394  0.060441  0.070245  0.069612  0.068912  0.069125  0.068517   \n",
-      "14  0.0  0.060291  0.060550  0.069845  0.069343  0.068782  0.068524  0.068007   \n",
+      "1   0.0  0.079729  0.074983  0.077280  0.078995  0.080168  0.068546  0.070577   \n",
+      "2   0.0  0.074983  0.071314  0.073127  0.075035  0.076519  0.065106  0.067183   \n",
+      "3   0.0  0.077280  0.073127  0.080979  0.082487  0.083517  0.075422  0.077387   \n",
+      "4   0.0  0.078995  0.075035  0.082487  0.084199  0.085447  0.076612  0.078725   \n",
+      "5   0.0  0.080168  0.076519  0.083517  0.085447  0.086942  0.077411  0.079671   \n",
+      "6   0.0  0.068546  0.065106  0.075422  0.076612  0.077411  0.072522  0.074203   \n",
+      "7   0.0  0.070577  0.067183  0.077387  0.078725  0.079671  0.074203  0.076007   \n",
+      "8   0.0  0.072638  0.069315  0.079368  0.080867  0.081977  0.075887  0.077825   \n",
+      "9   0.0  0.074671  0.071455  0.081315  0.082991  0.084282  0.077536  0.079615   \n",
+      "10  0.0  0.060425  0.057463  0.068676  0.069583  0.070161  0.067515  0.068912   \n",
+      "11  0.0  0.062197  0.059245  0.070486  0.071501  0.072183  0.069129  0.070625   \n",
+      "12  0.0  0.064048  0.061113  0.072365  0.073497  0.074293  0.070797  0.072398   \n",
+      "13  0.0  0.065974  0.063066  0.074310  0.075569  0.076491  0.072515  0.074230   \n",
+      "14  0.0  0.067967  0.065101  0.076313  0.077711  0.078771  0.074276  0.076112   \n",
       "\n",
       "          8         9         10        11        12        13        14  \n",
       "0   0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  \n",
-      "1   0.068168  0.068163  0.060924  0.060711  0.060534  0.060394  0.060291  \n",
-      "2   0.068876  0.069190  0.060401  0.060369  0.060381  0.060441  0.060550  \n",
-      "3   0.077210  0.076775  0.071600  0.071122  0.070671  0.070245  0.069845  \n",
-      "4   0.076818  0.076573  0.070601  0.070241  0.069911  0.069612  0.069343  \n",
-      "5   0.076371  0.076324  0.069522  0.069283  0.069080  0.068912  0.068782  \n",
-      "6   0.074495  0.073764  0.071006  0.070364  0.069738  0.069125  0.068524  \n",
-      "7   0.074004  0.073398  0.070141  0.069583  0.069042  0.068517  0.068007  \n",
-      "8   0.073520  0.073044  0.069265  0.068792  0.068339  0.067905  0.067489  \n",
-      "9   0.073044  0.072705  0.068375  0.067990  0.067628  0.067288  0.066969  \n",
-      "10  0.069265  0.068375  0.067400  0.066672  0.065952  0.065237  0.064526  \n",
-      "11  0.068792  0.067990  0.066672  0.066006  0.065350  0.064701  0.064057  \n",
-      "12  0.068339  0.067628  0.065952  0.065350  0.064759  0.064176  0.063600  \n",
-      "13  0.067905  0.067288  0.065237  0.064701  0.064176  0.063661  0.063155  \n",
-      "14  0.067489  0.066969  0.064526  0.064057  0.063600  0.063155  0.062721  \n"
+      "1   0.072638  0.074671  0.060425  0.062197  0.064048  0.065974  0.067967  \n",
+      "2   0.069315  0.071455  0.057463  0.059245  0.061113  0.063066  0.065101  \n",
+      "3   0.079368  0.081315  0.068676  0.070486  0.072365  0.074310  0.076313  \n",
+      "4   0.080867  0.082991  0.069583  0.071501  0.073497  0.075569  0.077711  \n",
+      "5   0.081977  0.084282  0.070161  0.072183  0.074293  0.076491  0.078771  \n",
+      "6   0.075887  0.077536  0.067515  0.069129  0.070797  0.072515  0.074276  \n",
+      "7   0.077825  0.079615  0.068912  0.070625  0.072398  0.074230  0.076112  \n",
+      "8   0.079786  0.081728  0.070305  0.072122  0.074007  0.075958  0.077970  \n",
+      "9   0.081728  0.083834  0.071659  0.073585  0.075587  0.077666  0.079814  \n",
+      "10  0.070305  0.071659  0.063876  0.065268  0.066700  0.068170  0.069669  \n",
+      "11  0.072122  0.073585  0.065268  0.066742  0.068261  0.069823  0.071420  \n",
+      "12  0.074007  0.075587  0.066700  0.068261  0.069873  0.071534  0.073236  \n",
+      "13  0.075958  0.077666  0.068170  0.069823  0.071534  0.073300  0.075115  \n",
+      "14  0.077970  0.079814  0.069669  0.071420  0.073236  0.075115  0.077050  \n"
      ]
     }
    ],
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter3.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter3.ipynb
index f183f152e..91b2e9d92 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter3.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter3.ipynb
@@ -489,10 +489,10 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Runtime: 0.0907788 sec\n",
+      "Runtime: 0.101292 sec\n",
       "Jackknife Statistics :\n",
       "original           bias      std. error\n",
-      " 100.022        100.012        0.148734\n"
+      " 99.9618        99.9518        0.148771\n"
      ]
     }
    ],
@@ -917,7 +917,7 @@
      "text": [
       "Bootstrap Statistics :\n",
       "original           bias      std. error\n",
-      " 99.7522  14.9594        99.7525        0.149991\n"
+      " 99.9169   14.873        99.9169        0.147934\n"
      ]
     }
    ],
@@ -975,7 +975,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "
    "
       ]
@@ -1328,13 +1328,7 @@
       "Error: 0.021592704588021178\n",
       "Bias^2: 0.010516485576646504\n",
       "Var: 0.01107621901137467\n",
-      "0.021592704588021178 >= 0.010516485576646504 + 0.01107621901137467 = 0.021592704588021174\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
+      "0.021592704588021178 >= 0.010516485576646504 + 0.01107621901137467 = 0.021592704588021174\n",
       "Polynomial degree: 11\n",
       "Error: 0.07160048164232538\n",
       "Bias^2: 0.014436800088896381\n",
@@ -1344,7 +1338,13 @@
       "Error: 0.11547777218876518\n",
       "Bias^2: 0.016285782696017142\n",
       "Var: 0.09919198949274803\n",
-      "0.11547777218876518 >= 0.016285782696017142 + 0.09919198949274803 = 0.11547777218876518\n",
+      "0.11547777218876518 >= 0.016285782696017142 + 0.09919198949274803 = 0.11547777218876518\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
       "Polynomial degree: 13\n",
       "Error: 0.2284246870217162\n",
       "Bias^2: 0.01975416527168255\n",
@@ -1634,16 +1634,16 @@
       "Mean squared error on test data: 0.17446471\n",
       "Degree of polynomial:  13\n",
       "Mean squared error on training data: 0.00759119\n",
-      "Mean squared error on test data: 1.08131003\n",
-      "Degree of polynomial:  14\n",
-      "Mean squared error on training data: 0.00472199\n",
-      "Mean squared error on test data: 0.81333804\n"
+      "Mean squared error on test data: 1.08131003\n"
      ]
     },
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
+      "Degree of polynomial:  14\n",
+      "Mean squared error on training data: 0.00472199\n",
+      "Mean squared error on test data: 0.81333804\n",
       "Degree of polynomial:  15\n",
       "Mean squared error on training data: 0.00410478\n",
       "Mean squared error on test data: 92.09172409\n",
@@ -1685,16 +1685,16 @@
       "Mean squared error on test data: 128664.31650694\n",
       "Degree of polynomial:  26\n",
       "Mean squared error on training data: 0.00076905\n",
-      "Mean squared error on test data: 19003.94822514\n"
+      "Mean squared error on test data: 19003.94822514\n",
+      "Degree of polynomial:  27\n",
+      "Mean squared error on training data: 0.00068946\n",
+      "Mean squared error on test data: 2379.66219404\n"
      ]
     },
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Degree of polynomial:  27\n",
-      "Mean squared error on training data: 0.00068946\n",
-      "Mean squared error on test data: 2379.66219404\n",
       "Degree of polynomial:  28\n",
       "Mean squared error on training data: 0.00062595\n",
       "Mean squared error on test data: 4082.19983530\n",
@@ -1707,9 +1707,9 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16213/626635268.py:73: RuntimeWarning: divide by zero encountered in log10\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/626635268.py:73: RuntimeWarning: divide by zero encountered in log10\n",
       "  plt.plot(polynomial, np.log10(trainingerror), label='Training Error')\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16213/626635268.py:74: RuntimeWarning: divide by zero encountered in log10\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/626635268.py:74: RuntimeWarning: divide by zero encountered in log10\n",
       "  plt.plot(polynomial, np.log10(testerror), label='Test Error')\n"
      ]
     },
@@ -2051,7 +2051,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16213/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10\n",
       "  plt.plot(polynomial, np.log10(estimated_mse_sklearn), label='Test Error')\n"
      ]
     },
@@ -3725,9 +3725,9 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16213/4162706317.py:6: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/4162706317.py:6: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.\n",
       "  cb = fig.colorbar(im)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16213/4162706317.py:7: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/4162706317.py:7: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
       "  cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n"
      ]
     },
@@ -4037,9 +4037,9 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16213/3777801602.py:6: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/3777801602.py:6: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.\n",
       "  cb = fig.colorbar(im)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16213/3777801602.py:7: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/3777801602.py:7: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
       "  cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n"
      ]
     },
@@ -4116,9 +4116,9 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16213/438060758.py:9: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/438060758.py:9: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.\n",
       "  cb = fig.colorbar(im)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16213/438060758.py:10: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/438060758.py:10: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
       "  cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n"
      ]
     },
@@ -4203,9 +4203,9 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16213/3544313922.py:8: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/3544313922.py:8: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.\n",
       "  cb = fig.colorbar(im)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_16213/3544313922.py:9: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/3544313922.py:9: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
       "  cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n"
      ]
     },
@@ -4266,7 +4266,7 @@
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      "text": [
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5c0a999571dDQUDUwMFAdPHiwumHDBhVQ33nnHS2fbTTZqVOnHB7/008/VXv27KkGBQWpAQEBatu2bdUxY8Zoo9z27Nmj3n777Wrbtm3VgIAANSQkRL3iiivUuXPnavv48ccf1WHDhqktWrTQXq/XXXed+ueff2p5HI0mU1VV/fPPP9Wrr75aO36vXr3UH374wS6Ps/9D2//36tWrnVx5IdxPZqAWQog67Msvv+TOO+9k3bp19OnTp7aLI0S9JMGQEELUEV999RXHjx+nS5cuGAwGNmzYwJtvvkmPHj1q/PEeQjQk0mdICCHqiODgYBYsWMBrr71GdnY2JpOJsWPH8tprr9V20YSo16RmSAghhBANmky6KIQQQogGTYIhIYQQQjRoEgwJIYQQokGTDtQVsFqtnDhxguDgYJksTAghhPAQqqpy9uxZIiMjK5y0VIKhCpw4cYJWrVrVdjGEEEIIUQVHjx6t8GHWEgxVIDg4GCi+mI0bN67l0gghhBDCFVlZWbRq1Ur7HC+PBEMVsDWNNW7cWIIhIYQQwsO40sVFOlALIYQQokGTYEgIIYQQDZoEQ0IIIYRo0KTPkJsUFRVRUFBQ28UQHszX17fC4Z9CCCHcT4Khi6SqKqmpqWRkZNR2UYSHMxgMREdH4+vrW9tFEUKIBkWCoYtkC4SaN29OYGCgTMwoqsQ2uafZbCYqKkpeR0IIUYMkGLoIRUVFWiAUFhZW28URHq5Zs2acOHGCwsJCfHx8ars4QgjRYEgHhYtg6yMUGBhYyyUR9YGteayoqKiWSyKEEA2LBENuIE0awh3kdSSEELVDgiEhhBBCNGh1Jhj6448/uOGGG4iMjERRFJYuXWq3fuzYsSiKYvfTq1evCve7ePFiOnfujJ+fH507d2bJkiXVdAaeb8CAATz++OO1XQwhhBCiRtWZYCg7O5tu3brxv//9z2meoUOHYjabtZ+ff/653H2uX7+e0aNHc/fdd7Nt2zbuvvtubr31VjZu3Oju4jc4a9asQVEUmVJACCGEx6szo8mGDRvGsGHDys3j5+dHRESEy/ucMWMGgwcPZtKkSQBMmjSJ33//nRkzZvDVV19dVHmFEMITWSwWEhISaNu2LQcPHiQ+Ph6j0WiXvnXrVqC4tthoNNZugYWoAXWmZsgVa9asoXnz5lxyySU88MADnDx5stz869ev59prr7VLGzJkCH/99ZfTbfLy8sjKyrL7qY+ys7MZM2YMjRo1wmQy8dZbb9mtnz9/PpdddhnBwcFERERwxx13aNf78OHDDBw4EACj0YiiKIwdOxaA5cuXc+WVVxIaGkpYWBjXX389Bw8erNFzE0I4ZrFYiI2NZfDgwbRr147BgwcTGxtLcnKylt62bVtGjBjBiBEj6Ny5MxaLpbaLLUS185hgaNiwYXzxxRf89ttvvPXWW2zatImrr76avLw8p9ukpqYSHh5ulxYeHk5qaqrTbaZOnUpISIj206pVK7edQ13y1FNPsXr1apYsWcKKFStYs2YNCQkJ2vr8/HxeffVVtm3bxtKlS0lOTtYCnlatWrF48WIA9u7di9ls5p133gGKg6yJEyeyadMmfv31VwwGAzfffDNWq7XGz1EIYS8hIQGz2QygvSfNZjOLFi3S0lVV1fKnpqaSmJhY8wUVoqapdRCgLlmypNw8J06cUH18fNTFixc7zePj46N++eWXdmnz589X/fz8nG6Tm5urZmZmaj9Hjx5VATUzM7NM3pycHHXXrl1qTk5O+SfkgjNnzqgrV65Uz5w5c9H7qsjZs2dVX19fdcGCBVpaenq6GhAQoP7rX/9yuM3ff/+tAurZs2dVVVXV1atXq4BqsVjKPdbJkydVQN2xY4e7il9vufP1JIQjZ86cUU0mkwqoBoNBBdTIyEj10KFDWrqiKCqgAmpERESN3JOEqA6ZmZlOP79LqzN9hirLZDLRunVr9u/f7zRPREREmVqgkydPlqkt0vPz88PPz89t5XSFrerabDZjMplISkqq1nb6gwcPkp+fT+/evbW0Jk2a0KFDB215y5YtTJ48ma1bt3LmzBntW2RKSgqdO3cud98vvvgiGzZs4PTp03bbXXrppdV0RkIIVxiNRpKSkkhMTCQmJoZDhw4RFxdXJn3btm0A9O/fX/oMiQbBY4Oh9PR0jh49islkcpqnd+/erFy5kgkTJmhpK1asoE+fPjVRRJfpq67NZjOJiYkMGjSo2o6n6qrBHcnOzubaa6/l2muvZf78+TRr1oyUlBSGDBlCfn5+udvecMMNtGrVik8++YTIyEisViuXXnpphdsJIWqG0WjU7i/R0dEVpgvRENSZYOjcuXMcOHBAW05OTmbr1q00adKEJk2aMHnyZG655RZMJhOHDx/mueeeo2nTptx8883aNmPGjKFFixZMnToVgH/961/069ePN954g5tuuonvvvuOVatWsXbt2ho/v/LEx8djMpkwm81ERkYSFxdXrcdr164dPj4+bNiwgaioKKC4dmrfvn3079+fPXv2cPr0af7zn/9ofaY2b95stw9Hj45IT09n9+7dfPTRR1x11VUAde5aCyGEEKXVmWBo8+bN2gglgIkTJwJwzz338MEHH7Bjxw7mzZtHRkYGJpOJgQMHsnDhQoKDg7VtUlJSMBhK+oT36dOHBQsW8MILL/Diiy/Stm1bFi5cSM+ePWvuxFygr6K2VVlXp0aNGnHffffx1FNPERYWRnh4OM8//7x27aKiovD19eW9995j/Pjx7Ny5k1dffdVuH61bt0ZRFH788Ueuu+46AgICMBqNhIWF8fHHH2MymUhJSeHZZ5+t1nMRQgghLlr1d2HybOV1wPLkDq9nz55V77rrLjUwMFANDw9Xp02bpvbv31/rQP3ll1+qbdq0Uf38/NTevXur33//vQqoW7Zs0fbxyiuvqBEREaqiKOo999yjqqqqrly5Uu3UqZPq5+endu3aVV2zZo1LHeKFZ7+ehBCirqlMB2pFVSvoQNLAZWVlERISQmZmJo0bN7Zbl5ubS3JyMtHR0fj7+9dSCUV9Ia8nIYRwn/I+v0vzmHmGhBBCCCGqgwRDQgghhGjQJBgSQgghRIMmwZAQQgghGjQJhoQQQgjRoNWZeYaEEEJUXuG5QlLnppJ31PlDq91J8VFoPqo5jbo1qpHjCVETJBgSQggPduztYxx+6XCNHjN1diq9Unph8JHGBVE/yCtZCCE82Pm952v8mPmp+RRlFVWcUQgPITVDQgjhyXTT5nb6ohN+Lfyq7VCHJh0ia31W8WFlvl5Rj0jNkKiz5s6dS2hoaI0ca+zYsQwfPrxGjiVEdVE7qmwu2IwlysLmgs2oXVVC+4eidnWcrl+nTyu9zrZdQWBBycGs9se2WCysWrWK5ORkVq1ahcViqdmTF+IiSM2QaFAOHz5MdHQ0W7ZsoXv37tV6nFdffZXffvuN1NRUIiMjueuuu3j++efx9fWttuOKBkhXQTN06FC2ndqGwWDAarViMplYt24dffv2xWw226UnJSUBEBsbi9ls1tJsD4q2WCzaOtt2r/EafekLQMaZDJo3b+40b+n9CVGXSc2QENVgz549WK1WPvroI5KSknj77bf58MMPee6552q7aKK+0QVDJ0+dBMBqLa62MZvNLFq0CLPZXCY9MTGRhIQEbZ0tzUa/zrZdESX9hHZs31Fu3tL7E6Iuk2CogRowYACPPfYYjz/+OEajkfDwcD7++GOys7O59957CQ4Opm3btixbtgyAoqIi7rvvPqKjowkICKBDhw6888472v5yc3OJjY3lwQcf1NKSk5MJCQnhk08+calMc+fOJSoqisDAQG6++WbS09PL5Pnhhx+Ij4/H39+fmJgYpkyZQmFhobZeURQ++OADhg0bRkBAANHR0SxatEhbHx0dDUCPHj1QFIUBAwbY7X/69OmYTCbCwsJ49NFHKSgooCqGDh3KnDlzuPbaa4mJieHGG2/kySef5Ntvv63S/oRwRbNmzQAwGIpv7ZGRkYwaNQqTyVQmPS4ujvj4eG2dLc1Gv862nV6X2C7l5i29PyHqtAqfa9/AZWZmqoCamZlZZl1OTo66a9cuNScnpxZKdnH69++vBgcHq6+++qq6b98+9dVXX1UNBoM6bNgw9eOPP1b37dunPvzww2pYWJianZ2t5ufnqy+99JL6999/q4cOHVLnz5+vBgYGqgsXLtT2uWXLFtXX11ddsmSJWlhYqPbt21e96aabXCrPhg0bVEVR1KlTp6p79+5V33nnHTU0NFQNCQnR8ixfvlxt3LixOnfuXPXgwYPqihUr1DZt2qiTJ0/W8gBqWFiY+sknn6h79+5VX3jhBdXLy0vdtWuXqqqq+vfff6uAumrVKtVsNqvp6emqqqrqPffcozZu3FgdP368unv3bvWHH35QAwMD1Y8//ljb90MPPaQGBQWV+3PkyBGn5/j888+r8fHxTtd78utJ1J6do3eqq1mtrma1mro1VV21apV66NAhddWqVeqZM2dUVVXVM2fOOEzXr9OnlV5n227jsI3asXJScsrN62h/QtSk8j6/S1NUVYYElCcrK4uQkBAyMzNp3Lix3brc3FySk5OJjo7G39+/ZMVll0Fqas0WNCICNm92OfuAAQMoKirizz//BIprfkJCQhgxYgTz5s0DIDU1FZPJxPr16+nVq1eZfTz66KOkpaXxzTffaGlvvvkm06ZN4/bbb2fRokXs2LGDpk2bVlieO+64A4vFotVEAdx2220sX76cjIwMAPr168ewYcOYNGmSlmf+/Pk8/fTTnDhxAiiuGRo/fjwffPCBlqdXr17ExcUxc+ZMp32Gxo4dy5o1azh48CBeXl4A3HrrrRgMBhYsWADAyZMnycrKKvc82rRpg7d32a54Bw8eJC4ujrfeeov777/f4bZOX09ClCNpdBKnvj4FQM/kngS0CaiRY/U60gv/KHmdirqrvM/v0qQDdXVITYXjx2u7FBXq2rWr9reXlxdhYWF06VJS9R0eHg4UBwEAH374IbNmzeLIkSPk5OSQn59fphPyE088wXfffcd7773HsmXLXAqEAHbv3s3NN99sl9a7d2+WL1+uLSckJLBp0yb+/e9/a2lFRUXk5uZy/vx5AgMDte1K72fr1q0VliE2NlYLhABMJhM7dpT0i2jevLnWYbQyTpw4wdChQxk1apTTQEgId1AUpZoPUPKnapXv0aL+kGCoOkREeMQxfXx87JYVRbFLs91YrVYrX3/9NRMmTOCtt96id+/eBAcH8+abb7Jx40a7fZw8eZK9e/fi5eXF/v37GTp0qEtlcaWC0mq1MmXKFEaMGFFmXUU1Ka58SDi6HrbOoADjx49n/vz55e5j165dREVFacsnTpxg4MCB9O7dm48//rjCMghRafq3TnXHQgbdAazO8wnhaSQYqg6VaK7yFH/++Sd9+vThkUce0dIOHjxYJt+4ceO49NJLeeCBB7jvvvsYNGgQnTt3rnD/nTt3ZsOGDXZppZfj4uLYu3cv7dq1K3dfGzZsYMyYMXbLPXr0ANCGtRcVVX723FdeeYUnn3yy3DyRkZHa38ePH2fgwIHEx8czZ84ch51QhaiMQmshm45vIr8oX0tTz5VEQxuObkCxVl9EpJ4vOdbGlI32wZEDjXwbEWeKq/4aKyEukgRDwiXt2rVj3rx5/PLLL0RHR/P555+zadMmbXQWwPvvv8/69evZvn07rVq1YtmyZdx5551s3Lixwrl1/vnPf9KnTx+mTZvG8OHDWbFihV0TGcBLL73E9ddfT6tWrRg1ahQGg4Ht27ezY8cOXnvtNS3fokWLuOyyy7jyyiv54osv+Pvvv5k9ezZQ3NQVEBDA8uXLadmyJf7+/oSEhLh0DSrTTHbixAkGDBhAVFQU06dP59SpU9q6iNqoORT1wqB5g/jjyB92aS8feZkBDADg1sW3cirklIMt3WNS8iSu5VoA7vr2Lo6HVdwd4IG4B/j4BqkVFXWbfFUVLhk/fjwjRoxg9OjR9OzZk/T0dLtaoj179vDUU08xc+ZMWrVqBRQHRxkZGbz44osV7r9Xr17MmjWL9957j+7du7NixQpeeOEFuzxDhgzhxx9/ZOXKlVx++eX06tWL//73v7Ru3dou35QpU1iwYAFdu3bls88+44svvtBqp7y9vXn33Xf56KOPiIyM5KabbrrYS+PQihUrOHDgAL/99hstW7bEZDJpP0JUxbn8c2UCIQBFLal1UanefjyqUrJ/g+rax8fP+3+uruII4TYymqwCVRpNJmqNoigsWbLEIx+tIa8nUZ6zeWdp/J/ie1DrkNaMjh0NQI9XehCxtri2cfUXq8ltllttZegyvQstV7QE4I9Zf5Adle007webP+Bs/llMjUyceOJEtZVJCGdkNJkQQtQz+lqfS8Iu4Y3BbwCw88OdnOY0AM/1f65aH9S6Z8EeUimeNuSJ3k8Q1DnIad4FSQs4m3+22murhHAHaSYTNWLYsGE0atTI4c/rr79e28UTwnPVZKxRiaH1yoXM0vggPIHUDIkaMWvWLHJychyua9KkiduOIzde0aDVoaH1thFkUjMkPIEEQ6JGtGjRoraLIIRH0wf6dkPVa3CeIX1bwtlNZym0FDrN2uFAB3zzfbG0tVRzoYS4eBIMCSGEB6vJ2lB9ELb3/r3l5n2WZwFYdcUqeLpaiyXERZM+Q0II4QH0zU2Ksyqgaq4ZCuwYWOlteuzpUQ0lEcK9pGZICCE8ma5i6M8//yT+mniMRiMAFouFhIQE4uNL0i6G6UETBn8Dll0W0lLTCI8ofn6h7W/9lBD73tlHQF6A3TxIpbm7fEJUlQRDQgjhYZz1Gbr11lvxN/mTlJQEFD982Gw2YzKZSEpKuuiAwyvAi4BbA7gs9jLMZjPh4eEoikJqaqrdMSwWC1kfZBGQFwDW4qCn9LEtFovbyydEVUkzmRBCeABX+gapqJjNZhITE0lISMBsNgNoae6g329aWhqpqalljpGQkFDSrKfi8NjVVT4hqkKCIVFnzZ07l9DQ0Bo51tixYz1y1moh9DVDKiqRkZHExcURHx+vPf7FluYO+v1GRERoz9rTHyM+Pl57dIeC4vDY1VU+IapCgiHRoBw+fBhFUdi6dWu1H6tNmzYoimL38+yzz1b7cUX95EoH6sXfLGbnzp0YjUaMRiNJSUmsWrVKS3MH/X537drFrl27yhzDaDTi7VPcC8OAweGxq6t8QlSF9BkSohq98sorPPDAA9pyo0aNarE0oj7SN59d1f8qfI2+2rLRaGTQoEFuP2bp/To6hr5myNX9CFFbpGaogRowYACPPfYYjz/+OEajkfDwcD7++GOys7O59957CQ4Opm3btixbtgyAoqIi7rvvPqKjowkICKBDhw6888472v5yc3OJjY3lwQcf1NKSk5MJCQnhk08+calMc+fOJSoqisDAQG6++WbS09PL5Pnhhx+Ij4/H39+fmJgYpkyZQmFhycRviqLwwQcfMGzYMAICAoiOjmbRokXa+ujoaAB69OiBoigMGDDAbv/Tp0/HZDIRFhbGo48+SkFBgUtldyY4OFhrSoiIiJBgSLiFsw7Udum1zVYUmYBaeIA6Ewz98ccf3HDDDURGRqIoCkuXLtXWFRQU8Mwzz9ClSxeCgoKIjIxkzJgxnDhR/pOQ586dW6aZQlEUcnOr76nOnuSzzz6jadOm/P333zz22GM8/PDDjBo1ij59+pCYmMiQIUO4++67OX/+PFarlZYtW/L111+za9cuXnrpJZ577jm+/vprAPz9/fniiy/47LPPWLp0KUVFRdx9990MHDjQrmbEmY0bNzJu3DgeeeQRtm7dysCBA3nttdfs8vzyyy/cdddd/POf/2TXrl189NFHzJ07l3//+992+V588UVuueUWtm3bxl133cXtt9/O7t27Afj7778BWLVqFWazmW+//VbbbvXq1Rw8eJDVq1fz2WefMXfuXObOnautHz9+vNPnq9l+UlJS7MryxhtvEBYWRvfu3fn3v/9Nfn6+6/9BQuh43KNmFNuvOhSgCeGEotaRd9iyZctYt24dcXFx3HLLLSxZskTr0JqZmcnIkSN54IEH6NatGxaLhccff5zCwkI2b97sdJ9z587lX//6F3v32s+Uauvw54qsrCxCQkLIzMykcePGdutyc3NJTk4mOjrabn6Nyz6+jNRzqS4fwx0iGkWw+UHn16K0AQMGUFRUxJ9//gkU1/yEhIQwYsQI5s2bB6ANl12/fj29evUqs49HH32UtLQ0vvnmGy3tzTffZNq0adx+++0sWrSIHTt20LRp0wrLc8cdd2CxWLSaKIDbbruN5cuXk5GRAUC/fv0YNmwYkyZN0vLMnz+fp59+WguMFUVh/PjxfPDBB1qeXr16ERcXx8yZMzl8+DDR0dFs2bKF7t27a3nGjh3LmjVrOHjwIF5eXkDxMGWDwcCCBQsAOHnyJFlZWeWeR5s2bfD2Lm59fvvtt4mLi8NoNPL3338zadIkbrrpJmbNmuVwW2evJyEA0s+n0/TN4vfSde2v46c7fgJg+3XbObPsDAB90/vi08Sn1sqotzB8IeEnwznnf47rc66v7eKIBqi8z+/S6kyfoWHDhjFs2DCH60JCQli5cqVd2nvvvccVV1xBSkoKUVFRTverKEqlgh93SD2XyvGzx2v0mFXRtWtX7W8vLy/CwsLo0qWLlhYeXjyh2smTJwH48MMPmTVrFkeOHCEnJ4f8/Hy7gALgiSee4LvvvuO9995j2bJlLgVCALt37+bmm2+2S+vduzfLly/XlhMSEti0aZNdTVBRURG5ubmcP3+ewMBAbbvS+3Glw3RsbKwWCAGYTCZ27NihLTdv3pzmzZu7dD4AEyZM0P7u2rUrRqORkSNHarVFQlSVXW1LTT6brBK0PkPlTLooRF1RZ4KhysrMzERRlAqHXp87d47WrVtTVFRE9+7defXVV+nRo3qnh49oVLPBV1WP6eNj/w1SURS7NFv/A6vVytdff82ECRN466236N27N8HBwbz55pts3LjRbh8nT55k7969eHl5sX//foYOHepSWVypoLRarUyZMoURI0aUWVdRTYorfSkcXQ+rteTR3OPHj2f+/Pnl7mPXrl1Og3Nb7dqBAwckGBKV5nFPf5dmMuFBPDIYys3N5dlnn+WOO+4ot+qrY8eOzJ07ly5dupCVlcU777xD37592bZtG+3bt3e4TV5eHnl5edpyRc0ijlSmucpT/Pnnn/Tp04dHHnlESzt48GCZfOPGjePSSy/lgQce4L777mPQoEF07ty5wv137tyZDRs22KWVXo6Li2Pv3r20a9eu3H1t2LCBMWPG2C3bAmBf3+KRNkVFRRWWqbRXXnmFJ598stw8kZGRTtdt2bIFQJtbRYiq0gf3dl8k6lDcYasZ8rQYTjRMHhcMFRQUcNttt2G1Wpk5c2a5eXv16mXX16Vv377ExcXx3nvv8e677zrcZurUqUyZMsWtZa4P2rVrx7x58/jll1+Ijo7m888/Z9OmTdroLID333+f9evXs337dlq1asWyZcu488472bhxoxaEOPPPf/6TPn36MG3aNIYPH86KFSvsmsgAXnrpJa6//npatWrFqFGjMBgMbN++nR07dth1tl60aBGXXXYZV155JV988QV///03s2fPBoqbugICAli+fDktW7bE39+fkJAQl65BZZrJ1q9fz4YNGxg4cCAhISFs2rSJCRMmcOONN5bbrCuEM67UntbF0WRSMyQ8QZ0ZTeaKgoICbr31VpKTk1m5cmWFHaJKMxgMXH755ezfv99pnkmTJpGZman9HD169GKLXS+MHz+eESNGMHr0aHr27El6erpdLdGePXt46qmnmDlzJq1atQKKg6OMjAxefPHFCvffq1cvZs2axXvvvUf37t1ZsWIFL7zwgl2eIUOG8OOPP7Jy5Uouv/xyevXqxX//+19at25tl2/KlCksWLCArl278tlnn/HFF19otVPe3t68++67fPTRR0RGRnLTTTdd7KVxyM/Pj4ULFzJgwAA6d+7MSy+9xAMPPMBXX31VLccTDVhdr3mp6+UTgjo0mkxPURS70WRQEgjt37+f1atX06xZs0rvV1VVrrjiCrp06cKnn37q0jZVGU0mao+j146nkNeTKM+p7FM0n15cM3nDJTfw/e3fA7Dt2m1YVloAuDLzSrwb140K/y9bfknk8UhyfXIZmu9a30Eh3MkjR5OdO3eOAwcOaMvJycls3bqVJk2aEBkZyciRI0lMTOTHH3+kqKhIezhgkyZNtCaYMWPG0KJFC6ZOnQoU1xD06tWL9u3bk5WVxbvvvsvWrVt5//33a/4EhRDiIrjUgboOtUjJaDLhSepMMLR582YGDhyoLU+cOBGAe+65h8mTJ/P998XfgkoP5V69erU2i3BKSgoGQ0nLX0ZGBg8++CCpqamEhITQo0cP/vjjD6644orqPRlRxrBhw7Q5jUp77rnneO6552q4REJ4LmczUNcptj5DEgwJD1BngqEBAwaU20HQlda8NWvW2C2//fbbvP322xdbNOEGs2bNIicnx+G6Jk2auO04dbDVVwi3cPbarqujyWwkGBKeoM4EQ6J+a9GiRW0XQQhRg1x5UKsQdYUEQ0II4WH0AUZhgf2DimuKxWIhISGB+Ph4jEZj2Qy6ZrJDhw5x6NAh4uPjUbYrpK1O49ixY7Rs2RKAY8eOERYWRnp6Oi1btiQgIICcnJyS9Ox0ujzWheYdXJ8BXojKkGBICCE8gKMO1BaLhY0bNhJLLFDcTzIsqPpnN7dYLMTGxmI2mzGZTCQlJZUJiPTlbde+HapV5YqmV/DG6TcA8MILM2bt7wwy7NJKpy/+ZDG3pd7mOPAS4iJ51DxDQgghSmqAEhISyMsvmTHflWfwuUNCQgJmc3HQYjabSUxMLJOnyFo8y7uiKlq/ppDTrk1w6kjL/JYOjyOEO0jNkBBCeABHHajj4+PZ67sX8ouXu/foXiNliY+Px2QyYTabiYyMJC4urkweg3fxd20DBpRGCmqhWlxrdbp4/Xde37GvyT6g5FmTqqpiDDXywgsv8Oqrr5KRmcG/Cv5FM7UZBoOBTl071cj5iYZHgiEhhPBQRqORK664guy12QCENgmtseMmJSWRmJhIXFxcuX2GANSJKiiQvTkbfixO23P9Hpb3WF52O+DHMz/Co8V/3/+/+2l2uhl4wyWfXMKcm+YwKnaUm89INHTSTCbqrLlz5xIaGlojxxo7dqxHzlotGiZ9B2pvr9r5Tms0Ghk0aJDTPjy+3iXPI7QNr/cq8tLSCg2FZbZxxDYqzaAayC7I5tOtrj09QIjKkJoh0aAcPnyY6OhotmzZUmYCT3das2aN3SSien///TeXX355tR1b1E9OZ6DWTzNUhx7U2iqkFQUUAPBQ4UOoBpUOhR209V1bdMWvvV+F+2nk3wgoCajyi/KrobSioZNgSIhq0KdPH62Dqc2LL77IqlWruOyyy2qpVKK+cBr01J1YiADfAC0YGv366DLrn736WZrdXPEzJjdN20T20WytNkwmVhXVQZrJGqgBAwbw2GOP8fjjj2M0GgkPD+fjjz8mOzube++9l+DgYNq2bcuyZcsAKCoq4r777iM6OpqAgAA6dOjAO++8o+0vNzeX2NhYHnzwQS0tOTmZkJAQPvnkE5fKNHfuXKKioggMDOTmm28mPT29TJ4ffviB+Ph4/P39iYmJYcqUKRQW2s+z8sEHHzBs2DACAgKIjo5m0aJF2vro6GgAevTogaIo2qNcbKZPn47JZCIsLIxHH32UgoICl8pemq+vLxEREdpPWFgY33//PePGjatT396F53AaBNTR2CCwY+BFrbexvV9sNUMuPaNNiEqSmqEG7LPPPuPpp5/m77//ZuHChTz88MMsXbqUm2++meeee463336bu+++m5SUFHx8fGjZsiVff/01TZs25a+//uLBBx/EZDJx66234u/vzxdffEHPnj257rrruOGGG7j77rsZOHAgDzzwQIVl2bhxI+PGjeP1119nxIgRLF++nJdfftkuzy+//MJdd93Fu+++y1VXXcXBgwe14Euf98UXX+Q///kP77zzDp9//jm33347l156KZ06deLvv//miiuuYNWqVcTGxmoP+YXi59yZTCZWr17NgQMHGD16NN27d9fKP378eObPn1/ueezatYuoqKgy6d9//z2nT59m7NixFV4LISpkhZzkHFDBmmMtSa9DcXbbN9oS2DGQglNlv1CEDgglqFOQazu68JXdoBb/ITVDojooqryyypWVlUVISAiZmZk0btzYbl1ubi7JyclER0fj7++vpW++bDP5qTXbru0b4ctlm11vfhkwYABFRUXaw1OLiooICQlhxIgRzJs3D4DU1FRMJhPr16+nV69eZfbx6KOPkpaWxjfffKOlvfnmm0ybNo3bb7+dRYsWsWPHDpo2bVphee644w4sFotWEwVw2223sXz5cjIyMgDo168fw4YNY9KkSVqe+fPn8/TTT3PixAmg+Fvk+PHj+eCDD7Q8vXr1Ii4ujpkzZzrtMzR27FjWrFnDwYMH8fIq7uR56623YjAYWLBgAQAnT54kKyur3PNo06YN3t5lv2Ncd911APz8889Ot3X2ehIC4HjWcVq+3RKfQh8WzFlAk+Nln+nXr6CfNqS9vki4PIGzm89SpBRxzcvXcFXUVfxx7x+1XSzhAcr7/C5NaoaqQX5qPvnH634nv65du2p/e3l5ERYWRpcuXbS08PBwoDgIAPjwww+ZNWsWR44cIScnh/z8/DKdkJ944gm+++473nvvPZYtW+ZSIASwe/dubr75Zru03r17s3x5ydDbhIQENm3axL///W8traioiNzcXM6fP09gYKC2Xen9uDIZXWxsrBYIAZhMJnbs2KEtN2/enObNK/84gGPHjvHLL7/w9ddfV3pbIWxszUMdjndwGAj5mnxRDHWoashdLsR20kwmqpMEQ9XAN8K34kx14Jg+Pj52y4qi2KXZ2uqtVitff/01EyZM4K233qJ3794EBwfz5ptvsnHjRrt9nDx5kr179+Ll5cX+/fsZOnSoS2VxpYLSarUyZcoURowYUWZdRTUprvTTcXQ9rNaSJoiqNpPNmTOHsLAwbrzxxgrLIERFvKwlAXtgp0Aa9WiEwc9AxLiI+hkMXTglAwZQpZlMVA8JhqpBZZqrPMWff/5Jnz59eOSRR7S0gwcPlsk3btw4Lr30Uh544AHuu+8+Bg0aROfOnSvcf+fOndmwYYNdWunluLg49u7dS7t27crd14YNGxgzZozdco8ePQC0PkJFRUUVlqm0V155hSeffLLcPJGRkXbLqqoyZ84cxowZUybYEqIybEGAfo6hpjc1JWZqTG0VqUboAzxFVaRmSFQLCYaES9q1a8e8efP45ZdfiI6O5vPPP2fTpk3a6CyA999/n/Xr17N9+3ZatWrFsmXLuPPOO9m4caNdR2VH/vnPf9KnTx+mTZvG8OHDWbFihV0TGcBLL73E9ddfT6tWrRg1ahQGg4Ht27ezY8cOXnvtNS3fokWLuOyyy7jyyiv54osv+Pvvv5k9ezZQ3NQVEBDA8uXLadmyJf7+/oSEuPa8pKo0k/32228kJydz3333VWo7IZyxdSQG6lSH6Wpjd7qK1AyJalG/etqJajN+/HhGjBjB6NGj6dmzJ+np6Xa1RHv27OGpp55i5syZtGrVCigOjjIyMnjxxRcr3H+vXr2YNWsW7733Ht27d2fFihW88MILdnmGDBnCjz/+yMqVK7n88svp1asX//3vf2ndurVdvilTprBgwQK6du3KZ599xhdffKHVTnl7e/Puu+/y0UcfERkZyU033XSxl6Zcs2fPpk+fPnTqJM9UEm6ijwUaQDAkNUOiJshosgpUZTSZqD2KorBkyRKPfLSGvJ5EeVIyU2g9ozXxB+OZ/vl0AFq/0JroV6Mr2NKzbem/hcw/MgG49oVriWsdx4b7N1SwlRCVG00mNUNCCOFBbKOqihdqrxw1xa5TuCqjyUT1kGBI1Ihhw4bRqFEjhz+vv/56bRdPCI+h70DdEIIh/aeUQTVInyFRLaQDtagRs2bNIicnx+G6Jk3KzplSVXKjFPWV9trWvcSTk5MJtYQ6fXJ8XWOxWEhISCA+Pt5pmcvk0QV80+ZP49d7ftWW80/nc+BfBzibdJbzReeJfjaaNne2cflYQthIMCRqRIsWLWq7CELUC/qaoc8+/4y7Vt1FUlJSnf/At1gsxMbGYjabMZlMDsvsKI/Vt2Sur64pXbH+ZIVXipfTPk/j5JfFk8IqKGy6ZxMh1xWPDq3oWELoSTOZEEJ4AFtfGbuh9YDZbCYxMbE2ilQpCQkJmM1mwHmZHeWx9LeQSaaWxy/LT/u7IN3+uWeNihqRmJjo0rGE0JNgyA30sxQLUVXSxCdconuZWLESGRlJXFxc7ZXHRfHx8ZhMJgCnZXaUJ+7BOP4Z8U8tj7eia9Aodev1wou4uDiXjiWEnjSTXQRfX18MBgMnTpygWbNm+Pr6uvTYByFKU1WVU6dOlXkkihCl6ZvJ7r33Xt59612PaAIyGo0kJSWRmJhIXFycwzI7y5O4JZEdpuLnBOrPX7Xaf4Hw8/XTtqnoWELoSTB0EQwGA9HR0ZjNZu2p6UJUlaIotGzZ0u5hsULYaI/j0A2tb9uurUd90BuNRgYNGlTpPMYw3Tnq459SlalqUUmCK8cSwkaCoYvk6+tLVFQUhYWFVXrelRA2Pj4+EgiJCjW4ofWUnYVaU7qHgvRYEFUkwZAb2Jo2pHlDCFFdtMkGG9jjOAC781SszpvJbE+1l+4KorKkA7UQQngQfc1Qg/nQ1wdD5dUMOUsTogISDAkhhAexG1rfQO7giqJgVYqjHH0w5GgEZpnaIiFc0EDeSkII4dkczUDdYJrJAFUp24FcaoaEu0gwJIQQHqRBNpNR0mfKrmbIQS2Q1AyJqpBgSAghPICjYKAh1gzZ1Yw5qAXSD68XwlUSDAkhhAdpiEPrAYd9hkrPM1ScsWbKI+oXGVovhBCepIH2GbKda0FhAfEfxwMwMmkkveltl+3r2K8pMhSV3fYGuPu9u2ugoMITSTAkhBAeQJuBWt9nyNBwoiGtA7VVIdFc/ODVgdkDy+SLPBbpcHvr/6ykPJZC1CVR1VdI4bHqTDPZH3/8wQ033EBkZCSKorB06VK79aqqMnnyZCIjIwkICGDAgAEkJSVVuN/FixfTuXNn/Pz86Ny5M0uWLKmmMxBCiOpnN7S+4cRC2qS2Bgz4GHzwMfjgXer7fIFXQZkf64V2MwMGLGmWGi+38Ax1JhjKzs6mW7du/O9//3O4ftq0afz3v//lf//7H5s2bSIiIoLBgwdz9uxZp/tcv349o0eP5u6772bbtm3cfffd3HrrrWzcuLG6TkMIIapFg56BGvD19gWgU1gn8l/MJ//FfMZ2G6utv3zX5QwuHFzm5+A1B0t2In2rhRN1ppls2LBhDBs2zOE6VVWZMWMGzz//PCNGjADgs88+Izw8nC+//JKHHnrI4XYzZsxg8ODBTJo0CYBJkybx+++/M2PGDL766qvqOREhPJzFYiEhIYH4+OJ+Gba/nT0QVJ+/dB7burZt23Lw4EGnv8vbf3nHKO/YVeVon9ZCKyd3nGTnzp1ERUWxe9duADp17kRKSgpRUVGkpKQQNySOJs2buOWYpdNtmmc11/5uSEPrbeeanZHNvt/3kZKSQuMTjbX1WVlZrF+1vsxrqsha0n/I0SSNQkAdCobKk5ycTGpqKtdee62W5ufnR//+/fnrr7+cBkPr169nwoQJdmlDhgxhxowZTo+Vl5dHXl6etpyVlXVxhRfCg1gsFmJjYzGbzYSHh6MoCqmpqZhMJpKSkhwGO7b8pfPo1xkMBqxWq9PfzvZf3jHKO7Y7zt+2z2CvYDZeupGCowV4480JThBCCAAnOKGleePNGsMartp7Fc3aNbuoYzo6v+/WfsdLi15iYFJJP5nzOecv6nw9idZnKFXhxIDi632ekvO/7vrr2Hp6q91rat26dSQfTqYjHQE4d/ZcrZRd1H11ppmsPKmpqQCEh4fbpYeHh2vrnG1X2W2mTp1KSEiI9tOqVauLKLkQniUhIQGz2QxAWlqa9l4xm80kJiaWm790Hv06q9Va7m9n+y/vGOUdu6oc7TNjdQYFRwtc2r6JtQk75u646GM6St+VsMsuEAJIyUup1LE8WWGTQqfr8snnwOkDgP1ratGiRRQWlmx38NBBh9sL4RHBkE3pKmFXnk5c2W0mTZpEZmam9nP06NGqF1gIDxMfH4/JZAIgIiKCiIgIACIjI4mLiys3f+k8+nUGg6Hc3872X94xyjt2VTnapzW/ZOKafexjlYN/e9mr5WnTqs1FH9NResdLOtpt90XjL+jxUI9Kn6OnumT2JfwW8FuZa7+CFbwT+g6NIhoB9q+pUaNG4eXjpe0jpk1MrZRd1H0e0UxmuyHbquttTp48Wabmp/R2pWuBKtrGz88PPz+/iyyxEJ7JaDSSlJREYmKi9qFs+9tRE1Tp/Po8+nUxMTEcOnTI6W9n+y/vGOUd213nbzQaOWk9qa1vN74dg58ezLZt2wDo1q0bhw4dotnaZpyZfAaAwMDAiz6mo/TU06nkkAPAwdiDTPtzmtv6SXmCFv1bMOH4BIevp6fingKwW2e7ljExMXChQigwoHL/N6LhUNQ62KNMURSWLFnC8OHDgeLanMjISCZMmMDTTz8NQH5+Ps2bN+eNN95w2mdo9OjRnD17lp9//llLGzZsGKGhoS53oM7KyiIkJITMzEwaN25c8QZCiHol7cs0dt9Z3GG63TvtaPnPlmXyHJ95nP2P7geg42cdiRgT4fZy7Nq7i5MdiwOzo5cd5e5NMoGgKz657hPaL2sPQKNfGnHZtZfVcolETanM53edqRk6d+4cBw4c0JaTk5PZunUrTZo0ISoqiscff5zXX3+d9u3b0759e15//XUCAwO54447tG3GjBlDixYtmDp1KgD/+te/6NevH2+88QY33XQT3333HatWrWLt2rU1fn5CCM+kf9aV4uWkiV3/hIhqelCofr+qoc59h6279P9lctmEE3UmGNq8eTMDB5Z0Dpw4cSIA99xzD3PnzuXpp58mJyeHRx55BIvFQs+ePVmxYgXBwcHaNikpKVp7MUCfPn1YsGABL7zwAi+++CJt27Zl4cKF9OzZs+ZOTAjh2fTPunLWy7IGPnDtHkDacEbUXzx9oFr3GkJEHVFngqEBAwaU+0JVFIXJkyczefJkp3nWrFlTJm3kyJGMHDnSDSUUQjRErtQM2Q3KqK7PW91+tSe4iwrZXSu5bMIJjxpNJoQQNU3fPOVKM1m1feDqnj0qzWSVUANNmMLzSTAkhBDl0T8A3dkdU5deXU0xdh/kcud2nfQZEi6oM81kQtQLRUXw44+gGwwgPJv6V1OgNQDKiuVw5kyZPMrGMKBN8cIvKyHztPsLcjoTuLq4TFkWeOst9x+jHlJO5wKXAKAuWwZ7/6ydgkRFwU03ga9v7RxflEuCISHcaf58GDu2tksh3EhlOPCv4oUFX8KCVQ5yDQOKp/3gm2/gmx/dX44mkdiCIdJPw5Ovu/0Y9ZHa5pGSv7/+Gk7vqr3CvPUWXBgcJOoWCYaEcKcLk/EJz5SDiRTuIJ9QLS2XSO1vxW5omV71P0peVUv2Kx2oK6P6/29cJveHOkuCISGqy2uvQYcOtV0KUQmH32tE2h/+TtcbnvwX9Hy47IrVfjCz+E/1gQfh2jHuL9yhk/DMhWOYwuHtRe4/Rn30wSE4XPyn+tB46O7+CTHLdeIE/OtfNXtMUWkSDAlRXa6+Gnr3ru1SuCR7TzbZO7NruxhuFdQpiKDYoEptk/HOeiDP4bozEWd44JJ55Ofll1kXWxjLP/gHAO8X/MXWvK0O99Hpr060TmpdqTLZeJ3zIvbC32pIEMiUIS5RFnyi/a32iINb+tRsAfbtq9njiSqRYEiIBi5zXSZbrtxS28WoFt1WdcM4yPXndx05fYQIimsORk0cRZGhZChZRmAG6gnHzVNFJ4u0YGjXyV0sO7CsTJ6oU1E8PfPpyhTfKcVbZl10lUodmmdIJn2ssyQYEsKdPPBml7k2s7aLUG0y12ZWKhgqyi8Jfk4Hn3a5i4m+D4+iOt4oIsM9zTMFXgW0v6O9W/bVIMjQeuECCYaEaOD089dEjI0g6NLKNS3VNef3nMc8ywxUfs4fQ2HxBD4FhgJSn0zFx8vHpe0sX1k4uuQoAG9c8wazH55dJk/WsiwOf3EYgLCHwwi7P6xSZbMJaRVCUDPP/j+qUTUwB1S5FKnF8wQSDAlRXTzlJqj7fDgec5y4cXEAJCQkEB8fj9FoxGKx2C0DZdIqWnbGlq9t27YcPHhQ++1oP7ZyOcpjexxPh6YdYFbZcyv3EhSpnP7+NKYUEwCFXoX45PuQmJhY5liOFPgVaH8fPXgUn1SfMttYfUpGop3MPUkjYyO2bt0KFD+OSH+u5Z3fgOgBBCHBkMt0b8Pdu3fT2dK5zGvY2WuvPK6+vu14YM1xQyHBkBANnL5m6IWXXiD5/WQURSE1NRWTycS6devo27cvZrMZk8lEUlISALGxsVpa6TyOtnH0gWGxWLT9GAwGrFar9rv0fsLDw7Vylc7Tu3dv0tLSALhcuZxpTAMg93yuS9cg7as09ty9R1su9CokNja2zLGcnYf+A/eDmR+w5MMlZbbRP+Ns9pzZLJi7QKupiIiI4K+//tLOtbzzi4iIYNeuXa5/ADd0uv+bme/P5KWPXirzGnb02nP6f43967aivMIzyKTuQjR0dv1LVdLS0khNTQXAbDazaNEizGaztpyYmEhCQoJdWuk8jrZxRL8fq9Vq97v0fvTlKp3HFigAWNWSGhjbthXJ3m4/km5L6y0Oj+XsPEr3LXK4jW6KIitWuyab1NRUu3Mt7/xSU1Odl0OUS0Fx+Bp29Nor7xqXfv2X+//hKTXEDZzUDAnhTh5WDb46eTWHDhyiLW0BULupBLUuboLJPpdNo+BGHGl3hKAbg7Tln3N/BrBLK53H0Ta//fpbmePn5uVq+VAoDswu/C69n6BGJeUqk+eGILKziwMa1aLChcFxBwoP8Ouvv1Z4Hdofbk+bC4/TmNdvHp/3/pyIzyLsaoYiIyOJi4tzuL1iKPnAU1AcbqOvgbNiRVEUu5qhUaNGMWPGDLuaisjISEaNGsV///tfu5ohZ+UQDui/8ivY/Z+YTCaHNUPl/V8DxMfHa9tWlNeOh90fGhIJhoRooA5nHGbQvEGMOTKmJBi6VCW7fUktyTnOMXPHTIgrWf7v5v8WL8Q5z+N0G0ecfI6U3k82ZedB0vLE6xIPoQVDf5/4m9lry3ZmLm38sfFaMLS57WYahTZi165dJCYmEhMTw6FDh4iLi3PeFKL78v/w+IeZ9vS0stvoaobGjx/PG0+/wbYLMxL3798fo9FIUlKSw2Pu3r2b33//3S6vcI2i+895ePzD3PL4Ldr1K329Xfq/Brv/q4ryCs8gwZAQ1aWOV4/vS9+Himr3YVEfHvOgn1fG2TD30uyuASrD2g/DaDQyaNAgAKKjoyvagaZ9u/a0im5VZht9zdAlHS+hZXTLMnmcHdNoNDJ8+HCXzkXY07+mL2l7iV3g4uh6V/h/7WBb4fkkGBKigbI10egDhjcGvwFX1VaJ3GQ9MK/4zzsuvYPbx9xe4SZKilK8HfDRDR/Ra3ivyh1TFww5Hb6tf6yZ9NasMYruS4m6RyXj94xy8xv8DQRfHmzX9HmRBSj5W5rJ6iwJhoRwJw+62dlqUPTBUI8WPTBGe3aVv+WIhW0UNz9FhUTRNrpthdscaHyAYxwDIDY8FoNSuWhFsfvAc5xHXzPktg9aUTH9f81Ula1Tt1a4SdiNYXT5rkv1lUnUOfL9RIgGylaDYVB1t4F68BntSmBSml1tTlWugSuzHBfp/pY7b43Jjqr8M/fSf0qvhpKIukxqhoRooFRHn9r1IBiq0uMX9LFQVWpt9PGX1fFB7WqGvOrDhfYMaVelMXX4VNqcasPtl95Oq5BWzvN+nka+Od++SfNi1fG+g6KYBENCVJc6fhN01GeoXjTfXGQwVG01Q9JnqHZ4wYruKwC4bcxt5TabZv6RWRwMqcXvD8Xd72EPakZvaCQYEqKBstUM1bdmMpc6M5d2kcGQ/kMzZ38OZ1adKZMnO6mkuaZeBJ0ewq4DdUXRsZfub2upZVGvSTAkhDt50Dc/h4FCPaixqO0+Q6lzUkmdk1p+/npwnT2FUon/UH2QqlpV9zRn1vEaYlFM3pJCNFC2x1boa4bc3ixQGy62z1AVrkFgp8BK5Q/qJA9arQ0V1hTqPxHd2W+opADVsFPhDlIzJER1qeOBhaOh9fXi61Et9BkKbB9It1XdyFiTUWHe4CuCCb4iuPIHEVVSmWay0jVDouGQYEiIBspRB+qG2mfI7oOvitfAOMiIcZBnz9FUH9nNLl4bNUN1/EuRKFYfvgcKIapAqxnSfVjUh2ayqvQZuujRZKLOqsxrutprhqSZrM6SYEgId/Kgm53DmqH6cEeojXmGhEeocDRZdfcZEnVWfbj1CSGqwGGfofoQB9TGPEOizqpMM5n0GWq4JBgSorrUYJOTxWJh1apVJCcn2/22WCx2623LUHyzv3/V/dy86eaSIldQK1L6OPr9lc7jaF1VzqnS+9GdwtGUo3bbO9tnXm6ew+0vRkX/J6Jm6JvJss5mlf9/oftEzEjPAMq+ZvTLFb1GLRYLa9etK0nwoJrjhkY6UAvh4SwWC7GxsZjNZgwGA1arVfttMplYt24dffv2xWw2YzKZSEpKwmg04rXLizvX3mm3r3P55wjG8UgnR8fR7690ntLrqnpOld2P/sPv+++/567Yu0hKSgJwuE+LxcLixYsZyEAAzmadpRGNKl1mZ+V39H9S1esiKk9fM/TQ+Iew/G1x+n9RaC3U8l7V9yqWbVhm997Rv5fCw8NRFIXU1FSH/6e214CP2cyRmjtdUUUSDAnhTrXwzS8hIQGz2QyA1Wq1+202m1m0aJG23mw2k5iYyKBBgyDDfj+rWEXRuSJMmFw+jt3+SuUpva6q51Tp/di1+ina9qqqOtxnQkICuTm52ja79uzC1MfxNahK+R39n1T1uoiLY+lhgQ5gvdAhyIyZwfMG06RJEwBuOHYDXSh+Wr0hzsCd794JPdHeE6WXofjvDP8Mu/0ApJ9Jx3yNGX/gWiAqE6Z4n6dFzZyqqCQJhoTwcPHx8bSKaIUl1YJBMWBVrdrviIgIRlw7gk/++wnH0o7RJLIJcXFxgH2fiHkt5vGL+gtPxD9R7nFMJpNdbUdkZKS2v9J5Sq+r7Dm5Yz+A3faO9hkfH8+6gHWQU5y/c+fOVT6Wo/KXrhm62PMRlePn7Vey4CDGTchI0L4YXFl4pZY+c/lMWO7aMXJ8cnjB5wVWtl1pv6It5AK21Can9zPN1YKLGiXBkBAermhdEfPPzS/+tmuLb2y/U+FYj2N8wieoBpXmI5uXVOXrKrEuu/wy3vr0rXKbboxGI0lJSSQmJhITE8OhQ4eIi4uz20afp/S6yrio/ehqhm64/gZemveStr2jfRqNRoYPH47lq+J+H41DG1epzM7Kb7tWzq6ZqF63dLqFDzd/yJHMihur0kLSqnSMgIIABuwaQGLbxHLzpXrnlrte1B4JhoSoLjXUgTp1TirWcxWPA1asCumfpMM7xcv6kTVhTcNc+oA2Go1a8050dHSFeS5Glfeju+wtIluUCdYc7dPXx7dkczf9vzm6Vs6umag+7cPac/CfBzlfcL7CvAX3FpD2ThoFxwtc2ndRVhGZyzIBGHvpWCY/O7lMngO7/iTu+38ALgztF7VGgiEhPJw1ryQQCh0UisG37CDRzHWZFGUVYc3XBU31dDj5RU+6KGNs6x0vgxfBfi48AiUKmrzVpOJ8F2TvzmbTsk0A+Cg+Do/RyKekM76EQnWXx7zt27Rpg6IoZX4effRRh/nXrFnjMP+ePXtquOSiQamNobO6+CZ2USxdf+5a5iewY2CZvPo+Q/VqokGZZ0jUFBce/VIfZnVvCDymZmjTpk0UFRVpyzt37mTw4MGMGjWq3O327t1L48YlfQCaNWtWbWUUojaoRRUHNVq6WnzTVhSl/n5NrcqzyXT55MNLuMru/ebkpWYfm9fXN53n85hgqHQQ85///Ie2bdvSv3//crdr3rw5oaGh1VgyIZyoqQ9VfXchLyd5Sj9mwEtqhuxIzZCoCv1rxUm3PUUpefNJKFR3eUwwpJefn8/8+fOZOHFihd/ievToQW5uLp07d+aFF15g4MCB5ebPy8sjL69kNtqsrCy3lFmI6uJKUKN42T9mQPFS7GtN6lEAoL8nFGUVkXMop8Jtis6W1DrXp2shqlklm8mkZqju8shgaOnSpWRkZDB27FineUwmEx9//DHx8fHk5eXx+eefM2jQINasWUO/fv2cbjd16lSmTJlSDaUWoprov5E66wXo4AGUdjdvj+k96ALdB9Spb05x6ptTVd5eiPK40lnf7tlo1VweUXUeGQzNnj2bYcOGERkZ6TRPhw4d6NChg7bcu3dvjh49yvTp08sNhiZNmsTEiRO15aysLFq1auWegov6r4Y7UCeaEzl19hR+FE8styBpAfiUzdf0fFMtz1fbvgJ/OHDqABFEAPY3bE/nG+6L4qug5lf+/8IQYMAnzMEFFMIRB18yzu08R/a2bC05+7iVa7ZfQ1pIGmpjeS5dXeVxwdCRI0dYtWoV3377baW37dWrF/Pnzy83j5+fH35+fuXmEaIu+OXALwz9YijvnnxXe4TAmO/GYPUq23lh+unpxBMPwP3f3U+uby5XHbqK/lzoc1ePaoZ8wnyI/TqWU9+cqtSTxxUvhea3Ncc72ONui6K2lGomy9qYRWKvshMvPs/zAPx+9ac1VTJRSR73rp8zZw7NmzfnH//4R6W33bJlCybTxT1zSAiXVXMH6vXH1hcfRi05jtXguBenVSlJt+XX1wa1aFy/npjU9KamNL2paW0XQ9RzpZvJMv/KLDd/uLl9NZdIVJVHBUNWq5U5c+Zwzz334O1tX/RJkyZx/Phx5s2bB8CMGTNo06YNsbGxWofrxYsXs3jx4toouhBuZ+vzY1BLqnXeu+49h3lbL28Nh4r/nn7NdKyNrDT2bQxfF6e1CKlfwZAQNaL0yEXdd5GIcRE06tGI9N1HsMy8MKO1Wn+ao+sbjwqGVq1aRUpKCuPGjSuzzmw2k5KSoi3n5+fz5JNPcvz4cQICAoiNjeWnn37iuuuuq8kii4amBvsM2UamaDVDBvi/K/7PYd7txu2c4QwAD3R/AJ8mPpw8fJJd7CreR30aWi9ETdE1L6tW1a5ZNuwfYTQb0YyCVeaSYEjUWR4VDF177bVOhy/OnTvXbvnpp5/m6aefroFSCVE7bO8FL7V4cqHyAprSQ+uL/9BncHvxhKj3yowmczSy0672SN5odVWVuk3OmzfPbi4em/z8fK2ZSghhz2KxsGrVKpKTk+1+WyxVG2GiouKX70fkmQujKh28m23HLCgq+WaafiAdgHNnz5VkrMf36NLX3WKxOEwTQs/2GrG9NkovA3bvm5NpJzmfXfIw2O3bt2OxWDh3rmRkmSLBUJ1VpZqhe++9l6FDh9K8eXO79LNnz3LvvfcyZswYtxROCI+m+9ZosViIjY3FbDZjMBiwWq3ab5PJRFJSkktPjdcLOhjEN299Q6O84gdB5ubnYrFYtP3oj/mG3xtcwRUA7O29l1NTTjHl7Sk8xmMA5ORUPDGhJ3J03cPDw1EUhdTU1Iv+PxD1k/51YzKZWLduHX379tWWtdeKLrb5a91fHN92nNGMBuCFl18geWYy7bxDeY0Pa+lMhKuqVDOkPduolGPHjhESEnLRhRKivklISMBsNgPFAwH0v81mM4mJZYfjVqTZX820QAggjTS7/eiPeTTvqN22R2YfITOjZOTLsePHKn18T+DouqelpZGammqXVtX/A1E/6V83ZrOZRYsW2S3bXiv6pmkFhWxdLZCKSlpaGmcsGVqatUimXayrKlUz1KNHD+3p74MGDbIb0VVUVERycjJDhw51eyGF8BhO+rTFx8djMpkc1gxFRkYSFxdX6UMpBSU34lSvVD4xfsL3cd87PObKZivxPe/LDdk3ABDWOAxjqBEyivO2iqqfE4s6uu4REcUTTeprhqr6fyDqJ/3rJjIyklGjRjFjxgxtWXutlKoTCAkOgbPFf1spfq0ZDSFwofXMYKhHE3rVM5UKhoYPHw7A1q1bGTJkCI0alXwr9fX1pU2bNtxyyy1uLaAQ9YHRaCQpKYnExERiYmI4dOiQ9jsuLq5qzTO6uCvr+Sy+f/x7u/3oj2m7eW8N34pSoODr7ct/pv6How8X1xgFBgVe1PnVVY6uu+1alE6TJjJhU/q942gZsAuG+vTqQ8RVEaS9mQbA1P9MJe7BOFI3JpE2rLA4uyrBUF1VqWDo5ZdfBqBNmzaMHj0af3//aimUEPVCqaZko9HIoEGDAIiOjrb7XRX6kZWXdLjE4Ye5/pgAXj5eWAusqIUqQYFBurJWuRh1nqPrDjhME8Km9Hun9DJg974JaxKGn2/J0wviLisOmnJCgklDOujXdVUKU++55x5yc3OZNWsWkyZN4syZ4vlLEhMTOX78uFsLKIRwTLHq+iu4OE+Q4l2cTy1SZWi9EBfJ7n3nZGi9ff9aeaPVVVUaTbZ9+3auueYaQkJCOHz4MA888ABNmjRhyZIlHDlyRIbXi4arJh/UqrvxOhrQ4IhtviG1ULWfs0vu0UJUXqkZqPWTLtoCJbtO1jK0vs6qUjA0YcIExo4dy7Rp0wgODtbShw0bxh133OG2wgnh6bI2ZnF85nGs5x0/M8zGJ9yHqKei8G9dtaZn/aSK5eZzUjPkajAlhNDRVwxZVcc1Q/pO0zKYrM6qUjC0efNmPv744zLpLVq00IasCiFgz9g9nN9zvuKMgDXbSsc5HV3fuf7G62Iso9UMlW4mk36dQlRa6RmoK6oZkirYuqtKwZC/vz9ZWVll0vfu3UuzZs0uulBC1AuKQu7RXJez5x0rO6t7ufTNZK4+W6z4yR3kH8/n8JTDuh1U7tBCCOy+RGStz+Lc1nNl1hkUaSbzBFUKhm666SZeeeUVvv66+JHXiqKQkpLCs88+K0PrhXAg4JIAuv3arUy6NdvK3x3/rtpOqxAMeTUqjobUQpW8lJLgyyvAq2plEKIBU3yU4i8YRVB0roiic0XaOq/AC+8pL6kZ8gRVqhyfPn06p06donnz5uTk5NC/f3/atWtHcHAw//73v91dRiE8R+kO1BcWDb4G/Fv6l/nxbeGr27TqHQpcDYainonCO8wbxUfRfhr3bkzY9WFVPrYQDZWXvxdRz0ZhCDKUvKd8FZrd2oygrsVTVyhKycesIn2G6qwq1Qw1btyYtWvX8ttvv5GYmIjVaiUuLo5rrrnG3eUTwrPZbn5OYpUyT72uDEdPyK6A6V4TpntNlTyQEMKZmNdiiHktxul6GVrvGaoUDNlcffXVXH311e4qixD1TwXBUOmhuZVShaH1QoiaZfDSjyaT92ldVaVg6N1333WYrigK/v7+tGvXjn79+uHlJf0QRAOmKCVNX9UQDOk7Y7o6tF4IUbN0rWQoUjNUZ1UpGHr77bc5deoU58+fx2g0oqoqGRkZBAYG0qhRI06ePElMTAyrV6+mVav6+QBIISrDac2NvpWskn2G7PLL0Hgh6qSLagoXNaZKt9DXX3+dyy+/nP3795Oens6ZM2fYt28fPXv25J133iElJYWIiAgmTJjg7vIKUbc56UDtzMXcKO0exyHNZELUSYq+mUxqhuqsKtUMvfDCCyxevJi2bdtqae3atWP69OnccsstHDp0iGnTpskweyEq6jPkKG9l900l5hkSQtQoReYZ8ghVCobMZjOFhYVl0gsLC7UZqCMjIzl79uzFlU4IT6YoWsBy9txZLBZLmSfLWzJce5p1/sl8jnx2hJS9KYSFhZGenk7w/pJH4VSmz5DFYiEhIYH4+HiHT7oXQlSNo/eWftLF6KNdWPq/pdz4yI0YDI4bZs5tO8fxpcc5dvQYHe/oSIurW9RI2Ru6KjWTDRw4kIceeogtW7ZoaVu2bOHhhx/WRpft2LGD6Oho95RSCA9l69ezb/8+YmNjsVhKgh+LxUL37t215cKCsl8wbLbfup3jTx/Ha7YXGdMy8JrtRbPkktnes7OzXSqPxWIhNjaWwYMHlymPEKLqnL23Sn9RCX0slGWfLnO4j4IzBST0SsA82YzXbC92D9rNyV0nq73soorB0OzZs2nSpAnx8fH4+fnh5+fHZZddRpMmTZg9ezYAjRo14q233nJrYYWo80r1GbIFQyoqZrOZxMREbV1CQgInUk9oy+fOnsOZs9uc17KeCj7F3py9LhUvISEBs9kMUKY8Qoiqc/beCggK5EjzJLu8+9bsc7iPnAM5qLkl9xBvvNnx845qKrHQq3Qzmaqq5OXl8d1333H06FH27t2Lqqp07NiRDh06aPkGDhzo1oIK4Yn0Q2kjIyOJi4vTluPj44mIiIALzzYOCgpyuh9vL2+KKOIMZ5ihzMCqWuEyUNupbGuzjWVdHH/TLC0+Ph6TyYTZbC5THiFE1ZX33hqZPpGvWk2g3dGhAISGhDreiYN+g+3bta+G0orSqhQMtW/fnqSkJDp06GAXAAkhSrlwc+vQoQM71++066NjNBrZsXMH25tuB4oDHmdsQZWxhZHP/vyMQ4cOMSttFgv2LwAgJCTEpeIYjUaSkpJITEwkLi5O+gwJ4SblvbeCivJppm4AioMhHy8fh/vQP/XeplFQo2opr7BX6WYyg8FA+/btSU9Pr47yCFF/6DpQNw5p7DDwMDbRpZU3muzCusDAQKKjoxk0aBCNGpXcJCszmZvRaGTQoEESCAnhZg7fWxc6UBt0TeiOgh7A/hE75aUJt6tSn6Fp06bx1FNPsXPnTneXR4j6yYVYpdxJF203RLtpiUryyzxDQtR1FQdDjtKdBk7Crao0tP6uu+7i/PnzdOvWDV9fXwICAuzWnzlzxi2FE8Lj6L/9qRUHK64GMY4e62G3f5nMTYg6zaCv4nEW3zhKl1ioRlQpGJoxY4abiyFEPXexky7aYiHd5IpSMySEB7jw3lSkZqhOq1IwdM8997i7HELUC6cMOTx7IxxoAsrqcUxmGgA7T+5kwlzHj6d5WXkZg2pg96ndTJw70WGeSfmT8Mefw5mHeWruUwDsPV0ynF5qhoSo2xRVVzPkrB+Q9BmqNVUKhvRycnIoKCiwS2vcuPHF7lYIjzSr0T4+bVn8t+F0gpaelZ/FH0f+cLiNrYbnXN45p3meLXoWgOyCbId5/L39L6bYQohqJjVDdVuVOlBnZ2fzf//3fzRv3pxGjRphNBrtfoRoqE4ZcksWVP2fFd/QXHlukaqU3c/o2NG0CW3jSvGEEDXN1kym2t0QHJM+Q7WmSjVDTz/9NKtXr2bmzJmMGTOG999/n+PHj/PRRx/xn//8x91lFMJj6IOe3/rPQX21+O8+UX3IeyHP4TbrX1uPWqgSZ4pzmmfDGxuwFli5NOJSuzwKitM5S4QQdYe+ZkiayeqeKgVDP/zwA/PmzWPAgAGMGzeOq666inbt2tG6dWu++OIL7rzzTneXUwiPoP8S56v4YAtbDAYDvl6+jje6UCGkqIrzPLYO1Eo5eYQQdZZB12dImsnqnioFQ2fOnNEewtq4cWNtKP2VV17Jww8/7L7SCeHB3DnCy3ZDlFFjQngmhao1k323+zvOrC2ZrqZF4xaM7DxS+gm6WZWCoZiYGA4fPkzr1q3p3LkzX3/9NVdccQU//PADoaGhbi6iEJ7Dbri7vg9QeTGMbZ0LQ+tl0JgQHqYSQ+uzcrLKpH21/StWq6vt0pItybzY/0U3FlJUqQP1vffey7Zt2wCYNGkSM2fOxM/PjwkTJvDUU0+5tYA2kydPRlEUu5+IiIhyt/n999+Jj4/H39+fmJgYPvzww2opmxA2qrMFF4Khcmegtq2q0jtWCFHbDC4MrT+ecdzBdmXf9DtOypPs3a1KNUMTJpTMlzJw4ED27NnD5s2badu2Ld26dXNb4UqLjY1l1apV2rKXl5fTvMnJyVx33XU88MADzJ8/n3Xr1vHII4/QrFkzbrnllmoroxA2+iat8pq3FEUprlEqLxZSpZlMCE+m6OuNnQRDhUWFZdIm9JzA/934f5w+f5oHfngAcG10qqicSgdDVquVuXPn8u2333L48GEURSE6OpqRI0fStWvX6iijxtvbu8LaIJsPP/yQqKgobbbsTp06sXnzZqZPny7BkKg21dZM5uDZZEIID6A9qNVK0YUkZ7XABYUF+GA/OjTeFE9ExwiOZR3T0sqtRRZVUqlgSFVVbrzxRn7++We6detGly5dUFWV3bt3M3bsWL799luWLl1aTUWF/fv3ExkZiZ+fHz179uT1118nJibGYd7169dz7bXX2qUNGTKE2bNnU1BQgI+PDEcW7qe/RWVnny9ZcCEYOnf2HBaLBaPRiMViISEhgfj4ePsdSzAkhMcL+zmMea3moaoqiqJgvdCEFpgTSHOa2+Xd/dRuDk07RFZ2Fh/lfsSp4FMcevhQbRTbJfp7lyfNO1ipYGju3Ln88ccf/PrrrwwcONBu3W+//cbw4cOZN28eY8aMcWshAXr27Mm8efO45JJLSEtL47XXXqNPnz4kJSURFhZWJn9qairh4eF2aeHh4RQWFnL69GlMJpPD4+Tl5ZGXVzKPS1ZW2Q5tQjijD4aeeeYZ3mABAIWFZau/NRcCnMOHD3Nn7J2sW7eOvn37YjabCQ8PR1EUvuIrAIqsRc73I4SoswKKcjh34e/Q7FBCs0Nd2k5JU8hPy8cffy7hEi4xX0KjHxrB49VV0qqzWCzExsZiNpsxmUwkJSV5TEBUqe6YX331Fc8991yZQAjg6quv5tlnn+WLL75wW+H0hg0bxi233EKXLl245ppr+OmnnwD47LPPnG5Tun+FK/0upk6dSkhIiPbTqlUrN5ReNBwl4VCGJVP7++zZs063KCoqCXDMZjOLFi3CbDYDkJaWRmpqqrY++3y2OwsrhKhuFz5v4tIPsi/6L/K98ikwFJT7c7zxcXKa5FCg+1dIyRcqrzPO+8vWpoSEBO3eZTabSUxMrOUSua5SNUPbt29n2rRpTtcPGzaMd99996IL5YqgoCC6dOnC/v37Ha6PiIiw+xABOHnyJN7e3g5rkmwmTZrExIklD8vMysqSgEi4TF8z1CQkFNKK/w5uHOx0Gy9vL6xYUVCIjIxk1KhRzJgxA7PZTERERHHfowv7CWoUVG1lF0JUHwNwb9QKWuf+D7PZjMFgwGq1Fg+guPBF3ZYW2SiStWvXajXEiqIQFhDGovOLAPD1rpsTr8bHx2MymTCbzURGRhIXF1fbRXJZpYKhM2fOlGl60gsPD8disVx0oVyRl5fH7t27ueqqqxyu7927Nz/88INd2ooVK7jsssvK7S/k5+eHn5+fW8sqGg59B+r/vPEm6s3Ff/v4On/N2WoqW0e1ZufWnRiNRpKSkkhMTCQuLg61UGV78+0AePtc9LOVhRC1xMfHR3tvx8TEcOjQIWJiYrSparp168ahQ4eIi4uzuw/ExMSwduVaeKh4P4Y6OsdG6XuXpzSRQSWDoaKiIry9nW/i5eVVft+Ii/Dkk09yww03EBUVxcmTJ3nttdfIysrinnvuAYprdI4fP868efMAGD9+PP/73/+YOHEiDzzwAOvXr2f27Nl89dVX1VI+IUpr3KgRWkOZCx2ogwKDtJuH0Whk0KBBAFgLSsbhKgbpQS2ERynVLUP/3rY9ycH2u/Tf+ry+1/iynwstIXV4MJm+zJ6k0qPJxo4d67TmRN/x2N2OHTvG7bffzunTp2nWrBm9evViw4YNtG7dGihun0xJSdHyR0dH8/PPPzNhwgTef/99IiMjeffdd2VYvahWVbpHVTTpoquTNwoh6raLGBJvN2+ZKjcCd6tUMGSrhSlPdYwkA1iwYEG56+fOnVsmrX///h7VgUt4PrvJ0FycZ8h2kyvKKuLkopNl91mg26fcA4VokOxqhetwzZCnqlQwNGfOnOoqhxD1jqKLXMqdOfrCqnxzPrtu3VX+PmUGaiEaJMVLdz+xyn3A3aQ3phDuZDXQb1c/Is9EkntU15xczr2rUfdGZKzOcGn3Qd1kNJkQHsVNX2AMBl2naakZcjsJhoRwoza7enL7insByNWvKOd+2PnrzpxefJqi7PInVPRp7kOzEc0uvpBCiNpxMX2GDNJnqDpJMCSEG4Webuk4vX+o0218m/oS+VBkNZVICFEfSDBUvSQYEsKddDepwEfziL4mDt8IXxr3bFyLhRJC1Bo3NZPp+wxJM5n7STAkRDXxjbfSbLg0awkhLriIZjK7PkNW5/lE1dTNaSyF8FD66muZIFEI4Tb6mTqkmcztpGZIiOoi9yshRDU0k9WFYCh7TzYFaQUu5fVp5kNQ57o9ElaCISHcST8/Yu3fr4QQdYm7mslquc/QsXeOceDxA5XaJuY/MUQ9E1VNJbp40kwmhFu5ONGiEEJUQl2adDH95/Qa2aYmSc2QEO6kq77evXcPLS1XVOrJzRaLhYSEBOLj4zEajWWWhRAexl3NZLr9hKaGkn4inbDIMLs8lblf2PK2bduWgwcPar8dbVs6b2huqLYueFwwmecyCQ0NJSMjg/CIcPz9/cnNzeXokaP4f+dfnLGOd/qWYEgItyq5Yb373ns8PvsNkpKSXApkLBYLsbGxmM1mTCYT69ato2/fvtqyq/sRQtRRbmomCz4XzPqW64lfH4+ppwkoe/8o736hz2swGLBardrv0ts6yvu+z/t0pjMAfef0JU/Ns9t+3bp1DOo9iFNpp/iVXwEoKHCtf1FtkWYyIdxI0T+nFTCbzS4/LDghIQGz2QwXtlu0aJHdsjx0WIiGS0EhNSRVW26kNmL37N3acun7R3n3C31eq9Vq97v0tn/9/RdmPzPEgLWNFWKgyFAyW35BmwK7deYAM68veJ20oDTU6JIbYpoljUOWQxdzCaqVBENCuJW+SlwlMjKSuLg4l7aMj4/HZCr+lhcZGcmoUaPsll3djxCi/lEUhVdHvool0KKlRYaXzFxf+v5R3v1Cn9dW42T7rd+2yFrEv/b8C8YCY0p+vJp6afuyjrHarWMMzMqfBWNAHVMSDKWcT6Htu235ef/PVb4G1UmCISHcSVczNGHi4+zcudPlpi2j0UhSUhKrVq1i586dREdH2y1LE5kQHshdfYZQ2NVqF9OGT9PS/P38tb9L3z/Ku1/o8x44cMDut37bI5lHOJhxsMz2BrU4dChSisqfQkS3zrbNyoMrXTndGid9hoRwq5J3f2xs50oHMEajkUGDBjldFkJ4sLVroYpfahSDCv8Eq6LrifzvqfDW19qiEXD1bqHPG13qt01haFFxrRDQ5ZSBmw75ABB5rjh0UCjihY1+5R5HpQgFL+2LovrhTLh9btmMbdvC5s0ult79JBgSwp3kmUFCCD0vLwgKguxsKCqCjIwq7qf4l6rrmKjm5kFuFffngiJdhBB/zMqry/IA2IRCNuCtlqQ5s+bCb1vNkJqXDxn5ZTNmZV18gS+CBENCuJXMMySE0PH2hhkz4L33IK/8wKE8iqIC++xrhsKaQdMOF11EZ4pC8nhg5WCu3XYtQYXerPMqDmgKiopnk1YMKrQv//jK3uLviMqFe6NqDIUO4WUztmnjxpJXngRDQriR3bPJJBgSQgDcf3/xz0VQrIXwqg+qvvr54Ufg1TcvsnDOFWzdwh09MkuWS633bhEKe/aUvxO/3yFf1e6N6l13wZfvubegbiDBkBDVRWIhIYSbaDUr+mYya/W2yxdaCrW/CwIKCI4I1pa9gryIet6Fx2tcuA9qwVAd7UsgwZAQ7iRPrRdCVANbTbNdM1kVZ3U+tfQUR6cfxZpT/g7OZ53X/j4y+Aj3f1f52i3FoKCiqxm6iIknq5MEQ0K4lTSTCSHcz501QwceO0Descr1XyoMLqw4kyO2miGkZkiIhkP/PpdZvIQQbuLOmqH8UyWjuRQf51/aVFQKigo42vQoxwYdq9KxbDXk2mgyqRkSomGRmiEhhLvpa4YOnj7Irr27Kr2PRgWNUFAo6lLE+UXnnebbdWoXz/76LABPtniy8oWFMn2G6ioJhoRwI0UtqQ6SYEgI4U4Kil3N0Hd7vmPmgpmV24dV4TfrbwDstuzmsQWPubSdl8Gr4kyOXLgl1vUO1FKRL0R1kVhICOFGlza/1K5myKBW/iPcy1oS1OgfuFqRLs27VPpYUPKlUDpQC9GQyGgyIUQ1+emOn/jJ7yeYVbzcp0UfTFebKrUPQ25JANW6aWv+ffW/K9ymQ1gHbup4U6WOU3LA4l/SgVqIBkqayYQQ7tQqpBV3dr+TBBIAaH+oPVf8cEWl9mHNt3Kc4wBEN41m+FXD3V1Me6XnGZKaISHqP5mBWghRnRSvkvvKua3nOLf1XNX3Vc5IMnex1ZDX9T5DEgwJ4SZrFqyh3X7dtzQJhoQQbhbYORD/aH9yk3Mvel9h14eVSbNYLKxZswaA7t27c/DgQeLj4zEajXZ5EhISyqQ7dOE2GJkRSb9d/aBqXY+qnQRDQrhBwq8JcLt9WnZ21b+xCSGEIwYfA+3XteeWLrdwJv0MBsWAVbVqv5sYm4ACZ86UXaegaDUzXk29+G30b3b7tlgsdOrUibS0tOJjGQxYrVZMJhNJSUkYjUYsFguxsbGYzWa7dGf0Hb6nfD2F35v8DiOq4cJcJAmGhHCDwxsOE0bJt6zU0BQMGVIzJIRwvy1JW/g9/ffiBVusYftt0WUsvU7vNCQmJjJo0CAtKSEhQQuEAKzW4mH8ZrNZy5uQkIDZbC6T7kx+p3wMaSWdtgP3BrpwhjVPhtYL4Q66m83ByA0My36Ibt261l55hBD1Vnx8PCZT8Sgyg8Fg9zsiIoKIiAiH6/T9GCMiIoiLiyuz3/DwcG3Ztl1kZKSWV39sfboz3b/uzpfNvtSW/f39K3OqNUZqhoRwA/0zgoK8/yKkIBdCQ2uvQEKIestoNJKUlERiYiIxMTEcOnRI+20LThyti4mJYdu2bQD079+/TPOW0Whk9+7d/P57ca1Tt27dtH3a8uqPrU93pkmzJtz78b3k3Vz8LDQvpYqTN1YzCYaEcAO1qCQYUuroaAkhRP1hNBq15qno6Gi734DTdfo8zvY7fPhwbdlRfv2xXREcHEwexcGQYq2b3QekmUwIN9DXDClVfXqiEELUQ3YT0NbR74oeEwxNnTqVyy+/nODgYJo3b87w4cPZu3dvudusWbMGRVHK/OzZs6eGSi0aCv1EYlIzJIQQJSQYcqPff/+dRx99lA0bNrBy5UoKCwu59tpryc7OrnDbvXv3YjabtZ/27dvXQIlFQ2JXM6RKzZAQQtjoJ4qsq81kHtNnaPny5XbLc+bMoXnz5iQkJNCvX79yt23evDmh0plVVCN9nyGNTLoohBD2D62WmiH3yszMBKBJkyYV5u3Rowcmk4lBgwaxevXqcvPm5eWRlZVl9yNEZUifISGEKGEbog91t2bII4MhVVWZOHEiV155JZdeeqnTfCaTiY8//pjFixfz7bff0qFDBwYNGsQff/zhdJupU6cSEhKi/bRq1ao6TkHUM/bNZHX0q48QQtQCuz5DdZTHNJPp/d///R/bt29n7dq15ebr0KEDHTp00JZ79+7N0aNHmT59utOmtUmTJjFx4kRtOSsrSwIiUSG7ofWKBENCCGFjFwzV0Ypzj6sZeuyxx/j+++9ZvXo1LVu2rPT2vXr1Yv/+/U7X+/n50bhxY7sfISqke4NLB2ohhCjhCcGQx9QMqarKY489xpIlS1izZk2FE0c5s2XLFm0qcSHcxeHQeulALYQQ9qPJ1Lp5X/SYYOjRRx/lyy+/5LvvviM4OJjU1FQAQkJCCAgIAIqbuI4fP868efMAmDFjBm3atCE2Npb8/Hzmz5/P4sWLWbx4ca2dh6ifZNJFIYRwwgNGk3lMMPTBBx8AMGDAALv0OXPmMHbsWKD4CbopKSnauvz8fJ588kmOHz9OQEAAsbGx/PTTT1x33XU1VWzRUNg1k9VeMYQQoq7RPyBWaoYukurCCJ25c+faLT/99NM8/fTT1VQiIUrYN5NJzZAQQtjom8nq6u3R4zpQC1En2dUMSZ8hIYSw8YTHcXhMzZCoGywWCwkJCcTHx2M0Gmu7OHXC5499TtRHUdqyDK0XQogS+mDItM3EvFbzsGLFr4sfHawdyDyUScglIcT9GFdrZZRgSLjMYrEQGxuL2WzGZDKRlJTU4AOilH0ptPhfC7s0v6LcWiqNEELUPQGNArS/G+U2otGxRsULxyCLLBQUkg8mE22JrrXPFGkmEy5LSEjAbDYDxZ3VExMTa7lEtc+SasGgexvtMW3iyrRttVgiIYSoW5q3aM6WQVvI9c6lwFCA1UHHIS+rV61+pkgwJFwWHx+vzdEUGRlJXFztVWnWFVZryZv6x6gfaWV5CT+1qBZLJIQQdc/YRWMZ12wc11qv5eeon8usfyb8mVr9TJFgSLjMaDSSlJTEqlWr2LlzZ4NvIgOwFpUEQ61at2Lw4MElK6UDtRBCAPafH+3atyuzfu26tbX6mSLBkKgUo9HIoEGDJBC6QD+kPigoCF9f31osjRBC1F22zw9f/7L3ydAmoTVfIB0JhoS4CPoHtGIA5In1QghRLoOhbOhR20+2l2BIiIug7zMk7yYhhHCBo3tlLfcqkNu3EBdB32dI3k1CCFExRzVDtX3/lHmGhEvUIpX0H9M5v+e8lubT1IdmtzbDO7gBv4zKaxWTDtRCCFGWg8BnzrY5PND3gZovywUN+FNMVMapJafYNWpXmfSziWe55P1LaqFEdYO+Zqi227yFEMITOKoZenvj2xIMibove1u24/TtjtPrpXPn4P334eBBLcmabgBuK144egTSZSJKIYQoT8uQlrVdhDIkGBIu0Y+aajO5DYcnHy5Ob0ijpz7+GJ591j6t+aVowdDpk3DkcMk6R+3iQgjRwLUytuIoR+3S3rnunVoqTTG5WwuXqIUlQU9I/xDdilooTG1JTi6TZFWcvIX69YPw8GoukBBCeCAHt81r2l9T8+XQkZoh4RJ9zZDBR/dKbkjBkL4W7MsvITYWdeUOeLI4Sel6KXy/Dby9oVMn6UAthBAOKI7ujbV8u5RgSLhEXzOkeOtetQ01GLrkEujaFeuO0yVfchoFQteutVEyIYTwHDLPkPBUdjMte+nSG1KfIb0L32xUqy5IlNFkQghRoTL3SsVJbVENkmBIuEb3IHbFWymJ4htSLOQg8NMHQ7X9zUYIITxC6cijDkQi0kwmnFJVlaNZRykoKCBte5qWvjd1L6qioqgKWMvZQT2U6eNPWoCRA7+soXd0NGn70mhBi+KVdeANLYQQdV7pL4514Iuk3L6FQ6qqMvSLoXR8oyN/t/+bor9KqoZu+fEWrGpxFJR2Ns3ZLuqdP9LgL77lRNaXBD4Xx7Ym22jxegttfaG1sBZLJ4QQnqF0M1lBYQEWi6WWSlNMgiHhkPmcmRUHV9DtcDdMGSYtPd8rH0uQBVUpbh5Kz06vrSLWuP1HmhFQEOB0/fnA807XCSGEKOYX5We3nEYaiYm1O2GtNJMJh2y1HN5W+5fI1L5TKThegHqhs5DB2Tw79ZBa5PxcP7/kc6Y8P6UGSyOEEJ6p+ejmZB7MZPH0xWTkZrCh6Qa+j/u+VsvUcD7JRKXYRokZ1JKXiPUBK98u/Zaj7xzVaoaUutDYW1NUx+d6pMURpm+YTsuoujfFvBBC1DVeAV50fLUjj5x4hKGrhvL9vu8xGo21WiapGRLl0w2Wat+hPUajEatq1YIhAQZvQ62/kYUQwtMYjUYGDRpU28UApGZIOKE1g+lqhmyvFgVFW684qS2pl5ycq2qQwFAIITyZBEPCIVszmV2wc+FPRVFKmskkGKoTw0KFEEJUnQRDwiGt5kf3Se9whuWGVCni5FylyVAIITybBEPCIUcdqPWvFi0AaFBxgNQMCSFEfSTBkCiXvhlM/+yYBjmazCp9hoQQoj6SYEg4VF4H6lIZGxCpGRJCiPpIgiHhkPY0ev1zSHV9hqyKtcz6ek/6DAkhRL0kwZBwqMKaIdvIsoZULeJsNJm8i4QQwqPJbVyUy9HQetCNNnPSj6Z+ctJnSGqGhBDCo0kwJBzS5hlyMrS+QQYAUjMkhBD1ktzGhUPSgdoBmXRRCCHqJY8LhmbOnEl0dDT+/v7Ex8fz559/lpv/999/Jz4+Hn9/f2JiYvjwww9rqKSezdEM1A6H1jeoGaidJDfEWjIhhKhHPCoYWrhwIY8//jjPP/88W7Zs4aqrrmLYsGGkpKQ4zJ+cnMx1113HVVddxZYtW3juuef45z//yeLFi2u45J6nopohtUFVCV0gNUNCCFEveVQw9N///pf77ruP+++/n06dOjFjxgxatWrFBx984DD/hx9+SFRUFDNmzKBTp07cf//9jBs3junTp9dwyStmsVhYtWoVFovFbvn0kdMceOcAv97/K1uf2cqv9//K4a8Oo1ovPhgpfczSWp5uya1/3aot2z2O48KfTdObkjw3GWuhtcL9eYLCrELteh/88CBFOUUArP5yNe0OXOZ4I496FwkhhCjNu7YL4Kr8/HwSEhJ49tln7dKvvfZa/vrrL4fbrF+/nmuvvdYubciQIcyePZuCggJ8fHzKbJOXl0deXp62nJWV5YbSl89isRAbG4vZbMZkMrFu3Tr69u2L2Wzm+YDnuSbnGrzwIoMMvPDi8OzDUARt7mrjtmMmJSVhNBq19dZcK+9++i7G8yVp2eezS9bb5hkCjtx7hLOpZxn67lCn+/MUux7ZxZkvzuCFF0dnHyX/cD5nB5xFudN59Y9VtTpdJ4QQou7zmO+0p0+fpqioiPDwcLv08PBwUlNTHW6TmprqMH9hYSGnT592uM3UqVMJCQnRflq1auWeEyhHQkICZrMZALPZzKJFi7TlyJxIh9scWnXIrcdMTEy0W190qsguECqkkOSgZG15R5sddvl3/bir3P15ivRN6XbLqetSObLhSLnbnOt4rjqLJIQQopp5TDBko+/EC8UdfUunVZTfUbrNpEmTyMzM1H6OHj16kSWuWHx8PCaTCYDIyEhGjRqlLft5+wFQRBHzmKdtY4owufWYcXFxduv1zXD5hnweD3+cuGEled4d/S4fD/pYW27frn25+/MUgYGBdsuhoaEls3EDB1uspYfPMP4bM4kXWrzApPaTGPPemJouphBCCDfymGaypk2b4uXlVaYW6OTJk2Vqf2wiIiIc5vf29iYsLMzhNn5+fvj5+bmn0C4yGo0kJSWRmJhIXFyc3XLQhCByd+Ri8DHw5KwnOXnPSQD8/fzdfkw7upafg3EH+XPFn/Z5vCGhbQL8WrwY3Ci4/P15CC/Fy27Z28vbLjBs7LWekIJcPv9mJpvPnPHocxVCCFHMY2qGfH19iY+PZ+XKlXbpK1eupE+fPg636d27d5n8K1as4LLLLnPYX6g2GY1GBg0apH2w2pa9KP5w9vLxIiIyomQDN3RTKX1MPX1tSEBQQJk8BsVgP6LMWv7+PEWZjulWsBaVXGzlQv+gkJAQjz9XIYQQxTwmGAKYOHEis2bN4tNPP2X37t1MmDCBlJQUxo8fDxQ3cY0ZU9JkMX78eI4cOcLEiRPZvXs3n376KbNnz+bJJ5+srVOoNLXwQrOel2I/A7QbRpOVe9wK9q8oil0n6uouT40pFWSqVtUuTbEFgOU0zQohhPAsHtNMBjB69GjS09N55ZVXMJvNXHrppfz888+0bt0aKO64q59zKDo6mp9//pkJEybw/vvvExkZybvvvsstt9xSW6dQaWpRSTBkF7pWc+yhD25UQ9mDKSj2kw3Wk1iozHmo9rVkiirBkBBC1DceFQwBPPLIIzzyyCMO182dO7dMWv/+/evkyKZPt3zKqexTFebrdq4b/viTo+bw1Y6v6ExnoCRIqi52+3fwuV+6ZsgdzXZ1gaNmMn2aob6cqBBCCI3HBUP1xTsb32F72nZtOSwrDN9C37L5zr6DP/6cLTzLh1s+5F3eBWD/6f20pW3NFNZBY6qCYhckZWVnsW/LPm3ZP8ifqEuiaqBwbuagmUwfDEnNkBBC1D8SDNUBT3z/BNcnXl9uniJDkV2z1KlzFdcqXYwKm8lK1Qxlf5VN9lfZdnlWDFvB/T/fX32FrAYOa4Z0tWSKLVqSYEgIIeoNCYZqydtD3iYrr3h265DXQirMb2xnZGyPsSUJ1d1nqIJmuNYhrTmhnCg3T8tVLd1ZpJpR6rRVVbXrM+RRIw6EEEK4RIKhWnJ19NVA8Yft74W/A+Ad5k2TIU3K5PUK9qLF/7WAPSVpVRm9pRapDoMcg2/Zj3h9AOAoAvjkhk+YVzSvTHp6m3R803wJzgnGy+pVdsM6rsKaIVVqhoQQor6RYKiW6T9ogzoF0fmLzk7zKvt1H8CV7Md7+vvT7Bm7h0JLYZl1wZcH031Nd7wCS4IXu6DAQTDUJbwLUwZN4W/+tku//OHL+f393wlOCbZ/4r2nqKjPUL0ZNieEEMLGAz+t6hfbPEIAVFCR4uWlC1bUyn0on/jwhMNACODsprNYVpZ60rwuKLAbQq9j9xR7W5qXrmO1J8YNDobW69OkZkgIIeofqRmqbUUlfyre5X/AKl6KNutzZZvJrDkl0U3jvo1RvBTyjueRezC3uBjZRfYb6HfvrFiORpl5l8w/pDjdsO5QVZVvdn3D5hObARhwfgABBGjrk88ks+/0PtrQBgCDTLoohBD1jgRDtUxfM6R4lf8Ba1AMFNmip0o2k+lrkrr/2h2Dn4HjHxxn/yP7i9cX2AdXdn2LnNQfOnzYra52yxOayf5M+ZNbv7lVW47PjbcLhk5knuCIpeSp9YZK1sgJIYSo++r+p1U9Z9c5t4KaIYOX7r+rsnP/6fNfOIy+47Q1336Hds1wla0ZcjAUv67ac3qP3bKiKmWW9WkdTkszmRBC1DcSDNUyu2CoopohQ8l/V2X7DDnqEK346J51VqpmSN9M5iy4qbDPUBXKWdP05Xum7zM0C2hmtz62aSz3dy+ZKymoUJrJhBCivpFmslqSdFsSOftzKMwt6dSseClYLBYSEhKIj4/HaDTaLeuDoYg/Iviry1/kFebR8oGWNL23qd12NrbtG+c31tIOHznMoeRDxOTHaGn7Ju/jyAdHOH/+fHFZChW8bG1ezj73HT2mw0vBquoe4FqkVljjVRm28+nesTunXz5NZkIm5/PP0/rx1sQ8GFPxDkrLh4k/TKTDiQ6Ezw2HdPvV6m4V7xPeJc2THtkrXAghRHkkGKol53efJ3u7/YzNOWoOsbGxmM1mTCYT69ato2/fvtryl/O+1PIGZAeQvzMfBYUjTxxhyBtDSD6ZjMlkIikpSQukbPv7yOcjLuESANq3b49VtXKd8Tqe4ikAlFMK+afy8Xbwksj3ynd4DoaAshWL6dnpZJ8vOa8zZ87QtHnTyl8gB/TnMzJkJI9mPlpcdhT2jN9D6M2hNGlWdp6m8gT+GcgNCTc4Xa/kKRSdLOlc7kXehRVSMySEEPWFNJPVEsVbQfVWKbjwz4yZTaZNmM1mAMxmM4sWLbJb3pu9l2Xdl5HvlU+BUqDtyxtvzp48q+WzPZg2ISFB276ooOQD3VZzs9Kyksy2mVoZyvwzFHC42WESuzp+0K2P0QfrLVZyyaWAArazneUZy+1qhrYkbnHXJbM7HzXTvoYmUA1ky+bKH8sro6THdxFFFFBAJpkc4QjnOFfqimygMTuKM0swJIQQ9YbUDNWSyxIus6vpiIyMZO3TazF9Z9KWR40axYwZM7Tl2M6xjB8+nmnDp8FWePmHlxlQNACAZpHNOH3mNBEREcR0jsGSY6FtbFvCW4eTlpaGr9UX8os/8JVABdWqEhYRRusfWzN06FDS0tKKm71sXWKiFNQ7ihce7fqo0/Po8UkPYv/SncNda/nxgx+19d26dXPbNYuPj8dkKr4+xsZGyLJf371b90rvU9+X6s2Wb7LyxEqsVisREREApKamYjAYsFqtLPf3x5ArT60XQoj6RoKhWmQ0GklKSiIxMZG4uLgKl48XHC/ZuDtY91shqXjxzKgzYIRUUon5WNd35t7iX4UfFYK5uDO0+nRxAJBKKj0W9tDy6Km6vjH+/v6VOoegRkHa+tDQ0MpeFpeO1XJtS8yTzXbrq3QsXWzzj+v/wQdPf8ChQ4eIi4sDIDExkZiYGA4dOsRVb70Fy5YVZ5aaISGEqDckGKotI0fCvn0YgUG65PKWC/wK8boOii40bloNJZ/kXmr501fbhofrnzTvKtNHX8CTK5yuL11mJbtk9JV6RU9QispsU1W2Yx05eQ1wo/3KK3qCwXH/JmdUQw9s0WCrv9YRfdMnROvW284rGuDw4SqUWAghRF0nwVBt2b8fduyo1CbNgdkFsCgWrAqYzpYENgOSFSzpzrcNySuOoAwqDNvv+jHbp8O4NamQm+ryNmpEyQg5667dYM1z/YAu61r2uElJQG6l9qK2aaf9raSnw3EX/k8UBfz8KnUcIYQQdZcEQ7XF3x8CAyu92T37i38AducZSLuQ/vHKIIIMzve3KceLbMDXauXnJZU8rgGozCb6eYYCA6Aanl6vFvhBQanEgCBQKjkmwEv3FvA2VPx/4uMD48dDSEjljiOEEKLOkmCotmzceNG7UO7bA59eqLFJSITOQc4zd9kEO7MhKBDOZTvP5w6xn8KF7jzq0WMQWk65qkidnAxTjtgnpqZC40q+pP/5ObxX/Kfy2KPwxC/uKaAQQgiPIUPrPZh+Bmi7Z4k5YBs15fB5Ym6mf8p9ZR8o6zJH3ZCqcCj9DNSOZtQWQghR/0kw5Mn0rU8V9Yu2ra/h//HqehyHoyCrSsdy8Mw2IYQQDYsEQx5M/ywzl2uGaqL2Q3cIq7V65uVxeL5VqRnSBVX6x50IIYRoOKTPkAfTBzbpP6Vzfvd5p3kLMy+M8KqJz3t9B2o3NJNZ862cWXGGosyStrHsnQ76PVXlUPpYTWIhIYRokCQY8mS6ZrLDLx12bZsaqBjST9jojmBo30P7SJ3rwtD+izyUvqZNCCFEwyHfhT1YcFxwjWxTabpXlTv6DGWuz3QpX1WOpQ/WaqJzuRBCiLpHaoY8WPhd4fg09yHnQI5L+b2CvGg63D1PkC+Pu2uGbE1ZhgADMdNKHjWiKArH3jlGzv4c24GrvG+Q0WRCCNFQSTDkwRSDQtjQsNouRln6PkPuGE12YReGAAMt/6+l3aozv5xxWzAk9aRCCNEwye1fuJ+bgyFtH44qbvRpVTmUbhuDl7wdhBCiIZKaoXrAYrGQkJBAfHw8AAkJCbRt25aDBw8SHx+P0Wi0y2M0Gqu3QLoA5ciGI2z7fRtRUVGkpKTY/zanED/EeZk1F2pvCgoLsFgsdufTpLCJlu2P3/8gfrD9ttY8Kyd3nWTnzp1ERUWxe9duADp17kRKSgpFJ933EFkhhBCeSYIhD2exWIiNjcVsNhMeHo6iKKSmpmIwGLBarZhMJtatW0ffvn0xm82YTCaSkpKqNSCyqiVtT+dGn8Mbb05wwuHvt/3f5pPQT8qUWV9Ga1Hx/iyZxeeqP59pftO4nMsBGD16NH4mP23b3KO5bI7bTOHpQu2YIRQ/U8x2/La01cqam1e5h7wKIYSoH6RdwMMlJCRgNhc/CCwtLY3U1OIh6LbJDs1mM4sWLdLymM1mEhMTq7VMp4JPuZy3f25/h2XWlzE758KcQv5gHmDmH/P/gXmAGW6HnGYlnceVmxTMA8xc9/l13PDVDbw65VUKTxe6XJbD+YddziuEEKL+kJohDxcfH4/JZMJsNhMREQFgV8sSGRnJqFGjmDFjBmazmcjISOLi4qq1TIkjEjlWeIymZ5vCLhw+RyyeeIwY8cKLyPBITqSdsCuzvozZRdmEEorqrUIH2G3dDR0urNxask+lrQKNYYNlA1jA54QPgxkMwM6WO0k1Op+raFPbTTw28LGLP3khhBAeR4IhD2c0GklKSiIxMVELIBITE4mJieHQoUPExcWVyVPdfYYKmhfw0bUfAbBp4SYyT2Rq5bH9DnwhkLwNeQBsT9jO1j1by5TZxlZjpFbUQ7rUaoNaUvG5pOcSfuvym9NNuzXrxrWdr63MaQohhKgnFLW6nqRZT2RlZRESEkJmZiaNGzeu7eJ4hBu/upEf9v0AQNqTaTQPal4mz7Yh27CssABwZcaVeIc4j8u/Df2WJplNSA9Jp9/xfnbrjt55lKzvsgC4ZM8l+LT00dad/t9p0p5NA6DlZy0JuSXE6TGaBjaVSReFEKIeqcznt9QMCbfTBxXOYm3FpySPtaCCh7naRtYrCs2CmtmtOulzUvu7SUAT/IP8teVc71zSKA6GGgc2LrOtEEIIAR4SDB0+fJhXX32V3377jdTUVCIjI7nrrrt4/vnn8fX1dbrd2LFj+eyzz+zSevbsyYYNG6q7yA2aohtbv2TPEkL9Q8vkCc0JxZ/iwGVt+7WohpKgqbBzIRnTM1CDitN8rb62HTs6WIlScZf+yfYyu7QQQghnPCIY2rNnD1arlY8++oh27dqxc+dOHnjgAbKzs5k+fXq52w4dOpQ5c+Zoy+UFT8I99DVDD//0sMM8T1me4jquA8CQYT+o0WutF7PemMWqbqsAWKwuBkBVHNQylTPBo91zx+QhrEIIIZzwiGBo6NChDB06VFuOiYlh7969fPDBBxUGQ35+ftooK1EzekT0YOmepeXm+abXN7RIb0GzrJKmq8D8QELPhwIQlBdUZhtfbweBbHkzUMujNoQQQrjAI4IhRzIzM2nSpEmF+dasWUPz5s0JDQ2lf//+/Pvf/6Z587IdeoX7PHvls3Ru1pnjWcfLzzgGTlEyJ1Ho8lBCp4QCMLLjSAYOGQhA8DvBkA1hgWWfw2bX6VmayYQQQlSBRwZDBw8e5L333uOtt94qN9+wYcMYNWoUrVu3Jjk5mRdffJGrr76ahIQE/Pz8HG6Tl5dHXl6etpyVleXWsjcEvl6+jOw8stLbpR1KYzfFj8sYEDWAlr2KH8q61rCWQgodPztMaoaEEEJcpFr9iJg8eTKKopT7s3nzZrttTpw4wdChQxk1ahT3339/ufsfPXo0//jHP7j00ku54YYbWLZsGfv27eOnn35yus3UqVMJCQnRflq1auWWcxUV0/fr0ff30Y8mK7uRLpv0GRJCCFEFtVoz9H//93/cdttt5eZp06aN9veJEycYOHAgvXv35uOPP6708UwmE61bt2b//v1O80yaNImJEydqy1lZWRIQ1RSvkj/1TVxajc9FjCaTmiEhhBDO1Gow1LRpU5o2bepS3uPHjzNw4EDi4+OZM2cOBkPlP93S09M5evQoJpPJaR4/Pz+nTWiietn169E/wsMW0zhqJdPVFuWl5NnVABWeKXkumfQZEkII4YxH9Bk6ceIEAwYMICoqiunTp3PqVEmnW/1IsY4dOzJ16lRuvvlmzp07x+TJk7nlllswmUwcPnyY5557jqZNm3LzzTfXxmmICjhrJrP9XVEz2bZrtrm0byGEEELPI4KhFStWcODAAQ4cOEDLli3t1un7iezdu5fMzEwAvLy82LFjB/PmzSMjIwOTycTAgQNZuHAhwcHBNVp+4aIqNJP5t/Yvm+iAX0up7RNCCOGYRwRDY8eOZezYsRXm0wdGAQEB/PLLL9VYKuFudk1Z+pFg5TSTtXy8JWqRSu6RXCc7hbBhYQS0DXBXMYUQQtQzHhEMiYbBrpmsyLVmMp8wH2Jej6n+wgkhhKi3JBgStcpisZCQkEB8fLxdzU/y98lk5maSnp6OV35x+1mRtcjJXuz31bZtWw4ePKj9jo+Px2g0VudpCCGE8GASDIlaY7FYiI2NxWw2YzKZ2PBByQN0DVsNZGzNwEvXkWjvvr10sHRwGNjo92UwGLBardpvk8lEUlKSBERCCCEcktlXRK1JSEjAbDYDYDab2c9+1EAHD2O9YHPhZhITEyvcl9VqtfttNpudbieEEEJIzZCoNfHx8ZhMJsxmM5GRkcT1i6NwayHjeo7DYrFgUAxYVSsGxUCWmsVp02leiXulwn2VrhmKjIwkLi6uhs9OCCGEp1DU0s8wEHaysrIICQkhMzOTxo0b13Zx6h2LxUJiYiJxcXFaM5YtLSYmhkOHDmm/9XnK21dltxNCCFH/VObzW4KhCkgwJIQQQnieynx+S58hIYQQQjRoEgwJIYQQokGTYEgIIYQQDZoEQ0IIIYRo0CQYEkIIIUSDJsGQEEIIIRo0CYaEEEII0aBJMCSEEEKIBk2CISGEEEI0aBIMCSGEEKJBk2BICCGEEA2aBENCCCGEaNC8a7sAdZ3tObZZWVm1XBIhhBBCuMr2ue3K8+glGKrA2bNnAWjVqlUtl0QIIYQQlXX27FlCQkLKzaOoroRMDZjVauXEiRMEBwejKIpb952VlUWrVq04evQojRs3duu+RQm5zjVDrnPNkOtcM+Q614zqvM6qqnL27FkiIyMxGMrvFSQ1QxUwGAy0bNmyWo/RuHFjebPVALnONUOuc82Q61wz5DrXjOq6zhXVCNlIB2ohhBBCNGgSDAkhhBCiQZNgqBb5+fnx8ssv4+fnV9tFqdfkOtcMuc41Q65zzZDrXDPqynWWDtRCCCGEaNCkZkgIIYQQDZoEQ0IIIYRo0CQYEkIIIUSDJsGQEEIIIRo0CYZqycyZM4mOjsbf35/4+Hj+/PPP2i6SR5s8eTKKotj9REREaOtVVWXy5MlERkYSEBDAgAEDSEpKqsUSe4Y//viDG264gcjISBRFYenSpXbrXbmueXl5PPbYYzRt2pSgoCBuvPFGjh37//buNqTJtw0D+DF9NglbVmRuWtkKImpi9K70Kjg0BoZfrD6oBYGWkb0QUR8KhDRJCdMIorI3sCJNoTcspyARmI7UshC07B8bovSmljY9nw//5xksNVfqNt3xg8F23dd9c10H54dz9zb2jwt34flGyjk5OXlQfa9du9ZhDnMeWWZmJlatWgW1Wo3Zs2dj69atePv2rcMc1vToOZOzp9U0myE3uHXrFtLT03H8+HGYzWasX78esbGxaGtrc/fSJrSlS5fCYrHYHw0NDfZj2dnZyM3NRX5+PmpqaqDRaBAdHW3/7zkaWnd3N8LDw5Gfnz/kcWdyTU9PR0lJCYqKilBdXY2uri4YjUb09/e7ahseb6ScASAmJsahvh88eOBwnDmPrKqqCnv37sXz589RXl4Om80Gg8GA7u5u+xzW9Og5kzPgYTUt5HKrV6+WlJQUh7HFixfL0aNH3bSiie/EiRMSHh4+5LGBgQHRaDSSlZVlH/vx44cEBATIhQsXXLTCiQ+AlJSU2F87k+vnz59FqVRKUVGRfc7Hjx/Fx8dHHj165LK1TyS/5iwikpSUJHFxccOew5z/Tnt7uwCQqqoqEWFNj5dfcxbxvJrmnSEX6+vrQ21tLQwGg8O4wWDAs2fP3LSqyaG5uRnBwcHQ6XTYtm0bWlpaAACtra2wWq0Omfv5+WHjxo3MfBScybW2thY/f/50mBMcHAy9Xs/s/1BlZSVmz56NRYsWYffu3Whvb7cfY85/58uXLwCAmTNnAmBNj5dfc/4/T6ppNkMu1tHRgf7+fgQFBTmMBwUFwWq1umlVE9+aNWtw7do1PH78GBcvXoTVakVkZCQ6OzvtuTLzseVMrlarFSqVCjNmzBh2Do0sNjYWN2/eREVFBXJyclBTU4OoqCj09vYCYM5/Q0Rw8OBBrFu3Dnq9HgBrejwMlTPgeTXNf613E4VC4fBaRAaNkfNiY2Ptz8PCwhAREYGFCxfi6tWr9i/lMfPx8Te5Mvs/k5CQYH+u1+uxcuVKhIaG4v79+4iPjx/2POY8vLS0NNTX16O6unrQMdb02BkuZ0+rad4ZcrFZs2bB19d3UGfb3t4+6N0I/T1/f3+EhYWhubnZ/qsyZj62nMlVo9Ggr68Pnz59GnYO/TmtVovQ0FA0NzcDYM5/at++fSgrK4PJZMKcOXPs46zpsTVczkNxd02zGXIxlUqFFStWoLy83GG8vLwckZGRblrV5NPb24umpiZotVrodDpoNBqHzPv6+lBVVcXMR8GZXFesWAGlUukwx2KxoLGxkdmPQmdnJz58+ACtVguAOTtLRJCWlobi4mJUVFRAp9M5HGdNj42Rch6K22t6zL+STSMqKioSpVIply5dktevX0t6err4+/vLu3fv3L20CevQoUNSWVkpLS0t8vz5czEajaJWq+2ZZmVlSUBAgBQXF0tDQ4Ns375dtFqtfP361c0r92zfvn0Ts9ksZrNZAEhubq6YzWZ5//69iDiXa0pKisyZM0eePHkidXV1EhUVJeHh4WKz2dy1LY/zu5y/ffsmhw4dkmfPnklra6uYTCaJiIiQkJAQ5vyHUlNTJSAgQCorK8VisdgfPT099jms6dEbKWdPrGk2Q25SUFAgoaGholKpZPny5Q4/OaQ/l5CQIFqtVpRKpQQHB0t8fLy8evXKfnxgYEBOnDghGo1G/Pz8ZMOGDdLQ0ODGFU8MJpNJAAx6JCUliYhzuX7//l3S0tJk5syZMmXKFDEajdLW1uaG3Xiu3+Xc09MjBoNBAgMDRalUyrx58yQpKWlQhsx5ZENlDECuXLlin8OaHr2RcvbEmlb8b+FEREREXonfGSIiIiKvxmaIiIiIvBqbISIiIvJqbIaIiIjIq7EZIiIiIq/GZoiIiIi8GpshIiIi8mpshoiIiMirsRkiogkvOTkZCoUCCoUCSqUSQUFBiI6OxuXLlzEwMOD0dQoLCzF9+vTxWygReSQ2Q0Q0KcTExMBiseDdu3d4+PAhNm/ejP3798NoNMJms7l7eUTkwdgMEdGk4OfnB41Gg5CQECxfvhzHjh1DaWkpHj58iMLCQgBAbm4uwsLC4O/vj7lz52LPnj3o6uoCAFRWVmLnzp348uWL/S7TyZMnAQA3btzAypUroVarodFosGPHDrS3t7tpp0Q01tgMEdGkFRUVhfDwcBQXFwMAfHx8kJeXh8bGRly9ehUVFRU4cuQIACAyMhJnz57FtGnTYLFYYLFYcPjwYQBAX18fMjIy8PLlS9y7dw+tra1ITk5217aIaIz9x90LICIaT4sXL0Z9fT0AID093T6u0+mQkZGB1NRUnD9/HiqVCgEBAVAoFNBoNA7X2LVrl/35ggULkJeXh9WrV6OrqwtTp051yT6IaPzwzhARTWoiAoVCAQAwmUyIjo5GSEgI1Go1EhMT0dnZie7u7t9ew2w2Iy4uDqGhoVCr1di0aRMAoK2tbbyXT0QuwGaIiCa1pqYm6HQ6vH//Hlu2bIFer8fdu3dRW1uLgoICAMDPnz+HPb+7uxsGgwFTp07FjRs3UFNTg5KSEgD/fnxGRBMfPyYjokmroqICDQ0NOHDgAF68eAGbzYacnBz4+Pz7PvD27dsO81UqFfr7+x3G3rx5g46ODmRlZWHu3LkAgBcvXrhmA0TkErwzRESTQm9vL6xWKz5+/Ii6ujqcOnUKcXFxMBqNSExMxMKFC2Gz2XDu3Dm0tLTg+vXruHDhgsM15s+fj66uLjx9+hQdHR3o6enBvHnzoFKp7OeVlZUhIyPDTbskovHAZoiIJoVHjx5Bq9Vi/vz5iImJgclkQl5eHkpLS+Hr64tly5YhNzcXp0+fhl6vx82bN5GZmelwjcjISKSkpCAhIQGBgYHIzs5GYGAgCgsLcefOHSxZsgRZWVk4c+aMm3ZJRONBISLi7kUQERERuQvvDBEREZFXYzNEREREXo3NEBEREXk1NkNERETk1dgMERERkVdjM0RERERejc0QEREReTU2Q0REROTV2AwRERGRV2MzRERERF6NzRARERF5NTZDRERE5NX+C+Js72XMlDMSAAAAAElFTkSuQmCC\n",
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diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter8.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter8.ipynb
index 815adfb3c..e3b7593db 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter8.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter8.ipynb
@@ -295,10 +295,10 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0.26662339374864535\n",
-      "4.736115211426478\n",
-      "[[ 1.20561803  3.63264564]\n",
-      " [ 3.63264564 12.10207647]]\n"
+      "0.03822007730337899\n",
+      "3.989393825676568\n",
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+      " [2.80659468 9.73667253]]\n"
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@@ -340,10 +340,10 @@
      "name": "stdout",
      "output_type": "stream",
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-      "0.09318696260700278\n",
-      "1.9096305360355206\n",
-      "[[1.         0.65907898]\n",
-      " [0.65907898 1.        ]]\n"
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+      "2.0511284278960114\n",
+      "[[1.         0.68282072]\n",
+      " [0.68282072 1.        ]]\n"
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@@ -397,30 +397,30 @@
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      "output_type": "stream",
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-      "          0         1\n",
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@@ -461,37 +461,37 @@
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       "\n",
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+      "7   0.079546  0.079958  0.073337  0.073717  0.073955  0.074102  0.074193  \n",
+      "8   0.080384  0.080965  0.074161  0.074692  0.075064  0.075330  0.075529  \n",
+      "9   0.080965  0.081699  0.074752  0.075418  0.075911  0.076288  0.076588  \n",
+      "10  0.074161  0.074752  0.068701  0.069233  0.069621  0.069911  0.070139  \n",
+      "11  0.074692  0.075418  0.069233  0.069886  0.070381  0.070769  0.071086  \n",
+      "12  0.075064  0.075911  0.069621  0.070381  0.070975  0.071453  0.071853  \n",
+      "13  0.075330  0.076288  0.069911  0.070769  0.071453  0.072016  0.072493  \n",
+      "14  0.075529  0.076588  0.070139  0.071086  0.071853  0.072493  0.073045  \n"
      ]
     }
    ],
@@ -916,10 +916,10 @@
      "output_type": "stream",
      "text": [
       "          0         1\n",
-      "0  4.059118  2.009163\n",
-      "1  2.009163  2.004788\n",
-      "[[4.05911793 2.00916336]\n",
-      " [2.00916336 2.00478786]]\n"
+      "0  3.965838  1.971865\n",
+      "1  1.971865  1.997830\n",
+      "[[3.96583833 1.97186457]\n",
+      " [1.97186457 1.99783004]]\n"
      ]
     }
    ],
@@ -949,13 +949,13 @@
      "output_type": "stream",
      "text": [
       "Centered covariance using own code\n",
-      "[[4.05911793 2.00916336]\n",
-      " [2.00916336 2.00478786]]\n"
+      "[[3.96583833 1.97186457]\n",
+      " [1.97186457 1.99783004]]\n"
      ]
     },
     {
      "data": {
-      "image/png": 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+GNB2vO5MvUQLjwzQ4jq85wNqcSYxsk8TE4CzlTXRHkOiPabukikSw1M7fB4MPa81GkGivVm9j+0Hk+pzGRyegAU4TMy8PkPT+06O5FxXM7Nsmh2vpTQRt2PvevRF1X0zyrpw+GL7oZtbXQWw3FLdSxzofzcOfSa6uPF771SjwgUjHc/ebC1KoWKEIkJBpwUX8vxaZaHfw0IQISIIQk1RSETDBF0gTXem/PeAt2jh6Qm+uB7akXBEKuhYU7YNOqonX8rVTXR3tLA7/XHHfuPZCAO9Z86HN8Rd6Q6KgACADTiKRXUo4kJpIb3+ozUaQX9vl0MkEbxQlUQWTfs9tCOB/mxBLO0/bFkq3cVFiB6FSY5Mei5sBBdJJkxGXzo8akRiRO94yncOFbrPhTy/Vlno97AQpEZEEISaYqG5dl43we9MaZv6XTffH+8OocJLfX/clIxfjHf1dqm6BsBcu0DFltsPJh2zYnTjsWdPjjrqSnjEhW/by+yKogLcypw6TICM0Onr6cSzrLCWjiXXFeTs/rGRESkb22I4cW7SMQX4xLnMfjIibtzheaJ/xvqxEtxzhBxkM++l2dh27Gf05dfxVEiqpFBzsaVkRlbJmhfLtu2abUyenp7GqlWrcOnSJTQ1NVX7cARBqCB00SMxUcwCAsDh50EdL3pXQypt46tHz6iQ/9DjW/PugwpKdVdRojUawY93bwGQicI8f2oMo1MzDmdQfbHv7+3CN18ZwfTsvEt8mLbL36v++egdLXwffT256b3xaATx2ApHKsb0GhICTY11mJ6dV8KF15LwrqJCioV5xII+E/53M0Wn+Ou89sk7nvh7D0K+z3Whjy8Wiv0eFrJ+S2pGEISaQM9J81w7hf8XyvmpGWPtyPOnxlStRqnC6WNTM2o7J85NYnRqBhZyRaJchFBcZe/AEG5cswoAHOker+3Swt7d0YxXzzhrMEw1F6bpva/s3qJSLoPDE6polqCF59COBOLRCKZn5wFAiRCeruruaMbh+zarhcr0N93V24V9rO5lH0sh0WeSaI9h6PGtqlA4bXsbfXEhyPdl6ngqRAj4mYvxwuNin79YqETNi6RmBEGoCXQfBsq1U2Tg+VNjxrZbPydS7oFxbVODWnx5qJ/utinSEDScbvLR4FBK4ZmToxibmkFDXQhz82klduh1JAZoWzwiYVq69FSF3jLrh94qzFuJAXcKSBeAd9/civ1HTsPO/o5PA+7uaFaOr4C/SRlFh4BMCig5MolQdnuZ99jiKpj1gopY9b8F/zfveOKW/X6YzjW/1vBwyFssL8ZICGGqeSn1+xEhIghCTaD7ZPBFiPtakH+Gycxr/5HTePXMuNEBdG1sBcamZjA6NaMWUQtQC+KHN8Rdx8F/5vAFiVIpOrR4kq/I3HxavQ+iqbEO97D98hkx0zNXPbdL3Tx+dQ9e6SmK/JAI4WIBcIoRXv8BZBZbXijLIzz6TJ7jZydUGzL3WuH1Mdyllrc+0+fPIwmmRZ6LUP3vRujzeQoRIzrLzbSsUjUvkpoRBKFm4B0PJBb6e7scvhbPnxpTLa2mi+St63OtsbxrgxZuAGqhpaWND4/jx/H0iTeMbYq0IG0/mMT07LwxhaJD/hzcW2N6dl6lFHgE4FJWhFja6wkupnhkQ0850ese3LJe+YDQ+7/9iaM4fnbCIULi0QhSto2mxsw9alNjneoQ0jth4tEIbECJEX3f5PvBhdO6rFcJRYHob3ri7JQ6Buo6ovdFrqt6l4ape6OvpxP8aX4dT8VQSGv4Ysf0vkzvvxRIREQQhIoRxPV0Y1sMx0cmXV4RvBOCFuHujmak0rZ6XL+bpn3u6jUXlBJ+9uGmNkV+901RDgvmVAqQWeDp+HmHTFNjHZoib1N1EXTMtG9KgaRsG2nmNwLkIhsUKeB369QqTAtvLuWR+bmhLoTRqRkVraFjofehF6NyUcNrTKhwtaEu5OpsAaDqV/j7AaCiW/S35F4q+t+9kO6N/UdOI20DIQswZUl4x1OxeHVZLSURAlR2AJ8IEUFYphRrhb4QC/WgoW1ajPSc9KEdCVWTQGKERAstkvvYdkzh8tZoxLEA04Jrqi/gg+1M0OJNi6iXGBmdmsG7Hvu+SrV0dzTjjcm3MDY1g+nZebRGI0iOTOLUry+6WnmvW92I0akZRysuwVMnfIE0iRoqLCUBADgjQvwxC1B1K6l0RgSNZVt7TaJvbj6t9pV5L876G/1zsQDH77nAMv3dgyz+QdMIpRAMfT3OGTxLTYQAlR3AJ0JEEJYpxea7F5Inz3d3S7/zWkz0wjl+N81D7l6eE7xGg7bB/Tz0Vlr9WHlhJ3+unwghuAihaA4JojHWUUNQKsZUqMlbaHk0h3++JGroubywVK9VSbQ3K0EH5DxD9FoK+hxbswPxTOH56Zmrqs2XR03458MjI3qBLFnj6+dYX08nnnzptHHx5228JvFC9Sk6+YSzF5Uo4FxOiBARhGVKsYZFCzU68rq7pcd4vQZ/7rMnRzE6NaM8I0hs0EJGKQRa8Ph29BSBLlDWRCO4cHHWcVfO34cyFmMiLNEec3R6ZNIoQCpPxFrvBCFRwF/WUBfCxrYYdvV2oe3hF1zbmJ6ddwga/rdIpXNtyGHLcjyXCky5COGvJ0jgeBV2jk3NOLpluFgiwTU9O49wyHKkeXQBBOTqdXQhSrUIfDoxPfdKKq0Kl3f1drFUVItj27wAWBcLxRaYLiXTslpBhIggLGOKzXfnex1FDsh9lLuUKldStlhSvpkXE3IxQiJENwHTzbSAXGphcHgC2w4cQ3dHiyp4pNek0rY6jkR7zJX24MWXJGLI1IkgEcIXVxIhJrMyjqNANLbCtTjPzafx/KkxR8cKh7pUcu+hWX2GJ85NqghNyrYd3Sn0+QAZsbFG+x09lhyZVK+7/YmjjvZi3hZNn3O/5ipL0DFx4zOVjsmeFzxSwoXjLmaiZkoH0XHvP3La5eTKoc+pFA6hXgWcdEz8ZyE4IkQEYZlTbL7b73UUOdCFAq8d4IvliXOT6s7btGhw8yyeDki050bEq32zUD+3OU+0x1SdA5BbQGmkPUGpBF3sABmBErKQ3WfmMfIg+Q2LqLx+/hJ+dv6S7+cXtiy8Y3Wjp0fGaLbVWI8i8C4VU8suX+wpPeK1/XhshWO7o1MzuGdDHN0dLdg7MKRez71H6HMAcpEnAC4RwiHBoosRr6gOwWtaeKEsQYW4+QRFqQpMK1nAuZwQISIIy5xi891+r+MXfr748NoBfTEy1TmYFg2KYoQsy2UF3t3RjDcm3gIsOApSgUwEgx4jK3L6N0GpBA63NQcy3RhpbdHl03CvpNJG/w+dlG1jeuZq3udxIcEFBqUtKD3B6yQO37fZUZTqxetZscTTW/xvz63vyXHVlJoyFaaSgRv9rIsRntqgqI5JjJBJGq9x4VGZkBUsCsGFs5fLar6akUoWcC4nxEdEEJYoQcZ4694Q3CPA7/Xcw0N/HUGeA1THQQsqFS7S7BCyF+ev7+tx2rvzi/yu3i50d7QoQzISIWQRPnYx05ZKXhiEviiHsikh8teIRyPGO9r6sFOcUIcLh4RV49ucl9R8/iImwdJQZ74skw8JiSLy+KD0DUWFKMJzaEfCc/80+ZfPtNE9NsjDg7fWklDo7+3C4fs2I9Hu9DYhIdPUWIe5+UyhLIkQ+j8JSaKvp1MZkvVn6z24d8uu7DmiDzCkf6dtBPK00J16aTIv/73uSyJUBomICMISJV93i8mV0xTJ0F/PQ+VUa6HnyVPpTLqFj4vnkDunvl8SAtsOHHMtGuSoCuQWXb7IkZW6aUCbDr03mvLaamgjJa5kCz/i0Qju2RD3rPswpUCKCdTTAm6KzJCBGhcj9DcgF1MSE4PD48b9c1EI5CI5ei0F4OxgWvfwC8rXxFQE3Mq8UshbhBeq0t/pwsVMSsirpiLzPpxFp3r0rdBiUb22Q3dZraYp2ULa4ZcKIkQEYYmSr7uFwuF++W49XM7dP/kFnLdHkggZHJ7A6+cvOQQFYapz4GZiFHHYeWeu62F08i3XYs/F0lg2KgE4PSpM/HriTVUsC2Ts3Wk/JshX412Pfd/xeH1dCFfm08bXeIkgr6m6nMvsdXw7FF3iC/zJc1M4fnbSuDCb3oe+b9PfYnB4HMmRSdUOy+fL8JktNMCOn0c8lQKYC1V1o7R8JmV6ezcnX7Goabu89kSfvVNplpttvAnLtvN8I6pIIWOEBUEwQxe0Qsd4B309j5BwccLv2k3/N0VkvDxFTCJBX5jojrs1GsHa7Fj7oPDaC6/6Dr/fFQrVT5iOY0xr5QXg8ijRDdTqwyH81b/uwPGzE46W4nz7JHM3/W+x7cAx1YkC5CJkfAGnNmoAePXMOG5d3+L4Ox58ZcQhqPS/F73e79zSRYTu46KfO6bogV/EgURIfTiEoce3un5fKbxaghezY2sh67cIEUFYwtBFmHe3/NW/7lAXc37hpgFoVPzIL+D6BVu/6Ot23bSw6wWLup+EvgDqi4Yugjj8Mfo3iQXdPRVwL+YEtyk3iYNKontyxKMRnL84g7TtPn7LAmzbKcD095wPXWjoxaT67yiSpg/K43/PtG0jOTLpOh76G9G2Eu0xbFrXrIphuRigczGVth0CB8gJDmr/5edvISmOhQr0UlNrx7NQClm/pVhVEJYwFPbl+fUT5yaxd2DIVZhHiwsVP9Jrb3/iqCpYJCMp/bWHdiQcKQcSG7SwU1ifBp3xRSvRHlO1Ibu0iy8vWkV2GwBcRarkxkmRFi8RoheCtq6OqChHISIkHo2gHDWNfHGn7iKqn9VFlM0eDypC6sMhJNpj2WhEM149M+4qKubCkNpVeUHxc6fGVJqF4NN0KZKifzzclp+KXcnzhM6tbQeOYf+R0+pc1EXptgPH1LlHRa7E8bMTroJpet3egSEcPzvhesyv2LrS8HN9qdrGeyFCRBCWCQ9uWa8WHB1e+8FbaXkEY3jPBxx3za67VBZc5aKDoNoCWogS7c2qMJEvKPoUWR4J2dQeU50YRHJkwuHGaXp/9HxdbFiWubMlHo04FlodLhDy4dUFk49C0kBBRAiJt+6OFtV1RJOKaRHkA+f0CAMJFtoXiUmKnPB6nL0DQ+q80c8B7geiip6zjydHJpVZGT8Xc7VI3sZllCbaO+A1hbjF8VglpsoWgqkdfrkgqRlBWKKY6i10z43B4QlXKFi1MWppFj20rj+fHtdfp6cbuOuoaVExzYXR567oRaJUvwAAtz1xFGMeHTAcv1RMf28XvvnKiK8YoNSIF5Q6yIdfUS0QzDY+KPxv0RqN4EM3t+LEuUmVTqHPjHuE8LoRADhxdsrxuZrSZkBG+OzKLu56WklP/1BxLP+bmYpT86UruPDgx2Vy/a2lLhWpEREhIgiLgkIvoPrzyQyqPhzCg1vWI5W28fWXh9VjvFiPT7gd3vMBx2t5jYjuoEoXztufOKruiF/ZvUW9nqNfZPnx0uv9ijpNHTRc4ADuDgv+XK9i1nzCoByUe59eoojv11QUbLLQB4J1/ujbIHiBLP97cbOxP1jVgPMXZ111QKb6JB29a4jqWmpNfPD95+sWWoxiRGpEBGEJQou+Vw5cN2Li9RZ62Je2ZwoF8+dSOsXkoLore4E3db/cfXOrWuT469V7MThb0vvbfjCpXp9PhFDNCJCJluRE0binCKHnmrYLmP1Ayk2596mLkO6OZuWdQjx7ctRV+5Fob1Z/X352vWN1oyPlYmJl1lCOzg0Sh9Rm/euJN5UTbHJkwnHOXd98DQA4RIhXfVIQCv3uVBI/23gSUUsd8RERhEVCPl+QoGZO/I5Rf4zuiPUJt3pr7uDwOA7ft1l11+iW57t6u7Crt0vVhKxZ3Yjrm69RAiBl54zQ+B0pvyN/ZfcWZaLF4Ysn9xkhyFwrCK3RiMNDxKuzZqlxbHjC83PlXU37BobU8/jzx6ZmjHUp3PTtspbW4uevKQqjn2OcB7esdzwv37kO5MQLrx8yfXe4y6tpe+WOlohtvEREBKFmCGLJzovquh59sWAR4kVfT6cjDE/+DnrRIJEcmVQ/k+X63oEh1fVA+yaBQPUGrdGII21y2xNHHXekh3Yk1P7aDCKECFuW+hzoGDlB21g/vCEOIDdPRt9fsYWmJkp1zx0uwYboffb3djmiSsQ9G+IIW5bx889XxEvbbV2dex4fSkhQEMLrHAOgbPr9zkV9XAHtn7ph6PX0uP7doXO3FqMlywWJiAhCjRDUYZEP78rX5sfDvlSDQY/R72kflGbZ2JZx08y5a+Ym3HKTKx4y5ne75IpKi4/ufgpkFgSyZOfP7evpxKEdCbQ9/ILvZ5WybSRHclGQ49rsF8Dpu+FVa0KfN0/38FZYek2+wtQg2CjcFM1U21GqwlXAu4am0Noa/vd85uQofrx7C+uMyZw37Y+8oDqNKFoxODzu6Qgbj0Zw982tqo6J74uft/TdoHPIa2QBRfG8vjuFRhqF0iFCRBBqhKCpF7+pt4Cz6JOHfUno0HRWQrd9pzvAw/dtdpkskeW3aV/8+Ll7ZtrQBcE7cKhjgwTMN18ZCfR50R3y8ZFJY+Ek+Wv838tzeT1CeHfOG5NvubdVgsW/EBFCAsSvPsCvK8dUTMrFlOn3+Y7PArKC1C1EkiMTSsCNTc2oc5LOieTIpBIh7m6rXAvxky+dVi3Er+ze4jrXM2nDTPSLt4KT5wlta9/AkDr3+cgCr+8OP3dNE5+F8iKpGUGoIfKlXoIYMfGiTxPJkUnViqlHW3RTKN1QTB9GphcB0vOJE2enHN4PumnToR0JHL5vs0OkeC2GpuLIweEJ14LKnzc2NRPYqIxeR9EQvxREMUzPzgcO8wcpUPR7Tsq2XfviH5NJuN24ZpXve7YBZd1PUNHr4PAEzrN0GEUn/Obe6N4d5EWjF6aa0ixfPXrGVS+yi/1ef+99PZ3qXPX67ixnQ7FqIxERQagReHRBDx/zELdX6Jl+7uvJFXDq00UpBZEcmXQM+6Jt8Jz54PA4ujtajB4RhL5/AI7nc4MswDuaw++GdSitEnR2zMlzk77tsF6RBNq+7llSSsrVAUHRCJ6OSqXtgmzr871f8jMhoci7pXghKbmr0vlFx0f1ODxNQueFfm7z+UWmc53cWLn5nl86xcvEjLZH+EUahfIhQkQQagS6Y+OtjHRnSJ0sXm1+gHORM00X1T0haJGgRYSHzDOP59IletGfbsPOfwc46yzoPZBnBNWh0PslwWOaCmvD7YZqqlNoqAvhprWrcT472dUkQkic5FugN7bFlM39YsFr0F9QEeL3eajPTdNQ3JBsY1sMifZmx8Rm+ntyszl+bvGFXhfYfIKvSRCErJxLa5B0il+LbGY/TiHEIzkiRsqPCBFBqBF4JEOfdMov5iZjMx5xoHbDjW0xHGOCw+lk6Wx35bbb3KAMgLGoLzkyoY5Hx0IuvUHbof/oZ97uS4JHFxhesQPTnfvcfBpjUzP4cLZ11MTo1IyKhqgiVMN+nj81VhUvET/yRTaShmLdQtC33dRYh9mrKVxJ2Z6fBbVI663hpg4ZwJ0GJOFsEgmUZqHzWX89H7xHc2p49FBvuc3Xfhsk0iiUD3FWFYQaQRcB+SzVvZwYdRFDWMjMaqFFSy9Y5FbvdIcYsoC07exEoO1SV8Ou3i41Np7ghY+mIkg9dcItxYWF4VV0GqRYNmxZuKYhjOnZ+cBur15dL/qwQkoDFrOoe3nh0DHS9k3mevmoRcv3pYBYvAtChSjlRYxvy8tSnd8pmi7MevrFazHR58IQZP9usknnF3eyYG9qrMM7r2tSIqQ+bOFKynbsAzBHHuLRCGxkoieFtrXqLNQivZBaiqVKsWZufjNhuDihcQHFYPqe6YKYIiQ8eihUj0LWb0nNCMICCOr9wfESL7t6u9So83xFc17thqm0jdHJtxwiRF/kmxrrjGKFprPq0RZKF9H7HBwed2yXRAhtx1RcalrgaCCeBW+LcwtwWZGbKFSE6MJjsYmQhQo3E/xvVIgw+/JLQ0jbubogzzoN5qZLFCvk9WnRXz16xhERkULTxYW07wrCAtBbEIH8bqb55l5QvtqrPZfvW283DIcsJRIoZK0vWBR25yKku6MZNnLzQZIjE9iXFR7kdgo4Dcv07ZIYuGnt6sCf3+DwhK+IsLPb5S2jxEL8Lk2L7GLyzyy1COE0NdY5Pp98n0vazkTS1qyOOLpcePttd0cz1qxu9Gw1z+dqqj+P6krIU4S6sw7tSCyb+SxLCYmICMICKdQMyc+4DPB2huQ/A/7GZnsHMqPXU7atQu489M7FCp/x8cyJUVyencfg8AR+dv6Sulv1MrIy8ZM3LuZ9TqF39Kbn2ihtSqWcS1cpnFmByqSQVmaFCO2HDpufP3qXzpVUGuFQrp2WF10DzkJpvdVcfyxIqy1FD/W5MhIJWZyIEBGEEmDy/vjIN44hHLKM+erkyIS6Q6TX0aC5IO25foPsePcNkFk84tEIXtm9RbXyhi1L1XbwUHZyZAJjFzMRireupByD8IISZKEs1R393Hx6UQyqK1UlXqEixM99FXALG0pttEYjmJ656vg76VvhqRH+M52H3R3NqpWXztNtB46hNRpxHFMqbaM1GsHegSGV5tG7cData3YYltF3BjDXo+jfISlIrW1EiAhCCTBFJ+gOkUzFCN6S+38vX1Gv47brOl71J6Y7Rn2SLNVgbD+YVCIkZdsIWZbK6+sXdyAnfGih8TUJM1iGV4paFyHVJF+KQhc2adv2/TvHoxHEs5GQeDSi2rDpPOKC9XhW5HKhoDq2mPNpOGSpdm9K8+jCgtvAm0QI/Q4wRw+LqeUSKocIEUFYIF7RCe7ZQWKEixBKd+QLK+t3c9x3gfsshEOWsQCVhq3R49etjuD/+820uvMl6OLulTbxq+WolgjJx2KIltQC3HGXo58Lo1MzuDRzVaX1RqdmsGZ1Iz68Ia4EgoXMtGVKC9KMF1Mnlul85yZ+gFNskOCntnIdU/SQPy6D7WoTESKCsADyRSe4GKGJsqaQtV9YOd/dXKI9poaNtUYjjtqP0cm3MDo1g+nZefV4PLZCLS5jUzOuO+B8aZOFtspWklCe1MRSpND6m4a6kG+Lt46+7eubr3G07tpw1ibtP3IaNpyCYnB43BWF09M8gFuEBPnOBKnNksF2tUVZu2b27NmDjRs3YuXKlbj22mvxp3/6p/jVr35Vzl0KQsnZ59G1AmQuqPpEWiDXTZNK264aEV2E8OebOgj472574ihOnJtUE25pNgyFtseyooMu6rrAIBHEKVRU0POtErWZlLNbZbmJEKDwOhKv53Mx4DUMTz+feHcTL5AOW876DEq18BTLoR0JhD1OKi/B79dVZsLUaSZUn7IKkR/+8Id44IEHkEwmMTAwgPn5ebz3ve/Fm2++Wc7dCkJJ8WsxzFiTtxhf19fTiV29Xa4puAdfGXG0OfLnd3c049UzOYtsEkH0Oz0P72WnfZyF2PnF/fjIpKOl0o94NOI/jbVEa/zykwrlw0JGWASd8uu1DYIiepTm0+H+MhSJ4ecbiZCUbXtOgwYyxdtUw8R55uQo9g0M+c6KKaRd11TLJVSfsqZm/uf//J+On5966ilce+21eO211/Cv/tW/KueuBaFkLCS/rM+KoZ9Npktk0sQL53ha5tCOhGOiKeAcTMdTJvQcWgTCloVwyDmTw0vEEAtJv5TDcEvID5+8WwgUuaBzqL4uhCvzaewbGIIN7zQNEbYs3HvrOmUsRuddoj2GTeua8fypMVUrlbZt5ZVDhdV829Q9tndgCGNTMzhxbtLXKTVoVMM0q8Yr5SldNJWlooZmly5dAgDEYjHj7+fm5jA9Pe34TxBqAR4G7nr0xaJECOA2B8tngsb3S3eMpjvTsGXhld1bXKFtvihcSaXVgLBtB46pdA4n0R7zjYIEhURIfXgx2YQtX7gIAYArmoeIPrNIJ2XbeP7UmON86+5oViJkNFuLNDg8oYTzsydHjeJGjzCSaF8I+veLOtqo3Vj/Hi4koiQUTsVmzdi2jQ9+8IOYmprCK6+8YnzOY489hs9//vOux2XWjFAr6DNg/PDzEdl+MIk3Jt7C2MUZ34FgdHfGJ43yQkBOvrkyfnC/iUR7DCfOTS24vqKpsQ6rIm9bNIWty5UgQwnpfKNzSfcfCVtAyoZr7os+ZkD/v8mgjQ9fBODyESkGk48In8+0sS2moo9SwFoaanLo3QMPPIAXXngBP/7xj9Ha2mp8ztzcHObm5tTP09PTiMfjIkSEmoAuXPxCudALFgkbAK7t6YPseOGfnkvnF3ST8PBLldAiwrfRujqijM1KQTV9RgRvTEKAzhX9PNLTN/RaXbRQAeszJ0cdUTf9PNa3y/cXsoCRPXeV/P3qlOM7LWQoRIhUJDXz6U9/Gt/5znfwv/7X//IUIQDQ0NCApqYmx3+CUAvw0G6+GTBe6N03vHAO8E7VbGyLqVkwQK7+o7ujWfmA8MUknY2u8BSLX73Gzjszz52bT6OhLnMsCxEhXqH7hVCKdJHghpxpOVRwSqIg0R5zmeN1dzTjgTvWA8iZoBFUwGoSIYA7kkfimnffpO3Md2D/kdNq5lE5kC6a2qCsxaq2bePTn/40/uEf/gEvv/wy1q1bV87dCUJZCDL7IsgFjBee0mt1gyeTxwEVsZJ7JUEXbv2Cn0rbSI5MOAzN/KD9LdQfhO6QyxH3kPROeagPW7iSyqX66G9IwrG/twuDw+OOSByveaJiU154qkPnsV5ozUnZtsMaPs1+Lqfrqd+8JqFylFWIPPDAAzh06BD+x//4H1i5ciV++9vfAgBWrVqFSETucITFgV/rIP0+CLp44SKE/5vfnXERNDg87jAgo+1wAfHG5FvqrjVo5wrt754NcYdQKpRyD2MTzCykQ8kkQjjJkVxx6cZ1UdXNQpE7XvBp8gChwuzbnjjqqG3Sa0WIeDSiBjDqLq+lJqhBmlB+ylojYnmY0zz11FP4xCc+kff1heSYBKGW8BuyddsTRzE2NePKS9OFkOyreRGd7i6po1/QeSTEFBWxsDxdR2uRYm3o9QhWvgF3xUI1RIDTFZiOIW3bOH9xNvDx6v937y9XvA2gLK20Xl1qYvteOgpZv8uemhGE5QilYQaHx9VE3X0DQzhxbhJjUzOqjTZkZe6+qNWXPA7IdwHItPySsEmOuEPfluWuAbE9/s0fS6Vt1+JF4+plRkvlKPZz1hfxoCLEFPkwQedGim2We36EQ5ZnyoxENkHdNLRNvauGd4OlbLvs9RqlinIKpUFmzQhCgRQyUjwzDTcTYtYvvkAm8nH7E0dVASCJEu67cNsTR7E2O/GU4F0oheh9suAm4aJfcGlbNnKiRKhtCu1IuuX6aN52biD/Ysx/r0fk9NeuYcWs9N3g4huA6rIhkV7Oeg2/CItEQipPRQ3NBGEp4Gf5zs2QyIwMQDY6MuEKR3Mny0R7sypM7e5oVmJEt3WPRyOexmb5eHMuFbieQETI4uAdqxsdP3uZcTXUhQJ5ynCCnGPdHc1453WZ0Ht/b5fDzTfRnjOv5N8bOs/p99Rl093RrApiC+1KExYvEhERapZCIg+VpBDL976eTseEUUdO37IcTpa8iJWnazg0QVd5ihRYFyBeHksP3SHX63yYm0+r84kiGPk6pfLZu1vIpQ7JEZW7q4ZYnWAqnRMY1HYesnKdZIn2mCpUTaVtRy2KRCmWNiJEhJqFt7t6FZRVi6AjxfX2QCJfOJ3uGHUomlHsTBFCakAWJ5YFXLeqEZdn512RraApmoa6kNGwzES+59jIpFhIQJicSmkboaw3Ca8L4W3pJGT075DUayx9KuasWgzSNSN4tdjVSlW7n+W7LpiCtMbqXiFBf7cQZEDd4oKKTYOcD90dzRidfMsV9dBFy0I9ZHJiolnVffDvKz2ujyjwG28gLG5qpmtGEBZK0MhDpeDpIj3asf1gEhvbYtjV22UUIf29XXj25KhxhgdhWljI4MnLV2EhbZt0dywsDiwLylY9HluRV4h4RTO4COFRj2JF6RgrrjYZ/6XSNk6em8KVVNpxzlM9iIiQ5Y0Uqwo1TyVtmHUbds7+I6dx/OyEmoTLLd/pYn7iXEYsUHsg4DQs0+8688kHurifZ69raqzDmmyBYlNj3YJC12JCtriwszOBRrUCZp3WaMRli59oj6muKYLOr5WNdWiNRvBPj73P006fyj3IpKy+zrl8jE7NeLbEhkOWQ4RQ5YiF3HRd3c693PbuQu0gQkSoGvkWfboImWyYy0W+jhggd/GmOzmq56DH9x85jV3ZCzL3KxgcHgeQu5Bz9AWCIIdULmBWNtbh1Yd70BqNSDRjGRJEPI5NzbhE7/mpGdf5Qp1Zl2fnMTY1g3c99n3PFA2JIBpcd2U+7TpvTaKYp2fot5SWoZ/3Dgw5Os70DjRhaSOpGaFqBClGrbQNc76OGPodiQ6qEaGICM16Iairhyyrc6PNnXeztECYQuP6zx/ZuBb7j5x2hOXr60K4ItGNZcvOnk48f2rMKCK6O5rxhlYn0tRYh6bI25RgoRoROte8aktIBNEZrp+bFBEkth04ps57+l7QuZ+ybUedS2s04vi+8dZfnWp2zQmlR4SIUDWCLvoLHTa3kOPyqkuh2RpXUmlV/e9Xu6Knary6EaZn5/N2tOjj1QFgQ0CTKmFp8mQ2gmcSsm9MvuU4oeg5b86l1GO64Dg2PGGcP+NnckfntJcRWTiU+57QgDyechybmlHCXi/wrrWuOaG0SNeMUHXowqLPXimnj0iQbX/95WHPjhjd44NPJM23X3JYNYmRfMWCerdDfdjChraYiBDBhUnQktX6V4+ecbX6WshE8PYNDDleRxN6/Ui0x1T7LQlt+j7QdyXRHkPIslThNZ3L9eEQHtyyHk++dFr9TN+3Wu+aE7yRrhlhUcFNv3gxajltmPOlhbo7mj3Hg1NNCC+8oztBmqPBu2dIMFGxa7EpGsBtSHYlZYsIWaa0RiNq0rKOV8RtdGoGJ85NGv1GbGSm7eq/CSJ0yZisu6PZERkBoOqneNcXPYe+X8mRCSVC+Pet1rrmhPIgQkSoOqZi1HJfaPzSQl5eCATViPBhXfrj9L7o7o1y5WtWN6piVfodhak5UoQq5MOvddevHdc0aoD/Tn/N6ORbeY8lnW3DpUhff2+X+s7ookhPZVLEhKIoeh2Y142KsHQQISJUlUoWo+rpGC5GKCysixD9eZkQdLMjtcIvtDS8jqaU9vd2YXB4XN0NXt98jeN3JhHCKXQ2iCBwpmfnjdN2/czLeMHq6+cvYXRqxriNeDSCSzNXMT0774ryHWfRD9OwRr3jzFRfwsW/341KrY6CEIIjQkSoGqZ8bzmLUU3pmL6eTiVCwpaFjW0xJNrdBkv08+DwuBIRvAuA5+NPnptSr+P5drrY0h3nk9mLpBfUKikI+fAqIg2HLMzNp41Cwu/1FoBEe04Ez82nXcZ5o1MzaI1GMHs1hSspW32Xj4+YUz/0naEaKRIJ/CaEts+/byRyvG5UankUhBAMESJC1eAXIQ53YywlJpGz/WDSMaTL686Knp8Z3NXiuJvj6RkLUDNluDhpaqxzhcT5+6Pn8rC4mI0JQfFqOUilbVWgSp01Og11IZfDro2MCOAROTpf+XlN6aF4NIK0bWNweNx33g1vZ/e6CeFwEcKfo6du9MekqHVxIV0zwpLFK2RLFym6oOq5af3ipW+H/3z7E0ddtSJeBLHPjkcjuHBx1rWtcChzy5qneUEQFoR+HlOnC4kR+s6QoG6NRrA2tsKRXtHrT+LRCO7ZEHd9t/KlTQpNuXh13wnVQbpmhCVF0AuS/jwesgXgunCRuyO1GXqlhWg7yZEJbGyLqdAyzY3JJzDo937PsZDpgqALuN56KRNIhXLDBQOhzzeis5DXQvE5M7yLh9dAJUcy7bt6JIO7K+vfT78ZSqZrgRS1Ll7E4l2oefLZrpMNtP68vp5OdfHbOzCE42cn1IwYILPYp2zbMeeir6cT/b1dePXMuGM7dNF9/tQYBocn1LyPIEPj8v3e5PcgskOoJA11IayJRlTUgo8hsOAeSxC2LCTaM48l2mO4++ZWRzs7RSMO7Uio704oO6yGRh0Aue+sbudejMV7JUdBCKVFIiJCzRM0B2x6Hm9xPHF2SoWd6eLYmr34AlBFbabtHNqRcJiYUfGew3USbgGRzyWVoiVhC57dCYLghZ/TaSFcmU8b/W0oVaN3h6Vsm3WRZYzMbDhTOxStpLRnKm0j0d6sbha8IhbF1HdUehSEUFpEiAiLgqDGRqbnETz3TRfUtR6j1E1ihHcRAO50yS7mnQAAYQu+NR0WctGSlO220xaEfJSqwo82w1vN9dZz6hbj36tfXJh2PF8XAbq435f16dG/x4CzjX4hIoTvT8TI4kBSM8ucoBNwa4G+nk4VdvXLAevPM027BZzGSrwdl2+HjJm6Hn3RITJMcAMnwF+EALmLP3mTiAgRKkVDnfl7oYsK9+8n1HwloHDjPZo3Q3Oa9O8xuasWIhz8uu9M32uh9hAhsswJWn9RLgoRQkFzwPrzqJKfQ/UhYStTENfX02ms3ueiBnDnynXoAp35t+9TFd0dLYHcKwWhWPRTcW4+7elRw83GNq1rVlNwqSC1u6MZKdtW36mmxjqjYNcnUQO5eiv67l1JpR11W8XUd+zyiZ54fa+F2kKEyDKH3/XTl7+SPfhBhRA/pqHHt7qOWX9df28XHtyyXj2uO0nS5TFlZwyW9mnvnwQQiRqCi5qGuszXp6kxl+GkfHprNIKN67zHmHP2Dgz5Ol0KQrHQORokJkBiZXA4V9QdDlk4fN9mx0gDiiK+snsLujuas86qEw7B3t/bhUM7Ei4RwJ1USYyQIMr33RaWLlIjIlR1sFSQQlSa0+KVAx4cHsfh+za7XrfPMMtFLx6luzwAqs2QLrQ81829EUanZlAfzjlWmsLTl2auFvxZBPEZEYRC0NN9fsXTm1kxKk3Lpe/j6NSMiiLy1IlexO2H/v3sevRFh8gnpL5j+SEREQFA8PqLUkORBz20SwVshdSo6LliuhvjA8D0izD3QyD309ZoBMmRCUdNyJpoBP29XeoOk+o/6EJPjxOXZ+cxlvUYMWF6fHp23vP5glAI+vkI+IsQ00yjsakZJR7i0QhsmFMn1MaL7O+9Ihq6nfuVVBqU+dXTOFLfsbyQq54AoDoTcIFcaqa/t8shhAA+ZK4F3R0txqhJoj2Gw/dtBgBjLpg8C/p7u/D0iTdcEYdWFhGZnp1XkY8xgylTyPKe28F/pt+HQ5ZnhKPQxzmlatkUli6m89TvlDFFNM5PzTgmSpum4wJw1XcAuRsLAK4bA69WWy5o+OuEpY8IEaGqPfh6GJYuZjwqQv+mixtvHyQPAx1yWd20rlnNhnn25Kj7idrVOR5b4ajXeObkqMM5MmxZvt0tDXUhtPyLepy/OFu2uzkRIYIXTY11aIq8DWNTM+o8LTblR+ZkXIQAzu9sa7ZeSr92mDrR9g0MKVdiPc3KI5C1JEBksm9lkNTMMserB79WCsb4sQBwdbCYLhDbDhzDc6fGVLFdKm1j+8GkMgwDcqHrsYvOIlFu5ARkwtNhy3LMk/FrhpmbT+P8xdnA788qb1OSsMyYnp3H2tgKFVWkxxLtscBpP/48mitDIoSKuqn7ZWxqxjU9l39fdct2KlTVp+SqAtYaS8VUu6twuSARkWVOpSfg6nAhxOdEPLhlvesOSffxoFHi3CzpuVNjKq1Cxkm5iv+MUAhyh8jNz/h0Xsqz+83BCEp92MIVmWIneGBKATbUhfD/rGwwmvARr5+/5EizAsCpX190FIbWh0NofJu50Hp6dt5h1z6arRXp6+l0zG/a2BZDor3ZFQnJTKg2t+5SmpO2V+tTcmWyb2UQIbLM8QsrVuJLRkIIgOviyUO7fD4FFyr6MDouQty21Jm7vXtvXec5Ep3D7arp/zZK54B6tQAhUwrhIyweLJg7Xubm074iBMgVPf/TY+9TiyYXIeTfYepYIbhdOwl6wLkwm9Ix9HOm68ZZ88EjH9Xo0CuWanYVLhdEiAhVZRdrkzVd2Oj35PhIF1EgVxA3ODyB4yOT6qI5ODyh/D70Irzp2flAIgSAMm3iNSMUTSlFwahtBy88FRGyvDD9tfOdATzSNz0775lW3dQeMxantkYjDpGz887cAswjHKaFmUzPAKiICI9gklV8d0czNrbFcPLc1KKakiuTfcuL1IgIVSVIjQpFQ7ijI0VCCEqfbGyLqQhLISZhXi6ooyzCAuTuNq9b1VjwewXcbbtSeCoEobuj2eHaa4K6vvp7uxxTp3U34HRWsPNt9/d2KRFCBaiDw+Pquzg4POGoh3CPUWhR31deC5KLWk6qm4QT5yYX3ZRcmexbXiQiIlSVfDUqdCdFzyHzJAs5l1MSCynbxnOnxrA2tqLw48gjCI6PTKghdtOz80Ubj4lhmVAMfoZh3B/ERu67Q1FEEuy8Cw3IzDgKZcV7X0+n+q59eEMcAFwREB6V0xdm2r7e4UaQgyqJkcU0JVcm+5Yfy7Zr955senoaq1atwqVLl9DU1FTtw1lW1Erbmuk4Oh75nqOYVE+fLJRSO5xKfYewEILUJDU11uHGNavUIp9K2wiHLDXNtj4cwtDjWwFkusoAKP8djt/v6HvPvX/0VCqQETpcoBD0PdVvPGq5+NPr2Gr5mGuFQtZviYgIRnh1vNcXsFxw8aGLne0Hk47uFarq9xIPxYgUvp36uhCuLLAwVUSI4Ee+OqEghdF0zpII2dXbpb4rVFdFnSomkUHwFIvpe69HNAB3ASsXIVTwSi3wppb7SnXoFUO1uwqXCyJEBCPVbFsziaB9A0N4/tSYuphtbIth/5HTKiTtFcFYaKTkynwa8WgE92yIu9qHBaEUeImQ1tURl8+NFzSeAHDOfzG5ofp9d/N971NpW7Xsml43ODzuiIRQNOZKKq1EjMm1uVajCtXuKlwuiBARPKlW25p+MUylbTz16llVjEcX1qD3IhYyFxRySS2U0amZwJ02glAqgprd0QJPXWKUuuRGZPw7Re3ufJHlUUivrpgg3/vkyKSqPSFhRFOw9e4bQSCka0bwpVrD8HjnzFePnlHdKqNTM7j9iaPKqCwINjIFe8UUsRKFXjzFcVFYCHSu54PERn9vl8v9l4zIiL6eTjVbST8/KQpJNSL8ew94j1IgeNSku6NFpW940aqp+0YQABEiQh6q2bZGF0O6sE7PzqOhLqQu0FQb0hpAkJC3SFAWerGUuz5hIQQtlh6dmsG2A8eU5TqlQmzknIXpO7v/yOm8EcHkyCS2H0yq7z1n/5HTntOwXz0zruo/eF0FHderZ3KtwPLdEHQkNSN4Uu22NboY0l2eqfA0yAW7mC6YVNoumYOqIPjB22+LgcQD75ih4XK6i2l3RzPStm2sASFvES7aafo0j2qYuHV9rsiVUj76kDvaHyAD4wQnEhFZ5uwbMA+2y43mzuWGKzkMj4ug4T0fQHdHszFUTZESHZ62MXWoBxkAJiJEqASFipDWaMRhSEaFqnTDwA3FaGI0CfrM4y3qe9zxyPcc3TAcigkGiSSarg1cDJk6cCRFIxASEVnmeLXp5txMnbnhSrSt6ZGYfQNDSLQ34/Xzl1yiQz+KRHtMtSBS6+3luZRrH8X4hIgfiFBOdIt1L8amZtTUWxoiF49GjO20FEW0ADUCgX5PHiMWcgPseGeYDbgiIX7nv6nIVe+UEf8NwYQIkWWOV7sedzP1eo2JYo3Q+Ot4vhnI3Vn5QWmU7o4W5SRp8v9YSLpFRIhQTvKJED3FSCKE2tkJ+i7xiAgZAA4OT2DbgWPo7mhx+PE8f2oM92QdVQHnwMew5f4+e33P+3o68eRLuboy3josA+MEL0SICCVt081nhKbPvSBIbAwOj6vQ8rYDxxxtgH5kREiz4+Ksv65QczPTNgShFBRTt6Q/XzcWI/h3kARFfTiEDW1RDA5PIDky6Zj9Qt8L/TX839sPJlUrsL4Pvn8vEzUZGCf4IUJEAOCeLplK2y7joX0sr6tHNvRoh6kYjloHTa6Ng8MTaI1G1HwMLgJaoxFMz1w1Xrh5oR893yR2inFYHRyekIJVoSxMz847Fnw/Cj13+dwYbijGRQfNaiIhs+7hF5RTMT+mnXd2KnHPv7emSKqXiVpyZMLVeSdiROCIEBEAuNt0eTqELhr8LqhfEyHc9t0rwkKPmUQKADVsa+/AkCMSQSFrfhdpAQgx+2h+8RydfAujUzNojUbw4Q1xdSEtBhEhQrngqRETDXUhR7u6fv5TDcfg8LjLtj2Topx0bXNNNIILF2eVQKHvoA2nqOffV5rOa4qA0JRfqjchEULP4xHKQhxeheWFdM0sUby6YQC3HwAXEkOPb1XGQ7oPgde2TMVnuhEa1VfwC1zXoy+qi1Lr6ojjdSZ4RMRG7kKu31WOTs0gHo2gNRoRW3ahpvGLh8zNpzE9O68cVvXznzrDxqZm8JFvHMNtTxzF/iOnHd9JbkqWaI+5oiTbDyaV2LABhycPeYBk0jkTDg+QXKq1RXn9hC3Lkb6hSCevYalk552weJCIyBIl6NA6k5DgEQ3dh4Dsm031JPuPnMarZ8Zx6/pMp40pwpJoj6kLETdMWtu8whHGDRq25s/o7mjGG5NvYWxqJiNGsk6qUuch1ArFpPpMXwO9vsNCRpBQyz19v/l37Hw2spJoj+HwfZsdqRTqmtGjlHxuTaK9Gbt6u1zXEK+0iwyME4IiQmSJEnRoXZCLxclzU+piQ62xVIzGw7tcuAAwGqElRyYR0oZoUNiWXxgpvRIUqj/h/iGDwxMLNosShFIyN59GfdjClVTurAxbQKqAk5T8QMgGns9vGZ2aQXJkEuezYpzgz6WoBUUpSGToNyK0Ta/OFwCO64medpGBcUJQKiJEvva1r+GLX/wifvOb3+CP//iP8eUvfxm33357JXa9rAnSDZPvYqHXjgCAbpTEXR0B/wgEDebiDA5POERIoREMqgXZOzCk0jJ0Efa7vhdTwCoIC+WKpjoKESGZ52deQKmaRHumOHvvwJCqI9HP63de16Q60LYfTDqG3lGhOcd0Y8KL2Wl/XpFU0zYEwYuy14g8/fTTeOihh/Doo4/iJz/5CW6//XZs3boVb7zxRrl3LWBhQ+tMtSNUSEpzLXJujc45E/RcqgPJDMNyuqPWh0MO8dLd0awuqkDmzi8IY1MzePKlXL55dGoGDXX5T20RIUKlCOLkWyjxaMRRRNrd0WzsLOvv7cLh+zbj0I5E7iaCuZrmi14A7mL2weFxz0iqzJMRCqXsQmTv3r345Cc/iU996lP4oz/6I3z5y19GPB7H17/+9XLvWkDxQ+uCOCDyIjVq7yP3UZMASrNkN4+wkBhJ27ZydA1ZOSfIIIKEjoNad6XbRagFSBAX4+Sbj0waZsJxg2CCDP6oeLRQjyDTDYmpI4cIImwEgVPW1MyVK1fw2muv4eGHH3Y8/t73vheDg4Ou58/NzWFubk79PD09Xc7DW/IsZGidqXaEHuPtsCQoMnda48qRlQSQBbgEEAmPZ06OquI6GsZFrwecbbxBaj1Stl10YarUkgilxLIyRaYmQdxQF8L97+nAU6+eNQoUvaDVq8CVZswc9xAFdE4PDk+g45HvIWWb68H8yFfMzn8WhGIpa0RkfHwcqVQKb3/72x2Pv/3tb8dvf/tb1/P37NmDVatWqf/i8bjrOUIwvApTvVpy9ZbeXdnwKn/eruy2ePrkwS3rVbuvLiKoJZB+pt8PDo9j78AQxrLFc8mRSfV6Krzr6+l0Dq7T3p/XFNBiEREilIpwyDJ2ugAZ8fCrL2xFOGR5Rknm5tMqlRMOWS4R0t3RnDH5y77e1F1WHw45WnwpYlioaPArZpcUjFAqKuIjYmmhddu2XY8BwCOPPIJLly6p/0ZHRytxeEsS0wWET+XkFxCvaZjUAszFCI+q8NZegkaG9/d24dCOhEswPHtyVIV149GIEjUrsxfeweEJPH9qDLc9cVQVnpr45isjrscKmeUZsPxEEArmHasaPX83PTufTZGM+25jenYe/b1d2LQuN0OGjMUGhyewNtuazuF1UXSDwOugUrYdODVL7PKJoEgKRigVZU3NtLS0IBwOu6Ifv//9711REgBoaGhAQ0NDOQ9p2WC6QPCQKgkAv1oQUwiWLqD0/K5HX1R1IA9uWY9Xz4wj0R7z3AZdGPl8C/ImobQKPYeKV7kpWX9vF549OapESjy2Qr2ukHuzABYlglAUpuF15IvD29s5ptkzdJ4Tadt2uJUS/PvDvzN81AGPVAKSThFqi7IKkfr6etxyyy0YGBjAn/3Zn6nHBwYG8MEPfrCcu15yFDvVVsfU0suFgwmycTYZmOmtvU//5WZXLQpv/SN+N52rBTo+MqnCyHoni37RTo5MKD+EweHMvyndQ5GWlY11uBywOLC+LmSc0isIpWRTe0wJBPIRof/r816I303PAnC7EdP3qHV1BB/eGEdfT6dKq5InCH0/6LVec6AEoRYou49If38/Pv7xj2PDhg3YvHkzDhw4gDfeeAP3339/uXe9pAjqlBoE3ROATMr8tn3q1xeNBmZ+hbBcRHARQj+T9TvluEmE0N0jv+vr7+3CMydHlWlZoj1zoV2zulHt7+cXMsXNQUUIUFg6RxAKhReMjk6+pQRCU2Md7r11HY6fnchGOMYdIiRT5G0j0R5T5zd9Z0MW8NCdZj8guinhTqkccTUVapGyC5GPfOQjmJiYwF//9V/jN7/5DW688UZ873vfw/XXX1/uXS8pgjqlBsEUydCHWvnZOHMDs3yV9FyMtEYjsJATHLo4IUzFd998ZUSFrkenZlSNyEc2rnWIICKolba0+QpBMaVPAPia8Nns96M0eiAb+QuHLEdKkp6nd3BRXYf+nTVFQoNcByQSItQalm3XbrZ8enoaq1atwqVLl9DU1FTtw6kJaNGlC9JC2/G4NXsudJzbNuWjTc/f2BZzpYvo4nj87ATGpmZUvjxsWdjUHlN3g8X4KjQ11uFTt7cr0RGPRrAmGvH1NBCEcmNq/W5qrENT5G3q/Ncn23pNhNZFDU9X5sz/cmnIQr//glApClm/RYgsQniB6NDjWwO/ziuCwu3V+VyZDW1RxwhvfTs8D21K6RB8gB2/sOqCJEgUg98RclqjEVyauYrLs/NFCx1BqAZeAx71min6vnGxQgPsBKHWKGT9rkj7rlA6inVKBbw9Abj1s9PG2S1CgJyHwMa23CRdOg4uUoidd3aqgtjRqRk1apzEQms0gqbGukBpEprMqzM2NYPLs/OIM38FQagGXuMFmhrrHN8LICdC+BlNow9Gp2ZQH7bUa2m+kz7cURAWOzJ9dxGxEKfUfF03aY/AGDcv4/DtkEHZky+dVi2KFCkhXxEuHj68Ia6eWx8OYW22BTdoJMN090hcmrma9/WCsBD8IncWvOuOpmfnXekYOpfpjDYNl6TXWtnnU51VPBoxRkMK6aIrhFJ17gmCjkREFgleVst6RMILkzkZ3y65nvL5MEG33d3RAiDn3kiREiA3iZdEB7Xa0s9XUmmcPDeJhrqQutguBImGCOXGL3IXNM/NIxr83xvaoup7l2h3zlmy2f+bGuswOjXj+X3WzQlLQb5rSDn2KSwPJCKySPCzWqbf++HXdZOZ9ZIRE6ZumkJa/VK2jRPnJl1GZLTN5EjOyn1jWwwnzk1mxYoduNNFEKpFazRiNCwr9NzVjf0oZUNtvuTdY8JCRnBzc7SFdNEFpZSde4LAkWLVZYZX141X2sfrArOP3QHR83g1P6e+LoS3r2yAjUwtB118W6MRTM9cxezVFK6kzKdhQ10I82lbfA+EmsCv4yUIeocNuaJubIthV28XbmejDUanZvK2DNP/i+2iK4aFdu4JywMpVhU86evpdKRfvERHvrQPhWn56yiqwolHI7gyn8bo1AymZ66qC2w8e2c5PTuPxreFjcdqWZkwuIgQodpQ+oRPhDaRLznRqhWZJkcy0cNd2YnVDp8RKzMYjwbg0bapcJWiivz7DMAxvLIcmK4hgrAQRIgsM0xdN8VM2MxM4XVawydH3BfoOBvONT07r+7yeGh6OtvtolO7sTphuXFp5mreUQiAf40Inff9vV2O7hmybidRf/fNrY5uGkrDnP3bu9Dd0awiJIPDEzhxbtLxfa5ErcZCOvcEwYQIkWUEj3wMPb5VRTy8KuGBXF7YdLE5fN9mlafueOR7DodIgu7c+KWRt+2+snuLccaMCa+2SEEoN9Oz8whZliuiERRKsXR3ZGzXaTI1iRseXQiHLFX4TTOYqIVen2hN3WkPblm/4PcYBK9riIgRYSFIseoywSv9AuQfgmWac7NvYEgVmlJbIZBzf0yOTIACKV6h7LWxFSoczfESJlLIKpQLk6mY7nJK//YyIFPbClmuKCKlWAaHJ7D/yGk1DBLIpGdCVkaMUI0IRSLpO7b9YFLVkegTePkwSqB8Q+0Wcg0RBD9EiCwTFtJ1Y7rY0AWSRAMV4T1zclR1FXi5oBKDw+aiP8nICJWmLmwhNe88806emzI+10+EALnvki4MKAVJv9cXdl6oanI+fmPyLRW9pKF2JELCluXw8ShHXdVCO/cEwQvpmhECo1fL89bDQzsS6oJJ+A0D8yJomkYQSgWPYJjacOvrQriiPWaaL8PhC/b+I6dVR9ma1Y149eEeY3Rh38AQnj815vhOcafitG0rvx9eZE4RGpMLsiBUC5k1I3iyUHdEmnPDL368fVDH1H5oeq6FzCjzvQND4iciVA3qUOHnrH4O50vNADCKAv798vsekqA3tcfqc570/0srrVArSPuu4AnVe2w7cMxRYMbdEfcfOW1sAaRqef0OjC6YFpA1R8sVq5o8EEzzYiit093RLCJEqBrTs/Ouc1b/mYuQpsY6JV44VAvC6evpVCJ/l49g4N8pvT020ybf7Jg709/bpYpYpXBUWIxIjcgSIV+k49Uz47h1fYuj3oPMx6iug+e0E+0xdUF79cw4wiHLcefVGo1gcHgCtz9xVIkQG0DIsoxpGsCZdrmmIey6wI9NzWCM1ZsIQi2hF6HySEk8GsGabEdNcmQSrdFI0QWcpvZYvo2NbTEcH5lUYxL0wlGp1RAWGyJElgimzhbAGcrVf0+GZARV4utFdtwJlRibmkFDXQij2f9TFIMq/N+YeMt1jNwpki7gluX2C5HLqFCLmDphgJw/yD0b4o7aje6O5oJFQZDBltTeS0Jl24Fj6O5ocXTi8O3JMDqh1hEhskTo6+lUU3DpZ35RA4C0bTt+TxNwAagwL/kc8PDummgE8eyE3LFsId3r5y+pCzGJEBIsfgWqehSkdiuUhMUKjQ7Qz7ViIm35iqdJWHOzMxIDg8PjAMwRSQ6JBbqZ8GuPpX/rQoWim6abkH4RIUKNI8WqSwh+98QL3QA4Lki80p4X3tG/+Wup2j9fK65Xh4zXrAxBKAfdHc0YnXxLiYdSpPmCdHLxolG922VweEJ9D/RiUkphkl27nl7lIoW+i/o2+Pc+6KwoQSg3hazfEhFZQvC7Jz57Qr8gUSQkbFnYeWenuojRY3qRXHJk0rE9kyA5ZhAhYcvCjWtWFT0gTBAKgQzDOCYREqQriwuYizNX1fYzDqsAz7hQvRTtn/xAdBES1+pGSITQ6xLtzZ4Rjb6eTqTStkrBcHgEZu/AkMPgTESIsBiQiMgSg98dEeTSePzsBM5PzaiBWhQJ6e5oxhuTbykjMvqdXitC8It0fTiEq6k0bOSGcuknVDmjItLqK5gIEgnJd15SFHDN6kZc33yNY4QBFzyt2QGOfL/0f/25vONFdyMuZPq1F9ReXx8OYejxrYFfJwilRtp3lyn84kXRCyIcspAcmVTOjTvvzF3cqPYDyFxUqTWXT9flLbn8An+FiRAbcAiSSiAiRADc55wN96Rbx/OtXL2S1wyja5sa0N/bhfMXZ1URN0U/ujualYCguimaDUP7B3KzYOi5JEq4CKEiU2q/5QPwChEhMoxOWKyIEFki6IVpemqGT8bNFJSOO8QFkLko/nj3FvT3diHNAmXUTcMv9rp3wkr2s609rxI1IpUUP0Jt0dRY5zrnAChxbYLHgXUxy18/ODyONasbAWS+B7TNweEJfPXoGQAZITM4PKGm5XIswCE0/Ojr6XT4h6TStqeY0L1+ZBidsJgRIbJEoDkQAFwXJAD49cSbDrOx5MikujtrjUYykZBs4ruvpxOb1jWr5/564k10dzQ7LvZOp8nMz/r48UoWqtZsflEoOyYX1HjAKbkkOuLRCBLtMTTUhdSAOuIjG9cCyH0P+MRcICdkSBA1aaJ8+8EkAOCbr4w49k1Rx/1HTmP/kdPYduCYI6Jx4tykUUxw80H+s95tI2JEWCxIsWoNUowN+67errzTMSnPrXfKrM225nIhQduj+RbnL846cuFArpsglVUBJp8FqeEQKoWFnCAeDWiMR6JlNFs7BUCJkXg0gsP3bVbP3TswhPMXZ12RRNO2CCpE7fh/v6e+H3RclOLhNVh6jYju/2P6jsswOmGxI0KkBslnTuYV4g16QeLFcynbdviH7GN3WnQhJH5zcdaxXb+WRirKExEiVApablNpWwngIHNhdObm08qkTHc1BXLfH75tEumjBqFOx8SPk74f/LvodQNBYsSrG8bPrEy6ZoTFgHTN1CheDosLacnTO2r0i3SiPYZQ1tgMgPI2OH52QhkmhS0Lm9pjeVtyvTpuBKHckAihbrGnXj1bUIrQAnD2b+9yDZ/jHTAU1eD+OjwCQ8/VozImL5+VjXXYcXu7bwT06y8PSzeMsKiQ6bs1wkIn3ZJwME3hLBTd9IjurvLdMSbaY/jJGxd9Ixt+MzgEoZKQCIlHI3hl9xbjzCM/SDhQNIOb/N18/WokRyYdz3ll9xZjyzzfFsEn8vIp1g9uWV+x64AgVApp360RKMWSr9jMC72KfiEXn1TaRqI95uiqCVlQrbqZaEju+XE2wGtuPu17rCRCaKKuiBChWlBa5e6bW7H/yGklQpoa69Dd0aw6YLzY1dulREhTY53DaTg5MqmKtuk5VIhK8LZeLkJohAIVpqrOGNv2/W5JN4ywHJAakTKiz4no6+nEtgPHHDbNPGqiR0m2H0z6TuEslO6OFodNNB0bTdNN21CukXr9h6ngTR9Yl7JtiYYIVYUKTckSHchF6MjT49mTo571TfRdpddQjRQJmrSdq8OiaIueyuSt8kAuBcon8rpnxUxgY1vMERnJV3zOfxaExYxERMqMblREtRYERU22H0w6oiR8BkUhd0L7PJ5D++H77+vpVBda6oZJtJs7AkyQCOHtiiJChGpCEZG9A0MYm8wYjX3q9nb1exIhuomZ3glDIiTNirn7e7uybe8ZgXNoR0L5htSHQzi0I5EVQBMqosgNArlpIBcWVE9y4pzz2uBXfE71L4KwFJCISAXo6+lUNRn14RAe3LLecUdDhmHUucJFCOWUg94JeXXccKgKn/ZLWIBjNkZQblyzCseGJxyh6FIMGxOEYiAfkLGLMxi7OKMiIfx8p5onvaian7fHRybVqAM+kXp08i0AmYgFL1jl31vaJ496UGfNGOvGofQRRVM40g0jLBdEiFQA3XoZgIpwkEChi1f7Iy8gbTsL2ziJ9pjvnZBJsOhtv1Sxz6v6KXxMXgy6H4JekMoxFQOKCBEqBQlnKlRtqAthpSamnz056nALBuASGIn2GA7ft1kNraMhkPw7BADXN1/jSrFy34+NbTHHADvePk8pIxlOJwg5JDVTZryKzQA4ClEP7UigPhxSUz31FEnuQtdivFPiKRnT3IpEe0xZTVORHOAUITQrIx6N4J4Nccf2U2kbVh4f9fpwyGX97mX+JAh+tEYjrnPJi0/d3o54NKKiHHPzaVzffI3jOaNTMzif9cHhpzF9r0iEAHCc+ynbRscj31PfWbph4CIEyH3nyBjQlE7ZlX3+4fs2l6wIXRCWAiJEykg+62UeJaHCVCqg5/Ug/G7LKyqhd+jwjhsgU6hK26K2QYJy2BvaosrIiWbR8Iu2becu4iZNciWVdqV0CmmdFARibGoGTZG3BXru3oEhNcyRF5f2ZztgdM7+7V1ItMewd2AIz5wcBeD8fpAwodfyKdWDwxOq+6zY2g0ZTicITiQ1U0a8is0IugvjueVEe87S2ZS68Som1VMyQG4WBsEFDRXUjbIhXt0dzUpI8KJWnjfXTZxMNDXW4cY1q3D87KQU1AmK1tUR/GZ6Nu85UR+2cCVl+w6tM6F3wniZ6W0/mER3RwuSI5Nqci4AlW4BcsKEb4PXfXiRL7rhZVQY5LWCsFQRQ7MSEdS8zOtCxAvcAOcFkFInQXLJurmSyS2V7uroQs8v+Nw9EoCrVkQXS90dzaqoz4TMmhGKgc4bfb4RRy+I5gPv/MYPAGZ79pWNdbg8O+/rClwKU0F9G6VwTRaEWkMMzapAUPMyPUpCPx/akVBhXd5WC0B5EJjYl2393We4aFL6hXxCgJwPQsiyMDY1g7WxFY59HdNSKboIyfgmjKtJvvr4c8rr12fbI0WECDpB6oaoDdcvKmIjlyKMRyOqW8YkQro7mh3fIaqJ4m21JhFCx0rfJWq1N7H/yGnj91DtU9pxBcGIRERKSKnmwyjxwopI6e5N3xaldVqjEXx4Q1wZltFreM6cKvpJNHlFYejiTidGyAIeujP3nii6w/f9oZtb8fypMZWrz3dHKgiFopuLEUEjIfnMzGiOC6Vo9DZcbhevd7XpXTN+rbeCsByQiEiVMHWrFCtCujualb00FxR6ESsJjLGpGWVYRq/lEz7p3185mhNHFIXZOzCEJ1/KRXJsOEPe/EaN3guva/nx7i04fnZCGUWRGKkP52mzEQQDpgLTeDTiWPjpzCIn1SDil0SIafu8cHTTumZHCpPO+UM7Eg4xRJERPb2ab3SDIAhOpFi1xOjmZYXmfFNp23Unxi90ads2ehDwuzV6LTlAApl24JPnplSRaXJkQkU2nnzptIq46BNEqR6EoiWptI0T5yYxODyBlay9kor/yMdBIiJCsdC5Q+diyMo8tu7hF2DDab+etjNFraNTM55eN/T80akZZWymn58b2qLqXO/uaMavJ94EkCtaJQ7tSGD/kdN45uQoBocn0PHI9xyiX+o8BKFwJDUTgEKm6PpNygyyHUqb+BW0caFDI8H3ZcUJCQqezqELNk/Z0OOAf4utV/EqfzzIdgShUPwKnXk6MV/KBciJEb9p07r7Ku3Da0o2iRD+ehEhgpBBUjMlJmghar5JmUG2k6+gbXB43OVBsG9gCCfOTapUDuAsxiMDpnh27gXBB3Zx8yj+71xbcQytmgjhAoTP1xCEQjEVsM7NZ9rW9d/xwlH6rtx9c6vr9dwrZ3p2HhZyniArDWZpNAASyLQa02OmVMv+I6cd3yVyYBUEoXAkNROAfLbpXoWpXvNh/LaTD5OtNI9S8NbaVHZgF0F3jPqdH5AbVkfb4ikaEhlj2dC27n+gb18QCsUrmmZ6PJVNT/LvjD4wzhS543GQy9nzXY/4EWubV3h+L101Idkoy/aDSeNYBkEQ/BEhEhAuIkwzIvwiGfT7INvxwkvokKCIRyMqMmESGjpvZAd3EfFoBGuiESRHJo0D6+ii3tfTqVJMMthOKCcmDxte50SuqPw7wMVHa/Y7wbej10D5CaAgIkSv0RIxIgiFIzUiBdL16Iuu+oxKbMdUX7JvYAjHz04gZFmqBgTIdQC0RiM4PzWjLrz5hINfrQc3VeMiR8TI8sNvAGKhmAzLvM4pEhQmZ19qIac0CkXruDihCdFhy8LOOzuNhmV83yYhQmlQk1AhMSK1IoIgNSJlo1QzIorZzi7DxS0cspAcmUSivRmb1jWjv7fLcZFeG1vhuKDrF/f6cMiRf+c1I479ME8SnkcH4Gm0JtQuC20vLUaEeO3RZFhGgxc5ZFQWj0Yw9PhWJNpjAHLGeWtjK1RBKc2K6e/twnWrI+jv7UKivdkx4JG3q/NjpOfQdvTv5q7eLmxsM8+a4aaEgiAER4RIQPIVolZ6O4DTt4QWF36nyKv/qQOAcyWVdhSdcvjCkbJtlfrhiHHZ4qOU0YyGOve0ZS8K3aN+XnGvEJoVAwBX5tPq3CTvHiDTdtvX04mn/zIzUZe+c8N7PuCydwfgmDztNAIch47ppoCgKbuCIARHakQCUEghaim2U0i7sGnYnd5aS8WlXiTac2Frwta2YxIcFy7mHqsPh/D2pgYRJjVOKe/W5+bTeS38dZdev/ZZwN2yy8VuPBvhGxyewMlzU+o5a6IR/G56Tolw/v0yFZXTSAIbUEPv9BqTjW0xVfi9/WBS3FIFoYxIRCQApZoREXQ7QduFTdSHQyp0nGn3zRTQ8dkZdBdLW9k7MGS8Y020u1sn49EIdvZ0Zu8cobZzJZX2dK0Uli+6Sy+1la9Z3eh4Hp1nurAhEzISC2tjK1T6sT4cytYsTXpOg+bfOS5KuKhIZyMgvNCVbgTELVUQyo9ERALgdydUSFFa0O0U2uZL4WO6QPNoChWWZobUtWSfP2FMqzQ11uFTt7er/ZqK+UanZvD1l4cdF35b+70g6PDzLWXbuL75GljZwYuJ9hgO7UioAm6OPispbduO+qrkSC5dWB8O4cEt6x3fG91okL4/+7L/BnJpG+6smkrbaoSCFJ8KQnkpmxA5d+4c/v2///c4evQofvvb3+K6667Dxz72MTz66KOor68v125LSiEpklITtM13/5HTRm8R2gaFmE1ihiyzienZeSRHJlTdCYcvJHyxkK4ZgfBqh+WFpnQO8folOjdNUQ3ekg44Tcz4WANepM3PX6/2ev17y7/LeweGVJuwiBBBKD9lEyK//OUvkU6n8Y1vfAPr16/H66+/jh07duDNN9/El770pXLttqRQigRwRiz4gl4qTKKHz60xOTcGqTnhF1x+Md524Jgao05CoqmxzrNz5p4NcaM3iQ0Y2yktC6jdxvDFhZ/VeS0QtoCUnfGm4Xbr9XUhWMi5mlKahc82omgeTx2azj869/i5nmYn2INb1qvtUFqSp0wLiUYuZFaUIAiFUzYh8v73vx/vf//71c/t7e341a9+ha9//euLRoiUwgk1KCbRw+8SU3YmVMz3mc9E7dUz446feZiaPEf4XSC5q3L4oD1v3IpDREjpqJYIIYGRD3oOTYAmrl3ZoNpzSbBmnm+rotVfXJjOtqDHMDY142nI97PzlxyTcHkkEHBHNPQ6kKCYWutFjAhCealojcilS5cQi8U8fz83N4e5uTn18/T0dCUOy5dinVAXsh+C/s3D0vy5Qe7yMr4f46qdkaduyBekNRoxpmOATGg8X4vmlSCrlbDoWMif1RTZuJJKO1xJ+f/5aAISIdRaOzY1g8uz8wix2TGDw+MOYULoTsaF4DW2gW9XEITSUzEhMjw8jK985Sv4j//xP3o+Z8+ePfj85z9fqUMKTF9PJ5586bRnuLZU9SImMaKLHjVHJjupN0j9yt6BIRUBoVA4GUIB7jtZTkNdCNOz8yo9QD4UQfwoSulZQfjZcleD+rBVNiFWzfRW0HQQTbXV4X8jPcJB4oO3yKY1115dnJBdO3WS8WiITjGioVQt+oIgFE7BQuSxxx7LKxZOnDiBDRs2qJ8vXLiA97///bjnnnvwqU99yvN1jzzyCPr7+9XP09PTiMfjhR5iyeGTNvVwbaH1IkEKYEMWkLbhEj38bs+UytHtp/nv9g4Mqecn2mM4PzXjGgpmYm4+DcvKpQdIWPgJDFqcihUhfgWwr5+/VNQ2y0U5o0HVEiFe4sLkAfLPc+7nmdjYFsPxkUlWGzKhiqiBzPnU19OpzhndK6Q1GsHa2AoMDo8rEUKdLfR6fiNQ6M1B0FlRgiCUnoKFyIMPPoht27b5PqetrU39+8KFC7jjjjuwefNmHDhwwPd1DQ0NaGhoKPSQyoouNPiCTj8XkqrJVwCbqcmAZ45a3w/fFokQ3n5oOi6KjpjcUk0UuiDeuGbVgqIWfrujBTKcFWu1sjxUOnqh768S++e1HUS+9ZnSf+RYSq9vjUZyBmNMMND/+Swm3pILwJg66ddECNm8e30HvPZrQiIhglBeChYiLS0taGlpCfTc8+fP44477sAtt9yCp556CqHQ4vJP8ypM5WKk0HoRvwJYfaJnvhy1qX6FRzgGhyccIXG9u6VUnh96GL8SqZNaK0uppAgxFZEuZP96BMQUDSHI7l8/d7zs/tPs+Vb29XSO8iFxPFKoF4wmRyZUlDAfXISELLPo5/sVBKH6lG367oULF/Ce97wHa9euxd///d8jHA6r3/3BH/xBoG1Ue/quVxqF7tZCFjCy566itk0XTLrY6iJEf56f4NEn+W47cAzJkUnH3aupE2Eh0B04LWL0f6oLCeovslAfEmkTLh767FujEXx4Q9x3Gi2JzXx/Ly9BwgfKDe/5gBIDVCvCo3n8e3D7E0fV9riQpn/zSKXpMX17fL+HdiSK/egEQchDIet32YpVf/CDH+DMmTM4c+YMWltbHb8rk/YpOaZwbana+3S/Am48pj8P8M5Rm46nu6MFSZaPB+DwbihFwadt5xYdfkedStsF+V7QIncllS5KUCySU6miBB1GSB/d2NQMnjk5anzOJlZPxF8DZEToO69rwtjUjGrTpboj8vhIjkzmRGpWGHc88j0VGdnYFkM4ZCm3XxIJJBr4++BeIXrhuJf3B4mRvQND6jsgIkQQaouyCZFPfOIT+MQnPlGuzVeFUrb36QLCq4DVb9tex2OapssjI4A5fdIajbjGsutpALqz7e5oxs/OX0J92MI7r2vC8ZFJtUjpIsRPmHgVRpaTxdCNshAKSbnR56//3YHM+UCFoWRSxv/+GdHQglTaVhENsmsneBqkr6dTiZCwZbnEANWSDA5PqOcBuXOWirQJEt70b/3mQE+Deu1XEITqIrNmArLQ9j49B65bVRcqaCj9oh8P92Awhdvp9yYBwBej7o5mvH7+kus5+lTepsY6VfxK8G3nW3grLUKA/CKkHG3HwMJFV6kFFLVm61BEZWxqBisb6xy+MxTB4JEGinSY0op6zRMvWN1+MKlEgUk0WMhEJb061AaHx121WvrNAbXek6gxGQMKglBdRIgEZKHtfXTx1q2q6WJNF3W+Tb9WX9MdLG0LgDKD4jTUhTA4POFYgHSzNCCzEKVt23PR5NEU/hyKqPDHatma3ItytWouVHT5iZBixJPpb6On2+auptTvEu2ZSBt9F7hoMPnreE2+5bUaXBToooG/G69aKV0E64ImOTLhED+m75kgCNVFhEhAFtrexy+QlAM3pVb4YuLX6juWzcXz35NZGQBHxwCFrGnhof/zi/ozJ0eVuFnDRAyJC1NkQ7/DN4mjarMUh/Lpf4t8UadCIjGj2b81N7HTzcX0bhOveimvybcAcGhHwhW92H4w6SkaTDcC9Bj9m9DPaaoJ4alLESOCUDuIEKkgXIxQp4sp1WN6fnJkwnEx1dM63H6eXgOYIx46JGyAzKJl25k0gGnKKSfI4lZtIaAP9lsIhdR3lLMWhLZLKbJ8+yk0EsMFazwaUecdQeca4J0SIfYNDOH4WWc3GEX6gIy5Xiptq3MsHo3g7ptbXekfUzQyn1kZFyH8uGi7YlImCLWBCJEKo3fL5Lsj43UfVMCnp3XCluXYnmnRMHXKcAFDfOr2dvW77o6MX8yhHQm0PfxCUe93ZZ678UoUb5ZquSmk26sSKSlKlRwbnijqPVLNiZdQo4m5/LwziRDALJqBTFQvOTKJ7o4WFfHjkT5ePE1pIZ6OLFY0BEmlLnQkgyAIpUGESIWhbhkSD6bCuW0HjgEADt+3GUBGCNBiYAHKNZX7JPDweCptY83qRpy/OIsrqYz3A5/f8Xf/64xaKLkI8Zpr86xHa2c+TO29OoulhqRUgqmUESIe5dILWYMcr237P4+iSZQuAaD8c0y6gItmr84Vk4lYKp0zOTOJm2JEgzilCsLiQYRIAILMhwlyofSzi+edAVSARxdz6jagRWz/kdOO7hVTQSCfVGojk3IZHJ7A6ORbnkWKJit5vtgV4j/S1Fin7m6nZ+cDL8CViJAUw0KPid6XzX6+mkoHcgs1oYs7EiHdHc0YnXwr02oboMvG731xc7qUbQdqXTfVfnBMKUQS0XwQI8G/FxLFEISliQiRAOSbDxPEKjqIXTz9zC/SfBopiQC6U3W1RmrdDNzYiooPvTwmRqdmsP1gEhvbYupiz4tfw5YVSISQ4OAGZ3TM+nNMzM2nq+ItEhRanAsVTLor6XzKRtonLZKP6dl5l+8L9/D4w8++iLn5tOdxBjE985uyTNEPOkf5eWMaPcDTOl5GZN0dLcbp0vr3TESJICwtFtfwlyrR19OpFniqvwhivc4x5az7ejrVXeCXXxpybK+vp1OZO5EIiGe7WWjxirPBYXtZASCQWZRe2b3FYW5mWpDCLHIyODyBE+dy7ZC0yOmDzhrqzKeNZeWiL374LbzUsWFpj+s/VwtaIIuJkJDFOU930GPFsDa2wvEzRcH2HzmtBN2746vV9mkvFK3SseBOnfxBU4N6DQD1HaD6JHWOhpzvoa+nU0U66sOZ80U3HdNN/ZDd/97sFOm9A0OqGFuPxOj7EwRh8SJCJCBcjHQ9+mLBU3d3eTyXCkJp4i4PRfNBYWHLUvbZJEIoisGPhQQPry/xwgIwvOcDDrHyxuRbav/UdaCLEFrk+KLVUBdSaQAuJFqjESWg/CBxQws87ZGOzUu85BM9xaKLLb4fPUIQ5P2p19q2Eh/UovqO1Y3G/eSDImVA5nOm2gw6B/7psfdlIhosrdfd0YymyNuM27ORS8XR3+/65mvQ39uF6dl5ta9nTo6q+qTRqRnj90AXGXSODj2+VX2PTI8BGTHCBbhXu7sgCEsDESIFoN/lmS6G+1jURGf/kdPY59NGy+8U6UKvL1qHdiTQ39uVqb/QLtSAW/BsP5j03J8NYN3DLziiLZdmrjou+NSZQfDUSXIkY+ltCv/TcV+auZo3BdDUWIe5+bTLhI0WJD8KSeEEvYem49H3YxIctBjr6EJGv4PnU2gvzVx17Mfv2FujEYdwpPTchzfEAUBFC3hXFZA5L+jz1P1e9PfV3dGMs397lyMdyMXBGDv3vEQInT80HyYfXOgDGVFOAnxweKIo8S8IwuJAhEgBmAbM6VA9if47U0iZX7D1AtbcLI9mPLhlvfqZClhJnIQtCxvb3EV+AHDbE0cdC7kppUL1JpTGuTw7j6dPvOE4nv7eLkf64N5b16njOT4yqcSJTsq2cTmAUPinx96H/t4u1wIZtFvHK1WkE7QWw0sMmASHl1DiQqapsU5FURLtMZWOS7Q3o7+3C5dZtIHgn3dTY52Kgo1NzSDNulgIWsgzxzTuKBjl0TLT3+l303Ou97T/yGklenVxAHi7qepRC4rO8NQmf+zVM+Pqu0LvYXB4XHWW0TketN1dEITFhxSrBkS/wG47cMzTkl13bqTXJtpjxrkZeuEekAu7ZwaJZSIhtM9nT446HCjDIctVwLf9YNKxsPu10trZ5yfaM/s7f3HWUWQ4ODzu2N+Jc5M4tCOBdQ+/oBZ3ihj4RT+8ilD/8LMv4pbrowByQ/ZM2/Iq7KRFP+jU2aDkKyTVa2cA93sMW5muIXqcUnGAsy2VFwYDcGyXf7Y8SkGCeHB43NUqe+LsFAA4omXUwUTC5o+va8KpX19U51w8GlGuuiSc6LVe4kBvP9drofSCUlORqf49yviONDu9RXza3QVBWNxIRCQAJtFACwqPflA0hM+OoZAyfw3gvmDzaAuQCcHzO9L9R06r19OCNLznA458+4lzkyr1k0rbaI1G1B3wxZmriEcjLiFANRyDwxPqPepFhtROvPPOTrVAcBFC0HGZpv96DVizrIyQoMV1UzZKYBIU+QphFyJC6sPuxM3mjmZjR1R3R7MjOkC0Gj5fqs/41O3tStTtHRhyFJY6bP1ZpIMXj1ItBqXKEu0xVVuRHJl0RBX0tIYecZiencfl2XmEsos7cc+GOA7ftxmH79vsEgskDiilxC3Ytx04pvaxq7dL+dzQ+9vHhEY4ZDnSkzwlQ/VOPBo4yuqUaH9eqU9BEBYnEhEJgFfHC4Cs8Bh33aUl2ptx8tyU0YUScN4pmmbO0AWX7ydfjQNFTwDg6b/MFKvuGxjC86fGMDo140qTmCIIz54cdRUZ0sJAx+jl5Gll37fJTr4+7K4j0WtLLAsuO3EAWLO6EfHYCiRHJgPXhBTSFptoj+H81IzrsxgcnjCmXvTHqMWVR6B4ZISKQLs7mpEcmVSFpbSt/t4ubFrXjJDWIm0DePKlzGexsrEOz54cdRWH9vV04tls8WimZqfZ8fejxXtweFwVMOvvQx8DYGpR9/KsocdJrJLY4K3nlIryanfn5zivezK1p/PzSyIjgrA0ECESAC+/Aq/ZMfRYEEzRFt1MjNvCA1ARDHJbJUHRqpmSAZlFkrpvTBEM9TzLwnWrG9UdqJeg8HtftODqAsckeIwpIhvqc+R8ZONa9PV04vYnjjq24yc2+OOU7vHi+MhkINFi2l8udZDbB4/+cLFFC/8YS7GY5vnwc4giG3+yZpVKVfC/8W1PHMVYNuVGwsm0zeTIpPps9fSOyU2Xu5r2Z6McifZm1zlK0RwSqvQ7EiEAlL27X7GpPvpgY1vMuD9C5sQIwtJBhMgCMc2O4Xf09eEQHtyy3nGR5k6tphQNz6NTmJvf5fK2XiCXEjG16uqLggnK+/MaBFrQuKEa4IwGcIHB/z06NeP6GXCKD1OK6PfTc0qErFndiOubr3EIortvbsWTecLyfL8rG+tgGfalw5e0Qg3A6LGUnYuM8Nc/cMd6o3jjgoELLB4BIOjvTH+b7QeTOLQjoUQIANyYFSqEPqiQF3yms9vTp+bq4gIIbpVOQsM0v4jXG3lFMfRz3MvJWN+vIAiLH6kRWSD6BZTy3AAcRk2J9phKt/DOGrrQU9sv76zhYW7utwC4nUq9/EJ4C6cXO+/sVK2zx0dyhmZfPXpG3YWnbdu1HYrC0L/13/X3djnqRaZn59Hf22Vsg7XgnHvD0xRUQ/DUq2cdrzHdE/PjuDw7X9TkWT0FtjJrAKa3FxP0PvkCTtvwiiCFrcxC+67Hvq+KiE1pj0R7TKVy0tno1+DwBNoefkGJEBIotA2qU6Jji0cjqsvlSiqN5Miky7+D15EU41jKu3Z4OjJfuzvgjAqajkkQhKWNCJEFYLqA8gWAX1SpOJHqSfQCPXKS1KMjQbwTqOvF6/hoATU5eNIC+uPdWxwdESQMyEhtTEuJEOc9CkRpoU3btuuxuOYIyp0+qRiVFmdayHk0xVQMq7MQ301qaSZ2ZAtN9fZi4tmTo46oUZD6lJRto+3hF9R7eud1Tcbai+6OFvx49xZVlKoLPn7OTc/OOwpB68MhJEcmVKTL5Olhcg0uFcmRibzt7l6pSREjgrB8WPapmWIH2gUVCbzeQ/cCobSHlzkUz8/TBZnXYNCCR/UBFLLnr+cdCDyiQQs7FbjSYD29JZXXoADuFIVpwaVtbD+YVEWM9Jhe5wE4Uyf6v+PRiCuqEGTmjZcQMLXc6vgNi9Pnu1jIiSbT5xx029T5ov/NKMpCj79+/pLjM9K9VmjTudbeCbRGI0i0N+PVM+PGwlRTSqZQuG8J3zelDL0G4ZkKwflzpBZEEJY+y16IFDvQznQBpcfo3wS/qFLNw5dfGkLazi2Mur07F0Dch4T7SdC2aMHmIgfI5PfpDtlUCNnd0Yx0dqqq/jsgJzq4cBjV0gEEr61IsRQCPXdjWwwnzk06Hju0I4G2h19Q2+CRBBJKfi25fNKs33PStq0EkZcI4cfPJ9nSZ5xojzneM/3duI8KvSe9PoPjJ3D2Dgw5ul0oHbP/yGkcP5vrTOFC1Ou962kik2g2naPFoJunAblzSD8n9e9a0BoUQRCWLsteiJgukEGiHaYLaNCLKi/m47n7TD3HuMrhex0jFxC6sKDoCQmZcMhSLZTdHS2uDglKJ6xZ3agiNHybpu4WmvzLfzc3nzYWqAJAOmuCxhdnisJwaFkMakzG26O9oPfziwvTvvUipgLVweEJvDH5FlqjEWxa14znXhtTv3vH6kZHZKShLoQ3Jt7yrMnxKoKlx2lblA6jbYQsS0XBiHs2xF0FoTokuLhwNbWflwIyY6Pvyz7tvNQN1yTKIQgCZ9kLEcB7bHmhF+sgaZ5wyHI4VAJQufugLb/6Aswv8Ly4lR7zC33r4XqqJ0mlbU9BoLuprolGVP2CXh9BJl6DwxOorwvhyjzd7Y+rO3xd7NyzIY59A0Ou9ApPRV2enceVVNoxidhLvNDnykfaWwDWaGkWghcZ0+9PnJvE2MXcc/VC0bn5NMYuzjjEG/8s5ubTrrSMBefsHkLvkiEr9HhshY9Pi4UNbTFjQTFFpMrFpnXNDpFrclMlJMohCIKOZdt5EuZVZHp6GqtWrcKlS5fQ1NRU9v2Rz0J9OIShx7cW/HqvSIq7ANFdt8EXPy/zqER7DCfOTqkoCrUF8xkjFE0p5IJPAgpwRl1Md/Z8MSf8vFN0TxJ9u1xABCnyND2nu6MZb0y+5VlMCmQiD7q7a6I9ZvQQ6e/tUuZhfnhFjkwGafkiIn77MJ1LgLPexe9vIIPiBEGoNIWs3yJEstAFngRBsRdvL5dU/e42HLJcRXz14RA2tEXx64k3cX3zNZkoAjseSp3QYmxafIo57m0HjjnSQUEjMwDYDBVzMSw/Lr9t0+v9CkU59WELV1LuqI3XfvTIiUlo6cecL0VEQoBvk9ejuJ6fFXFeM3dMmLqoMu8/V0uiR0nouLhoEzEiCEIlKWT9lvZdlNbHgLce8tHlG9tiajG4dX2LYwYIkDOcGhyeUCKEm1ABuYJTG1DW3cmR3GJa7HRSPjeHthMEWlB5YSpBqQmCH6d7/5kiz3g04hAhfFKxzoNbOl0zach1tK+n09WqbCPzGb+SbYXVj9c0hyceW+HbKmwylAux/daHQ47PslARAjiH4fFaDL1dnFJqfC4LnSf6dophn8/3gc+TEQRBKJRlXyMS1GLdD702hLuthi3L1QKsb1+/i6d5MVyMmJ7Lixp5wStFXDa2xVw1K9sPJpFK27h1fQtePTOOW9e3OI4naDRkpUckJGxZ2HlnJ/ayGg9uPw7kohPUCsvt6jl+RY0UZaJtUc3Hvqwnix4RADLCYf+R0w5RZAHY1B5DcmTS9Xz+vvzSRk2NdSq6ZUq18X//81x+EcI/Uz7Qjqfd6Jwj0ctfRzUhFCnR28aLodjuMkEQhHwseyFSCh8D/SJNbqsUIj9xzhyqJ3iBLOCu06BFkHc+8K6JRHsMh+/brBYF1frKWlv57JGmxjocPzupoir0+3xW8Jw/WbPKlRIg23k9+qEP2zv7t3e5jpV7mATx+gByQoGenxyZVLUZeuSBD+4jcumNFlV7w4UJwSM/plTN9Oy8Q0jpf0dejEynk5ew0VN61NabaI85zlNelExD5agglbxh9LbxhXSrFNtdJgiCkA+pESkRdFHWaxD0u1Ru6R4OWY45NUOPb3UUph6+b7MqoKXFNl9dCK8jAHJ1DvoiqouXIDUTOlww6DUYfq9tjUbw491bjH4blOIwGZ/R701pFb8he/Qa/rjJaIt/xnrXTlBxxP8++qyeICLPNHeIakv0bhRe26MLAwCeZnwLoVS1VIIgLG0KWb+XfUSkVPT1dKpOC/LZME1BJXb1drnm1NDCwxcWfaQ7dcaQLwhgdsl85uQoxljnhr6o02v1O10ORQHisRUOIzL6Ny3MetEmvdar+HNsasYRQeDPGxye8BQh9HsdElq8jVgvoiWreiAjhEztrDvvdH4WXHxQpIYmFPNWYl1wcWM7EkDk5aJ30/DPZg1zkeV/Sy+6O1qQHJl0tZ3TeyhHusQ05FEQBGEhLKli1WoX1N19c6taoGiuCtUN6F4OXgWyVNPhNceG7oAP37dZLVamwWU/3r3Fs9DS7y7WAtSgNSCzyJOo6u/twq8n3lTzYIidd7oLR4GcXTsNXiPBAMCRxrj31nUOwy59O5SW4DQ11jkKUkenZnDi7JT6HYmojW0x1IdDKu0CAB/eEFdCkD5jstLX3xd9hvqE4rN/exe6O5rVfgj6G9K/uzuaMTo1o4QjvZ7o7mhWzwlZlutv6Yc+aI4KY4OkS4r9rpjEsyAIwkJYUhERU0EdFS9yx1DCb5ZMsfsnEZKybXXX7+UF4VUgyx1O+e+5CRhnoY6Vz2TnldBxhywLYyyd09RYp8TR+Yuz6nX8Lp4vrnq0gO6g/bxJRqdmjOkPHh3iNEXehunZeVfUAoCjnuP5U2OO1Bavs9Hrg/TUBn3e+nGTKyxPufBoEC8spm6V7o4WxxyZRHsMIctS6TqKmiXam42iKAhU1BwkXVJM8alXa7q+DUEQhEJYUkLEVFBHIkS3uC51tT+vtTi0I6FECI+MkOihBfDVM+NIjkyoQXW0UJGr6atnxh2LJDlYmhYp6qSgzgiveSd8iFwqnSmkHWPtp3qtC/3ftL17NsRd+2qNRrBmdURZy/MW5ER7bhHu7mhxdOmYRIoFZ1EkvY7XXZjqSWgGCx07FyG8e8TkAMoXWV5/se3AsexxtriKR3ktB0/rAHAZzO0bGHIUkhL02RcijPk57GX57uX2S8XJQYtPS9FdJgiCYGLJFKvyC65eUEcLkqmorxQXTy/nVL12Qt8fLeBeIqA1GsGHN8QBuMPtpkVLf70Xusig/evHpS/kvNOD3iNvTQWcaZ/bnjiKMc32nf8NTDbuXs6rXgZx9H+9VoN+5kMFeTFwkNRFoVOZ9UJh/fMoJbqQ5uc7329Qt998xafFTqkWBGF5siwNzehulO526cJKRYrUqspNxkq1QNCd9KEdCccCObznAw5RocOff9sTR9HX0+kQCR/eEFdRA1MKQTf8opoBXpRJ9Pd2qfTJxZmr6O/twnWrI44oAW2bRseviUZUfQWQERP14RBas8WXFO3gR/HMyVFsO3AM+4+cVpbrNjsW+j35jPDX0naBnBEXfRZ6OkX/rLmBmoVcsaw+VJA+o3ypj10+5wf/OxB8wdfN1MoBL4jVa4mAnIGZqYaIH+uhHQn1+fgVn+b7PESECIJQLEsmNaPXWOh1AYd2JByzZIoVIaY7Q7oI8wjH4PCE2p/uYcFfS+mKsakZtD38AoBcFOCrR8+49p/vjp7XkpAQIJ8JfUT903+Zad+lSb5efibc3+NKKjcplguUnINn5r3otRVrYyswlu2Y4QPjNrbF8PWXz+BKynY8ThGiZ7KdSKZ0CvfN0O/sedeM3qZbCgHK0zD0WVG7LvdCKVfaQi+2NaVL6DPjj+lDHU3Fp5JiEQShkiyZiAiQuQjraRH6efvBZEmq/XnkhaN3x/DaCLp7BzKLAdUbmEL5APDK7i2Ou1STZbxX+Hz/kdM4fN9mULCkPhxSdQ3bDhzDoR0JFRHIhedbfO+K6XP08tEgh1e9xoMKbvnfhKCW1hPnJnEllduuBag0EXX/eEUwdvVmrPP5HJ+hx7c6ullIrPDIwPaDSeP70LtF/DpLgIzA2zuQGXOve4YM7/mAKzpRavzM+PTPjEcJ6W8cZLRBtTvRBEFY+iyZiAiQEwO57g+nXbp+dzw4PI7D920uaB9BHCa3H0w6Igj7j5x2RCOSI5MqWgK4Dbhuf+KoQzQBCBQ+J5GUHJlA2s69hpxOyS7cZH7F96dHdgDguMcgNwAOgdLd0YyT56bUcX/5pYybqP43IcdY7hxL/9fvyv3u0Kkoli/IPFLC01fcPVbfh6l4OUhnCYk8cmYlIcq3z6MTpayn8NuGqdjU9DfOV3wq1u6CIJSbJSVEeHskXXB5V4ZuYkULM3U8BC3Eyxfq1h1VeUsuPa6LEL0DJB6N4JXdW4wTV73C53yhpe1xUUGW7KYUjG6QxueV7BsYUsJq47oofnFh2tOwLG3bjgWPbsp5rUZaK3yllufhPR/A9oPJgtIZpqgA/a3ob8cxpWm80l1BRCcAx1whrzQQj0BVevH2arvVO8n04+U/i7W7IAjlYkkJEf3umC8I1DJpssEu5q6vr8ftMOl1wafUBYkBnsLgImT/kdOullmK6ADOmSX6sdLx+tWoJNqbHZEV2pZe9Egh+kR7M5IjEypaQfNcgJyHCPc1Gc26hpJHhp6q0Y+foG3zbh2vv4cuCnXLfJOQ0F/nJyRNf2e/5/rVWOht0noEwus9lZKgdSSm96z/HOTzEgRBKJQlI0TyXXCDXEQLueszLUD63TkXK2HLUkWhgHMiK4kN/vrtB5P49cSbDiM2vmCZFmr+el6Ym5sMO+44Zqpt4NvgYoRs4nVvFCAnOgD3HBayMddTTiTKONwFlbcMk5+K6e9rgsTk4PA4ujtaHEKBXscXfZOQBLwFDf87mratC19+7pnM1IK8p1JQiqGO9HyxdhcEoRwsGSGS74L75EunfS+ihdz1eS1AprtdvvBT9EB/HS1e/K740I6ErxkVvWcOT0no9QCZ6IZ7QBrfntfiqcy2DJNxTZ4lJCTSzBI9nY2mcD+S1mgEY1mfEt3XhCI4ps/bhLNrKhelMUV8TJ8RRQZM0TF6LpCJ3FDxZhCDLy5geG1KpdIbhdSR+CHdNYIglIslI0TyhbZNfhI6Qe76gjpM6s8jcy9+V8xfNzg87tpfMYsI328qbeP5U2Oqo4V3y3gVsKbSuc9Jr3mg9/Kux76vakN0R1OSKFSwmmiPqW0kRybVc/SW6rBl4e6bW9WkWVM9i/6edaGmR8AA9zRcvxSa6W/J/63X1OSLNOiLN9ULLbb0RpDPSxAEoViWjBDxopCLaJC7viChbpNY+dDNrapOgG+30BB5oe+VT6JNjkyoBR6AqllxtvI25+2uuPfWdeq9cKjoFICKIHR3tHj+DfSWaj36k08UmqIXfT2dePKl0ypqYyomDiIk+c+A2yGV2p5N5KsXWkzpjUI+L0EQhGJY0kKkkItoUMESJEqxzxBy9+vkKNWF3FSjAmTeK9Vg8DZcvYCX+3Hoj+vvhQpjOVR0yuED/Ejw9PWYu3v0iFI+UWj6W/LW6RTr4OGCL0jNRF9Pp2o91kVDPvHodd7Re+Zt3bW+iJeqxkQQBMGLJTNrxkTQ+Rh+NR5LoU1RN04LWxZ23tmJvQNDjrSBV1eH/hnw7XlN1G1lFvW6fwtvbd7YFlORDX1+TL4aHP0YeV0Lj/wA5pkvfucHRYLyzWAxYdouf+/8Pefbrsx4EQRhMVLI+r2kIyJBayyC3PUt5gVBT1dk2nAnHK285BkCZBY/vdWV7nx1UUOCge72CbJr526dPIKhixPeLRTEaMvr/YUtS4kQXtNheq1X27bXMELTvk14DcMznWP5tiuGYoIgLHWWtBAJip+AIJ8RwJzOobkutbwg6OmKOBsux+szABgXN120kfkZvXcASGuBNWq/pc/WZJBFhaq6KyqljEzHYEoF6B09pkV/cHjct0uIftZFiNfzTHiJVTLa80rJ+aU3ghRCC4IgLGaWrBApVQSDh9Dp7p7g3RS1uiD43d0DwNubGnBPNoUCOFuLTZ+R7jCrb8/ZWdKsnsfp6/HuTiq0U0hflLcdOOZo36XX8fdk2ibvZuEiRH+en2jwil6Q0R43p/N7T17PWYwdN4IgCPlYskKkVCFtvgiYxEgtLAheoosKSpsa61wLKwA01IUwOjWDJ19yD/ArJuyvi4qFdCcFwRQZOHzfZs9Uitc+dGFk+qz8Xq//vhzRCz/xJgiCsJipiBCZm5vDpk2b8NOf/hQ/+clP8O53v7vs+yzlosC3RdbogHvhrRZeooumvk7PzqvFnuphqKaDOl2ogJWnmoK8N9qHLiq86mtMNSHFtoEW09HhVUhKXiYL7WYpV/RCDMUEQViqVESIfOYzn8F1112Hn/70p5XYncIr7F5MuobfkQL5B9BVEi/RxWtXuHurPpOGaiuo4DPowsn3oadpuBihx/VWXp420o89SOqsGMM3XbSZOnkW6o9R6uiFGIoJgrCUKbsQefHFF/GDH/wAzz33HF588cVy784FXxR0m20iSCqC23wD3gPoqtVdE+ROXBdkvDuF5sjwWSo6fpENPmvHVBQ6ODyuFnq9KDTRnrGAr8SEWv456RORS7XQlzJ6IYZigiAsdcoqRH73u99hx44d+O///b9jxYoVeZ8/NzeHubk59fP09PSCj8HLZhsInq7hC5PXpFraXjXbLU134lw86IKMOjn0rpPtB5PGOgn+3nhaxPQZ6mmR7o4WJEcmjVOB+WA/k7gptXDjCzl9FqaFvhizrlJHL8RQTBCEpU7ZhIht2/jEJz6B+++/Hxs2bMC5c+fyvmbPnj34/Oc/X7Jj8FoUCpn5Qa+hllU9wkBixNSeSj9Xqt3SdCdO4iE5MuH4HW/h5QsxRSryOZkGsUz3ei0dR6I9Z4amp4UqERnxS5+Uqnh2odGLUg2tEwRBqFUKdlZ97LHH8oqFEydOYHBwEE8//TR+9KMfIRwO49y5c1i3bp1vsaopIhKPx4tyVs3nlkp3//XhEIYe3+q5nWJTLbSfYpw5g6Afl75wU9Fpd0dz9mennXrGNdTClZT7jpuLr8P3bS7Ze9NbfYFMhImbkQ3v+UBFhFs5/j6L2fROEAShlBTirFqwEBkfH8f4+Ljvc9ra2rBt2zb84z/+I6zsEDQASKVSCIfD+OhHP4pvfetbefe1EIv3ctl3FwKlIPKJnULZNzCkhs7pKQ1eEMrdTikNQu+ZU6gQ0d/bX/3rjrwLMPdj4UW/esEs/b8SIiSohbwgCIJQGGW1eG9paUFLi3nqKGf//v34whe+oH6+cOEC3ve+9+Hpp5/Gpk2bCt1twXjdeVLHSLE5/ELm15Sr3ZIMsijFRCPpefElda3c9sRRjE3NINHejJPnppQA4JGTYmpm+Hvjk3hNgoYXgwJwvJZHaoIUzC4UKf4UBEGoLcpWI7J27VrHz//iX/wLAEBHRwdaW1vLtVtfSrEIBSlGLXe7JT9mWuRPnJ1SA994oemPd28xpkRoO/z4CqmZ8aq7oe3y52Vs4ZvVMestxWk7eMHsQpHiT0EQhNpiyTqrmijFIpSvGJV+V+47bn2btIjnW7zrwyE8uGW9y++DF25SJ41+nDxlY3pvfkXAuoDZp31e3I/Er2C2GPYNDOH42Ql0d7QYB9INDo9j07pmqd8QBEGoAhUTIm1tbSiwHKXklKoDwc+zY9+AOa1RiNgJmv7p63FP1fXySAHgqA/RreqDpFrIRbW7w5ma4++N0j96J4ouAulvsf9Ixl6ei5tDOxLYduCYr0V8IYWf4ZCF5MikmkGjiyPTexIEQRAqQyj/UwQTfT2dauHmi+4un7RGX09nQYP2aJEmVMdPdlIun6oLQEUk+OtIPPT3dmHo8a0OAdLf26VqRPjvef0JbUt3UTW9t3DIctXFEF6fCwkUvSiWhAEdv9dnEIS+nk5H9GX/kdMubxipCxEEQagOyyo1U0rKWYwaxIvEa6our9UA4BIPeiol3+8XWjvCt2nCz1KfjoM+24V0t/Dt8c9HRIggCEJ1ESFSBJWY/eGX/uGzYqgmRBcQlALySxO9emY8bxrJK9XCKVcnit9nUAy8FgaonaGFgiAIyxkRIgVSyfZPL/fPIEW3+VJAVKTq9/ugUZ9ydqJ4fQbFoM8LqpWhhYIgCMsZESIFEnTRLYXLppcQqITtdyFRn3IeT6lSYF7zgsQ7RBAEobqIECkQWnRNQoN3Yxw/O+Hq0qDfBZmhUs3R77Vg+qW7x/LPIDkygY1tscBdM36FqSJGBEEQqosIkSIJYmzW3dFS1PC7aguBWjD9IhFCLrG0f25bH5SMoZp7aCH9e3B4XIzMBEEQqoQIkSIJ0tlCFFpsWW0hUAsTXze2xQDAYWzGi3Tp90HI934kEiIIglA9Ch56V0kWMvSuUgSZ4lqu4XfLgXJPMRYEQRBKTyHrtxiaLRAvYzPCVGwpBCff5ysIgiAsbkSILBA/ocFTNdzVVMRIcETICYIgLG2kRmQB+HW2AJUZfrcUoY4kAMbPd3B43GUJLwiCICxORIgUSb7OlkR7rOqdJ4sV3pFk+gyTI5NiRCYIgrBEECFSJEE6W/yG3wne9PV0YnB4XPmwAG7/FRFygiAISwPpmhFqFumYEQRBWJxI14ywJJCOGUEQhKWPCBGhZpGOGUEQhKWP1IgINUk1Z+0IgiAIlUOEiFBzVHvWjiAIglA5RIgINUe1Z+0IgiAIlUO6ZgRBEARBKCnSNSMIgiAIwqJAhMgiZZ/PzJr9R05jH7OaFwRBEIRaRYTIIoVs0HUxQoWeNKtFEARBEGoZKVZdpJi6SEzdJoIgCIJQy4gQWcRwMfLVo2fEBl0QBEFYdEhqZpEjNuiCIAjCYkaEyCIniA26FLYKgiAItYoIkUUMrwkZenwr+nu7jAWsUtgqCIIg1CpSI7JIKcQGXQpbBUEQhFpFhMgipVAbdClsFQRBEGoRsXgvgn3ZdIZpEd9/5DRSaRu7eruqcGT56Xr0RVVTMvT41mofjiAIgrAEEYv3MrNYay6CFLYKgiAIQiWR1EwRLMaaC/346GcANXm8giAIwvJAhEiRLKaai0IKWwVBEAShkogQWQB9PZ1KhNSymVihha2CIAiCUClEiCwAU81FLYoRv8LZWjxeQRAEYfkgQqRIpOZCEARBEBaOCJEikJoLQRAEQSgNIkSKQGouBEEQBKE0iKGZIAiCIAglRQzNBEEQBEFYFIgQEQRBEAShaogQEQRBEAShaogQEQRBEAShaogQEQRBEAShaogQEQRBEAShaogQWSbsGxjC/iOnjb/bf+Q09mWN2ARBEAShkogQWSaEQxb2GsQIucSGQ1aVjkwQBEFYzoiz6jLBZEFvsqoXBEEQhEpS9ojICy+8gE2bNiESiaClpQV33313uXcpeNDX04n+3i7sHRhC16MviggRBEEQqk5Zhchzzz2Hj3/847j33nvx05/+FK+++iq2b99ezl0Keejr6UR9OIQrqTTqwyERIYIgCEJVKVtqZn5+Hjt37sQXv/hFfPKTn1SP/+Ef/mG5dikEYP+R00qEXEmlsf/IaREjgiAIQtUoW0Tk1KlTOH/+PEKhEG666Sa84x3vwNatW/Hzn//c8zVzc3OYnp52/CeUDl4TMvT4VpWm8eqmEQRBEIRyUzYhMjIyAgB47LHH8NnPfhbf/e53EY1G8Z73vAeTk5PG1+zZswerVq1S/8Xj8XId3rLDVJjKa0ZEjAiCIAjVoGAh8thjj8GyLN//Tp48iXQ6DQB49NFH8aEPfQi33HILnnrqKViWhWeffda47UceeQSXLl1S/42Oji7s3QmKVNo2FqaSGEml7SodmSAIgrCcKbhG5MEHH8S2bdt8n9PW1obLly8DAN75zneqxxsaGtDe3o433njD+LqGhgY0NDQUekhCAHb1dnn+TmpEBEEQhGpRsBBpaWlBS0tL3ufdcsstaGhowK9+9SvcdtttAICrV6/i3LlzuP766ws/UkEQBEEQlhxl65ppamrC/fffj8997nOIx+O4/vrr8cUvfhEAcM8995Rrt4IgCIIgLCLK6qz6xS9+EXV1dfj4xz+OmZkZbNq0CUePHkU0Gi3nbgVBEARBWCRYtm3XbJXi9PQ0Vq1ahUuXLqGpqanahyMIgiAIQgAKWb9l6J0gCIIgCFVDhIggCIIgCFVDhIggCIIgCFVDhIggCIIgCFVDhIggCIIgCFVDhIggCIIgCFWjrD4iC4U6i2UKryAIgiAsHmjdDuIQUtNChObVyBReQRAEQVh8XL58GatWrfJ9Tk0bmqXTaVy4cAErV66EZVnVPhwj09PTiMfjGB0dXTama/Ke5T0vVeQ9L/33vNzeL1Cd92zbNi5fvozrrrsOoZB/FUhNR0RCoRBaW1urfRiBaGpqWjYnNSHveXkg73l5sNze83J7v0Dl33O+SAghxaqCIAiCIFQNESKCIAiCIFQNESILpKGhAZ/73OfQ0NBQ7UOpGPKelwfynpcHy+09L7f3C9T+e67pYlVBEARBEJY2EhERBEEQBKFqiBARBEEQBKFqiBARBEEQBKFqiBARBEEQBKFqiBApMS+88AI2bdqESCSClpYW3H333dU+pIowNzeHd7/73bAsC//n//yfah9O2Th37hw++clPYt26dYhEIujo6MDnPvc5XLlypdqHVlK+9rWvYd26dWhsbMQtt9yCV155pdqHVDb27NmDjRs3YuXKlbj22mvxp3/6p/jVr35V7cOqKHv27IFlWXjooYeqfShl5fz58/jYxz6G5uZmrFixAu9+97vx2muvVfuwysb8/Dw++9nPqutVe3s7/vqv/xrpdLrah+agpp1VFxvPPfccduzYgb/5m7/Bli1bYNs2fvazn1X7sCrCZz7zGVx33XX46U9/Wu1DKSu//OUvkU6n8Y1vfAPr16/H66+/jh07duDNN9/El770pWofXkl4+umn8dBDD+FrX/sabr31VnzjG9/A1q1b8Ytf/AJr166t9uGVnB/+8Id44IEHsHHjRszPz+PRRx/Fe9/7XvziF7/ANddcU+3DKzsnTpzAgQMH8K53vavah1JWpqamcOutt+KOO+7Aiy++iGuvvRbDw8NYvXp1tQ+tbDzxxBP4T//pP+Fb3/oW/viP/xgnT57Evffei1WrVmHnzp3VPrwctlASrl69aq9Zs8b+5je/We1DqTjf+9737BtuuMH++c9/bgOwf/KTn1T7kCrKf/gP/8Fet25dtQ+jZPzLf/kv7fvvv9/x2A033GA//PDDVTqiyvL73//eBmD/8Ic/rPahlJ3Lly/bnZ2d9sDAgP2e97zH3rlzZ7UPqWzs3r3bvu2226p9GBXlrrvusv/Nv/k3jsfuvvtu+2Mf+1iVjsiMpGZKxKlTp3D+/HmEQiHcdNNNeMc73oGtW7fi5z//ebUPraz87ne/w44dO/Bf/st/wYoVK6p9OFXh0qVLiMVi1T6MknDlyhW89tpreO973+t4/L3vfS8GBwerdFSV5dKlSwCwZP6mfjzwwAO46667cOedd1b7UMrOd77zHWzYsAH33HMPrr32Wtx00004ePBgtQ+rrNx22204cuQIhoaGAAA//elP8eMf/xgf+MAHqnxkTkSIlIiRkREAwGOPPYbPfvaz+O53v4toNIr3vOc9mJycrPLRlQfbtvGJT3wC999/PzZs2FDtw6kKw8PD+MpXvoL777+/2odSEsbHx5FKpfD2t7/d8fjb3/52/Pa3v63SUVUO27bR39+P2267DTfeeGO1D6esHD58GKdOncKePXuqfSgVYWRkBF//+tfR2dmJ73//+7j//vvR19eHv//7v6/2oZWN3bt348///M9xww034G1vextuuukmPPTQQ/jzP//zah+aAxEieXjsscdgWZbvfydPnlTFP48++ig+9KEP4ZZbbsFTTz0Fy7Lw7LPPVvldFEbQ9/yVr3wF09PTeOSRR6p9yAsm6HvmXLhwAe9///txzz334FOf+lSVjrw8WJbl+Nm2bddjS5EHH3wQ//RP/4T/9t/+W7UPpayMjo5i586d+Pa3v43GxsZqH05FSKfTuPnmm/E3f/M3uOmmm/CXf/mX2LFjB77+9a9X+9DKxtNPP41vf/vbOHToEE6dOoVvfetb+NKXvoRvfetb1T40B1KsmocHH3wQ27Zt831OW1sbLl++DAB45zvfqR5vaGhAe3s73njjjbIeY6kJ+p6/8IUvIJlMuuYXbNiwAR/96Edr7mT3I+h7Ji5cuIA77rgDmzdvxoEDB8p8dJWjpaUF4XDYFf34/e9/74qSLDU+/elP4zvf+Q5+9KMfobW1tdqHU1Zee+01/P73v8ctt9yiHkulUvjRj36Er371q5ibm0M4HK7iEZaed7zjHY7rMwD80R/9EZ577rkqHVH5+Xf/7t/h4YcfVte2P/mTP8Gvf/1r7NmzB3/xF39R5aPLIUIkDy0tLWhpacn7vFtuuQUNDQ341a9+hdtuuw0AcPXqVZw7dw7XX399uQ+zpAR9z/v378cXvvAF9fOFCxfwvve9D08//TQ2bdpUzkMsOUHfM5BpAbzjjjtU1CsUWjqBxfr6etxyyy0YGBjAn/3Zn6nHBwYG8MEPfrCKR1Y+bNvGpz/9afzDP/wDXn75Zaxbt67ah1R2enp6XB199957L2644Qbs3r17yYkQALj11ltdbdlDQ0OL7vpcCG+99Zbr+hQOh2uufVe6ZkrIzp077TVr1tjf//737V/+8pf2Jz/5Sfvaa6+1Jycnq31oFeHs2bNLvmvm/Pnz9vr16+0tW7bYY2Nj9m9+8xv131Lh8OHD9tve9jb7P//n/2z/4he/sB966CH7mmuusc+dO1ftQysLf/VXf2WvWrXKfvnllx1/z7feeqvah1ZRlnrXzP/+3//brqursx9//HH79OnT9n/9r//VXrFihf3tb3+72odWNv7iL/7CXrNmjf3d737XPnv2rP3888/bLS0t9mc+85lqH5oDESIl5MqVK/a//bf/1r722mvtlStX2nfeeaf9+uuvV/uwKsZyECJPPfWUDcD431Li7/7u7+zrr7/erq+vt2+++eYl3crq9fd86qmnqn1oFWWpCxHbtu1//Md/tG+88Ua7oaHBvuGGG+wDBw5U+5DKyvT0tL1z50577dq1dmNjo93e3m4/+uij9tzcXLUPzYFl27ZdjUiMIAiCIAjC0kluC4IgCIKw6BAhIgiCIAhC1RAhIgiCIAhC1RAhIgiCIAhC1RAhIgiCIAhC1RAhIgiCIAhC1RAhIgiCIAhC1RAhIgiCIAhC1RAhIgiCIAhC1RAhIgiCIAhC1RAhIgiCIAhC1RAhIgiCIAhC1fj/AZZqJImFGAVvAAAAAElFTkSuQmCC\n",
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       "text/plain": [
        "
    "
       ]
@@ -1044,12 +1044,12 @@
      "output_type": "stream",
      "text": [
       "Eigenvalues of Covariance matrix\n",
-      "5.288455813429108\n",
-      "0.7754499790100834\n",
+      "5.185584177293881\n",
+      "0.7780841853755783\n",
       "First eigenvector\n",
-      "[0.85299536 0.52191849]\n",
+      "[0.85044503 0.52606392]\n",
       "Second eigenvector\n",
-      "[-0.52191849  0.85299536]\n"
+      "[-0.52606392  0.85044503]\n"
      ]
     },
     {
@@ -1057,7 +1057,7 @@
      "output_type": "stream",
      "text": [
       "Eigenvector of largest eigenvalue\n",
-      "[0.85299536 0.52191849]\n"
+      "[0.85044503 0.52606392]\n"
      ]
     }
    ],
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter8_65_1.png b/doc/LectureNotes/_build/jupyter_execute/chapter8_65_1.png
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+       ""
       ]
      },
      "execution_count": 1,
@@ -1101,7 +1101,7 @@
     {
      "data": {
       "text/plain": [
-       "[]"
+       "[]"
       ]
      },
      "execution_count": 5,
@@ -1802,16 +1802,16 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[0.28836053 4.52113415]\n",
-      "[[4.19528375]\n",
-      " [2.90383424]]\n",
-      "[[4.19528375]\n",
-      " [2.90383424]]\n"
+      "[0.33196524 4.36593124]\n",
+      "[[4.09963157]\n",
+      " [2.99760425]]\n",
+      "[[4.09963157]\n",
+      " [2.99760425]]\n"
      ]
     },
     {
      "data": {
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\n",
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\n",
       "text/plain": [
        "
    "
       ]
@@ -1896,9 +1896,9 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[[4.16575256]\n",
-      " [2.8620652 ]]\n",
-      "[4.11520281] [2.85097049]\n"
+      "[[4.21639245]\n",
+      " [2.82985482]]\n",
+      "[4.15172236] [2.79589065]\n"
      ]
     }
    ],
@@ -2002,15 +2002,15 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[[4.20793824]\n",
-      " [2.75460639]]\n",
-      "[[4.106971  ]\n",
-      " [2.83724637]]\n"
+      "[[3.98919197]\n",
+      " [2.94015598]]\n",
+      "[[3.94925462]\n",
+      " [2.97087408]]\n"
      ]
     },
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "
    "
       ]
@@ -2389,20 +2389,20 @@
      "output_type": "stream",
      "text": [
       "Own inversion\n",
-      "[[4.31347523]\n",
-      " [2.69915639]]\n",
-      "Eigenvalues of Hessian Matrix:[0.28457442 4.43693489]\n",
+      "[[4.5424657 ]\n",
+      " [2.40026896]]\n",
+      "Eigenvalues of Hessian Matrix:[0.29830651 3.89658408]\n",
       "theta from own gd\n",
-      "[[4.31347523]\n",
-      " [2.69915639]]\n",
+      "[[4.5424657 ]\n",
+      " [2.40026896]]\n",
       "theta from own sdg\n",
-      "[[4.2891298 ]\n",
-      " [2.67783138]]\n"
+      "[[4.55687658]\n",
+      " [2.41165766]]\n"
      ]
     },
     {
      "data": {
-      "image/png": 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\n",
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diff --git a/doc/LectureNotes/_build/jupyter_execute/exercisesweek37.ipynb b/doc/LectureNotes/_build/jupyter_execute/exercisesweek37.ipynb
new file mode 100644
index 000000000..9fe8aa4ac
--- /dev/null
+++ b/doc/LectureNotes/_build/jupyter_execute/exercisesweek37.ipynb
@@ -0,0 +1,261 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "28222517",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "\n",
+    ""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c7ffd7b0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "# Exercises week 37\n",
+    "**September 11-15, 2023**\n",
+    "\n",
+    "Date: **Deadline is Sunday September 17 at midnight**"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f687d0b0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Overarching aims of the exercises this week\n",
+    "\n",
+    "This exercise deals with various mean values and variances in  linear regression method (here it may be useful to look up chapter 3, equation (3.8) of [Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer](https://www.springer.com/gp/book/9780387848570)). The exercise is also a part of project 1 and can be reused in the theory part of the project.\n",
+    "\n",
+    "For more discussions on Ridge regression and calculation of expectation values, [Wessel van Wieringen's](https://arxiv.org/abs/1509.09169) article is highly recommended.\n",
+    "\n",
+    "The assumption we have made is \n",
+    "that there exists a continuous function $f(\\boldsymbol{x})$ and  a normal distributed error $\\boldsymbol{\\varepsilon}\\sim N(0, \\sigma^2)$\n",
+    "which describes our data"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b0b5ae03",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{y} = f(\\boldsymbol{x})+\\boldsymbol{\\varepsilon}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a5442d69",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "We then approximate this function $f(\\boldsymbol{x})$ with our model $\\boldsymbol{\\tilde{y}}$ from the solution of the linear regression equations (ordinary least squares OLS), that is our\n",
+    "function $f$ is approximated by $\\boldsymbol{\\tilde{y}}$ where we minimized  $(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2$, with"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d9ac69f5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{\\tilde{y}} = \\boldsymbol{X}\\boldsymbol{\\beta}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6f42da1d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "The matrix $\\boldsymbol{X}$ is the so-called design or feature matrix."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5690cef0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Exercise 1: Expectation values for ordinary least squares expressions\n",
+    "\n",
+    "Show that  the expectation value of $\\boldsymbol{y}$ for a given element $i$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3834fc47",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathbb{E}(y_i)  =\\sum_{j}x_{ij} \\beta_j=\\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "bcfd68b4",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "and that\n",
+    "its variance is"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9551e381",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mbox{Var}(y_i)  = \\sigma^2.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e470afef",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Hence, $y_i \\sim N( \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta}, \\sigma^2)$, that is $\\boldsymbol{y}$ follows a normal distribution with \n",
+    "mean value $\\boldsymbol{X}\\boldsymbol{\\beta}$ and variance $\\sigma^2$.\n",
+    "\n",
+    "With the OLS expressions for the optimal parameters $\\boldsymbol{\\hat{\\beta}}$ show that"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6ece00ae",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathbb{E}(\\boldsymbol{\\hat{\\beta}}) = \\boldsymbol{\\beta}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "98bad716",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Show finally that the variance of $\\boldsymbol{\\beta}$ is"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a8dad13c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mbox{Var}(\\boldsymbol{\\hat{\\beta}}) = \\sigma^2 \\, (\\mathbf{X}^{T} \\mathbf{X})^{-1}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "94cddcc3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "We can use the last expression when we define a [so-called confidence interval](https://en.wikipedia.org/wiki/Confidence_interval) for the parameters $\\beta$. \n",
+    "A given parameter $\\beta_j$ is given by the diagonal matrix element of the above matrix."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8e5c2d66",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Exercise 2: Expectation values for Ridge regression\n",
+    "\n",
+    "Show that"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5d7e493e",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathbb{E} \\big[ \\boldsymbol{\\beta}^{\\mathrm{Ridge}} \\big]=(\\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I}_{pp})^{-1} (\\mathbf{X}^{\\top} \\mathbf{X})\\\n",
+    "\\boldsymbol{\\beta}^{\\mathrm{OLS}}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "44050008",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "We see clearly that\n",
+    "$\\mathbb{E} \\big[ \\boldsymbol{\\beta}^{\\mathrm{Ridge}} \\big] \\not= \\boldsymbol{\\beta}^{\\mathrm{OLS}}$ for any $\\lambda > 0$.\n",
+    "\n",
+    "Show also that the variance is"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c0bf3608",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mbox{Var}[\\boldsymbol{\\beta}^{\\mathrm{Ridge}}]=\\sigma^2[  \\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1}  \\mathbf{X}^{T} \\mathbf{X} \\{ [  \\m\\\n",
+    "athbf{X}^{\\top} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1}\\}^{T},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "371484f8",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "and it is easy to see that if the parameter $\\lambda$ goes to infinity then the variance of Ridge parameters $\\boldsymbol{\\beta}$ goes to zero."
+   ]
+  }
+ ],
+ "metadata": {},
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
\ No newline at end of file
diff --git a/doc/LectureNotes/_build/jupyter_execute/exercisesweek37.txt b/doc/LectureNotes/_build/jupyter_execute/exercisesweek37.txt
new file mode 100644
index 000000000..e69de29bb
diff --git a/doc/LectureNotes/_build/jupyter_execute/linalg.ipynb b/doc/LectureNotes/_build/jupyter_execute/linalg.ipynb
index 2f5f96d52..64a0a00c0 100644
--- a/doc/LectureNotes/_build/jupyter_execute/linalg.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/linalg.ipynb
@@ -225,8 +225,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[-0.87136737  1.4300745  -0.3322326  -0.66758934 -1.00283636 -0.27625974\n",
-      "  1.89249454 -0.25006757  0.73565195  0.33697405]\n"
+      "[-0.28587856 -0.73509675  0.35559283 -0.62819534 -0.15254784 -0.44792888\n",
+      "  1.5393681  -0.81784072  0.53476918  1.02055673]\n"
      ]
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@@ -662,26 +662,26 @@
      "name": "stdout",
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-      "  0.79577619 0.85212606 0.86811137 0.43001767]]\n"
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+      "  0.14491591 0.71135895 0.84723978 0.03416188]]\n"
      ]
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@@ -800,13 +800,13 @@
      "name": "stdout",
      "output_type": "stream",
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-      "0.03499693245669077\n",
-      "4.187268182169147\n",
-      "-0.19627430151896047\n",
-      "[[ 1.0622197   3.16232481  2.98018358]\n",
-      " [ 3.16232481 10.48442771  8.58039072]\n",
-      " [ 2.98018358  8.58039072 13.66351927]]\n",
-      "[21.70244042  0.07978179  3.42794448]\n"
+      "0.041129694365319464\n",
+      "4.025325212488352\n",
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+      " [ 3.73704762 12.59095724 12.81409445]\n",
+      " [ 4.12446443 12.81409445 20.04983109]]\n",
+      "[30.70850263  0.10254846  3.06293056]\n"
      ]
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diff --git a/doc/LectureNotes/_build/jupyter_execute/project1.ipynb b/doc/LectureNotes/_build/jupyter_execute/project1.ipynb
index 85d28025c..1dc204909 100644
--- a/doc/LectureNotes/_build/jupyter_execute/project1.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/project1.ipynb
@@ -143,7 +143,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_19350/39730396.py:11: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7740/39730396.py:11: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().\n",
       "  ax = fig.gca(projection='3d')\n"
      ]
     },
diff --git a/doc/LectureNotes/_build/jupyter_execute/statistics.ipynb b/doc/LectureNotes/_build/jupyter_execute/statistics.ipynb
index 99b1a0c6b..d905662e4 100644
--- a/doc/LectureNotes/_build/jupyter_execute/statistics.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/statistics.ipynb
@@ -1344,27 +1344,27 @@
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+      "   2.39969826 11.96804878  3.57488231  3.68232235]]\n"
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@@ -2001,15 +2001,15 @@
      "name": "stdout",
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-      " [1.81486046 5.44210344 7.06273487]]\n",
-      "[13.62123034  0.09662862  2.05480098]\n"
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+      "[[ 1.0120561   2.97409408  3.83858458]\n",
+      " [ 2.97409408  9.78515702 11.18409479]\n",
+      " [ 3.83858458 11.18409479 24.03654164]]\n",
+      "[30.9410965   0.08502185  3.80763641]\n"
      ]
     }
    ],
@@ -2638,7 +2638,7 @@
    "outputs": [
     {
      "data": {
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\n",
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\n",
       "text/plain": [
        "
    "
       ]
@@ -2764,12 +2764,12 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0.029574060388349064 0.9577775794806141\n"
+      "-0.026121042099059435 1.0617129312534124\n"
      ]
     },
     {
      "data": {
-      "image/png": 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\n",
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+    ""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "82315184",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "# Week 37: Statitsitcal interpretations and Resampling Methods\n",
+    "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University\n",
+    "\n",
+    "Date: **Sep 11, 2023**\n",
+    "\n",
+    "Copyright 1999-2023, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n",
+    "\n",
+    ""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7132df07",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Plans for week 37\n",
+    "\n",
+    "**Material for the active learning sessions on Tuesday and Wednesday.**\n",
+    "\n",
+    "  * Lecture from last week on calculations of expectation values\n",
+    "\n",
+    "  * Exercise for week 37\n",
+    "\n",
+    "  * Work on project 1\n",
+    "\n",
+    "  * See also additional note on scaling (jupyter-notebook) sent separately. This will be discussed during the first hour of each session.\n",
+    "\n",
+    "  * For more discussions of Ridge regression and calculation of averages, [Wessel van Wieringen's](https://arxiv.org/abs/1509.09169) article is highly recommended.\n",
+    "\n",
+    "  \n",
+    "**Material for the lecture on Thursday September 7.**\n",
+    "\n",
+    "  * Statistical interpretation of Ridge and Lasso regression\n",
+    "\n",
+    "  * Resampling techniques, Bootstrap and cross validation and bias-variance tradeoff\n",
+    "\n",
+    "  * Reads and Videos:\n",
+    "\n",
+    "    * Hastie et al Chapter 7, here we recommend 7.1-7.5 and 7.10 (cross-validation) and 7.11 (bootstrap). \n",
+    "\n",
+    "    * [Video on cross validation](https://www.youtube.com/watch?v=fSytzGwwBVw)\n",
+    "\n",
+    "    * [Video on bias-variance tradeoff](https://www.youtube.com/watch?v=EuBBz3bI-aA)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0928fd34",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Material from last week and relevant for the weekly exercises"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9ee88de5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Linking the regression analysis with a statistical interpretation\n",
+    "\n",
+    "We will now couple the discussions of ordinary least squares, Ridge\n",
+    "and Lasso regression with a statistical interpretation, that is we\n",
+    "move from a linear algebra analysis to a statistical analysis. In\n",
+    "particular, we will focus on what the regularization terms can result\n",
+    "in.  We will amongst other things show that the regularization\n",
+    "parameter can reduce considerably the variance of the parameters\n",
+    "$\\beta$.\n",
+    "\n",
+    "The\n",
+    "advantage of doing linear regression is that we actually end up with\n",
+    "analytical expressions for several statistical quantities.  \n",
+    "Standard least squares and Ridge regression  allow us to\n",
+    "derive quantities like the variance and other expectation values in a\n",
+    "rather straightforward way.\n",
+    "\n",
+    "It is assumed that $\\varepsilon_i\n",
+    "\\sim \\mathcal{N}(0, \\sigma^2)$ and the $\\varepsilon_{i}$ are\n",
+    "independent, i.e.:"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fd2470fe",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\begin{align*} \n",
+    "\\mbox{Cov}(\\varepsilon_{i_1},\n",
+    "\\varepsilon_{i_2}) & = \\left\\{ \\begin{array}{lcc} \\sigma^2 & \\mbox{if}\n",
+    "& i_1 = i_2, \\\\ 0 & \\mbox{if} & i_1 \\not= i_2.  \\end{array} \\right.\n",
+    "\\end{align*}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8be57b04",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "The randomness of $\\varepsilon_i$ implies that\n",
+    "$\\mathbf{y}_i$ is also a random variable. In particular,\n",
+    "$\\mathbf{y}_i$ is normally distributed, because $\\varepsilon_i \\sim\n",
+    "\\mathcal{N}(0, \\sigma^2)$ and $\\mathbf{X}_{i,\\ast} \\, \\boldsymbol{\\beta}$ is a\n",
+    "non-random scalar. To specify the parameters of the distribution of\n",
+    "$\\mathbf{y}_i$ we need to calculate its first two moments. \n",
+    "\n",
+    "Recall that $\\boldsymbol{X}$ is a matrix of dimensionality $n\\times p$. The\n",
+    "notation above $\\mathbf{X}_{i,\\ast}$ means that we are looking at the\n",
+    "row number $i$ and perform a sum over all values $p$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ee33fde6",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Assumptions made\n",
+    "\n",
+    "The assumption we have made here can be summarized as (and this is going to be useful when we discuss the bias-variance trade off)\n",
+    "that there exists a function $f(\\boldsymbol{x})$ and  a normal distributed error $\\boldsymbol{\\varepsilon}\\sim \\mathcal{N}(0, \\sigma^2)$\n",
+    "which describe our data"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "14124ae5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{y} = f(\\boldsymbol{x})+\\boldsymbol{\\varepsilon}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "02600bff",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "We approximate this function with our model from the solution of the linear regression equations, that is our\n",
+    "function $f$ is approximated by $\\boldsymbol{\\tilde{y}}$ where we want to minimize $(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2$, our MSE, with"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7df4b213",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{\\tilde{y}} = \\boldsymbol{X}\\boldsymbol{\\beta}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "996d8e2d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Expectation value and variance\n",
+    "\n",
+    "We can calculate the expectation value of $\\boldsymbol{y}$ for a given element $i$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "815b60ed",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\begin{align*} \n",
+    "\\mathbb{E}(y_i) & =\n",
+    "\\mathbb{E}(\\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta}) + \\mathbb{E}(\\varepsilon_i)\n",
+    "\\, \\, \\, = \\, \\, \\, \\mathbf{X}_{i, \\ast} \\, \\beta, \n",
+    "\\end{align*}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a93b64c7",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "while\n",
+    "its variance is"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "61c06c9b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\begin{align*} \\mbox{Var}(y_i) & = \\mathbb{E} \\{ [y_i\n",
+    "- \\mathbb{E}(y_i)]^2 \\} \\, \\, \\, = \\, \\, \\, \\mathbb{E} ( y_i^2 ) -\n",
+    "[\\mathbb{E}(y_i)]^2  \\\\  & = \\mathbb{E} [ ( \\mathbf{X}_{i, \\ast} \\,\n",
+    "\\beta + \\varepsilon_i )^2] - ( \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta})^2 \\\\ &\n",
+    "= \\mathbb{E} [ ( \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta})^2 + 2 \\varepsilon_i\n",
+    "\\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta} + \\varepsilon_i^2 ] - ( \\mathbf{X}_{i,\n",
+    "\\ast} \\, \\beta)^2 \\\\  & = ( \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta})^2 + 2\n",
+    "\\mathbb{E}(\\varepsilon_i) \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta} +\n",
+    "\\mathbb{E}(\\varepsilon_i^2 ) - ( \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta})^2 \n",
+    "\\\\ & = \\mathbb{E}(\\varepsilon_i^2 ) \\, \\, \\, = \\, \\, \\,\n",
+    "\\mbox{Var}(\\varepsilon_i) \\, \\, \\, = \\, \\, \\, \\sigma^2.  \n",
+    "\\end{align*}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "bb1eb3a5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Hence, $y_i \\sim \\mathcal{N}( \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta}, \\sigma^2)$, that is $\\boldsymbol{y}$ follows a normal distribution with \n",
+    "mean value $\\boldsymbol{X}\\boldsymbol{\\beta}$ and variance $\\sigma^2$ (not be confused with the singular values of the SVD)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ea804d82",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Expectation value and variance for $\\boldsymbol{\\beta}$\n",
+    "\n",
+    "With the OLS expressions for the optimal parameters $\\boldsymbol{\\hat{\\beta}}$ we can evaluate the expectation value"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "896c9968",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathbb{E}(\\boldsymbol{\\hat{\\beta}}) = \\mathbb{E}[ (\\mathbf{X}^{\\top} \\mathbf{X})^{-1}\\mathbf{X}^{T} \\mathbf{Y}]=(\\mathbf{X}^{T} \\mathbf{X})^{-1}\\mathbf{X}^{T} \\mathbb{E}[ \\mathbf{Y}]=(\\mathbf{X}^{T} \\mathbf{X})^{-1} \\mathbf{X}^{T}\\mathbf{X}\\boldsymbol{\\beta}=\\boldsymbol{\\beta}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "27adffa2",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "This means that the estimator of the regression parameters is unbiased.\n",
+    "\n",
+    "We can also calculate the variance\n",
+    "\n",
+    "The variance of the optimal value $\\boldsymbol{\\hat{\\beta}}$ is"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b3cb4e94",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\begin{eqnarray*}\n",
+    "\\mbox{Var}(\\boldsymbol{\\hat{\\beta}}) & = & \\mathbb{E} \\{ [\\boldsymbol{\\beta} - \\mathbb{E}(\\boldsymbol{\\beta})] [\\boldsymbol{\\beta} - \\mathbb{E}(\\boldsymbol{\\beta})]^{T} \\}\n",
+    "\\\\\n",
+    "& = & \\mathbb{E} \\{ [(\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\mathbf{Y} - \\boldsymbol{\\beta}] \\, [(\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\mathbf{Y} - \\boldsymbol{\\beta}]^{T} \\}\n",
+    "\\\\\n",
+    "% & = & \\mathbb{E} \\{ [(\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\mathbf{Y}] \\, [(\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\mathbf{Y}]^{T} \\} - \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T}\n",
+    "% \\\\\n",
+    "% & = & \\mathbb{E} \\{ (\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\mathbf{Y} \\, \\mathbf{Y}^{T} \\, \\mathbf{X} \\, (\\mathbf{X}^{T} \\mathbf{X})^{-1}  \\} - \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T}\n",
+    "% \\\\\n",
+    "& = & (\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\, \\mathbb{E} \\{ \\mathbf{Y} \\, \\mathbf{Y}^{T} \\} \\, \\mathbf{X} \\, (\\mathbf{X}^{T} \\mathbf{X})^{-1} - \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T}\n",
+    "\\\\\n",
+    "& = & (\\mathbf{X}^{T} \\mathbf{X})^{-1} \\, \\mathbf{X}^{T} \\, \\{ \\mathbf{X} \\, \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T} \\,  \\mathbf{X}^{T} + \\sigma^2 \\} \\, \\mathbf{X} \\, (\\mathbf{X}^{T} \\mathbf{X})^{-1} - \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T}\n",
+    "% \\\\\n",
+    "% & = & (\\mathbf{X}^T \\mathbf{X})^{-1} \\, \\mathbf{X}^T \\, \\mathbf{X} \\, \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^T \\,  \\mathbf{X}^T \\, \\mathbf{X} \\, (\\mathbf{X}^T % \\mathbf{X})^{-1}\n",
+    "% \\\\\n",
+    "% & & + \\, \\, \\sigma^2 \\, (\\mathbf{X}^T \\mathbf{X})^{-1} \\, \\mathbf{X}^T  \\, \\mathbf{X} \\, (\\mathbf{X}^T \\mathbf{X})^{-1} - \\boldsymbol{\\beta} \\boldsymbol{\\beta}^T\n",
+    "\\\\\n",
+    "& = & \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T}  + \\sigma^2 \\, (\\mathbf{X}^{T} \\mathbf{X})^{-1} - \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T}\n",
+    "\\, \\, \\, = \\, \\, \\, \\sigma^2 \\, (\\mathbf{X}^{T} \\mathbf{X})^{-1},\n",
+    "\\end{eqnarray*}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "98964900",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where we have used  that $\\mathbb{E} (\\mathbf{Y} \\mathbf{Y}^{T}) =\n",
+    "\\mathbf{X} \\, \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T} \\, \\mathbf{X}^{T} +\n",
+    "\\sigma^2 \\, \\mathbf{I}_{nn}$. From $\\mbox{Var}(\\boldsymbol{\\beta}) = \\sigma^2\n",
+    "\\, (\\mathbf{X}^{T} \\mathbf{X})^{-1}$, one obtains an estimate of the\n",
+    "variance of the estimate of the $j$-th regression coefficient:\n",
+    "$\\boldsymbol{\\sigma}^2 (\\boldsymbol{\\beta}_j ) = \\boldsymbol{\\sigma}^2 [(\\mathbf{X}^{T} \\mathbf{X})^{-1}]_{jj} $. This may be used to\n",
+    "construct a confidence interval for the estimates.\n",
+    "\n",
+    "In a similar way, we can obtain analytical expressions for say the\n",
+    "expectation values of the parameters $\\boldsymbol{\\beta}$ and their variance\n",
+    "when we employ Ridge regression, allowing us again to define a confidence interval. \n",
+    "\n",
+    "It is rather straightforward to show that"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ae46385d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathbb{E} \\big[ \\boldsymbol{\\beta}^{\\mathrm{Ridge}} \\big]=(\\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I}_{pp})^{-1} (\\mathbf{X}^{\\top} \\mathbf{X})\\boldsymbol{\\beta}^{\\mathrm{OLS}}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "862ec8d1",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "We see clearly that \n",
+    "$\\mathbb{E} \\big[ \\boldsymbol{\\beta}^{\\mathrm{Ridge}} \\big] \\not= \\boldsymbol{\\beta}^{\\mathrm{OLS}}$ for any $\\lambda > 0$.\n",
+    "\n",
+    "We can also compute the variance as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1c05ca70",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mbox{Var}[\\boldsymbol{\\beta}^{\\mathrm{Ridge}}]=\\sigma^2[  \\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1}  \\mathbf{X}^{T} \\mathbf{X} \\{ [  \\mathbf{X}^{\\top} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1}\\}^{T},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a714192d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "and it is easy to see that if the parameter $\\lambda$ goes to infinity then the variance of Ridge parameters $\\boldsymbol{\\beta}$ goes to zero. \n",
+    "\n",
+    "With this, we can compute the difference"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "bd80e6ae",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mbox{Var}[\\boldsymbol{\\beta}^{\\mathrm{OLS}}]-\\mbox{Var}(\\boldsymbol{\\beta}^{\\mathrm{Ridge}})=\\sigma^2 [  \\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1}[ 2\\lambda\\mathbf{I} + \\lambda^2 (\\mathbf{X}^{T} \\mathbf{X})^{-1} ] \\{ [  \\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1}\\}^{T}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "272d7c5c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "The difference is non-negative definite since each component of the\n",
+    "matrix product is non-negative definite. \n",
+    "This means the variance we obtain with the standard OLS will always for $\\lambda > 0$ be larger than the variance of $\\boldsymbol{\\beta}$ obtained with the Ridge estimator. This has interesting consequences when we discuss the so-called bias-variance trade-off below. \n",
+    "\n",
+    "For more discussions of Ridge regression and calculation of averages, [Wessel van Wieringen's](https://arxiv.org/abs/1509.09169) article is highly recommended."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c87b5aa5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Material for lecture Thursday September 14"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c946f771",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Deriving OLS from a probability distribution\n",
+    "\n",
+    "Our basic assumption when we derived the OLS equations was to assume\n",
+    "that our output is determined by a given continuous function\n",
+    "$f(\\boldsymbol{x})$ and a random noise $\\boldsymbol{\\epsilon}$ given by the normal\n",
+    "distribution with zero mean value and an undetermined variance\n",
+    "$\\sigma^2$.\n",
+    "\n",
+    "We found above that the outputs $\\boldsymbol{y}$ have a mean value given by\n",
+    "$\\boldsymbol{X}\\hat{\\boldsymbol{\\beta}}$ and variance $\\sigma^2$. Since the entries to\n",
+    "the design matrix are not stochastic variables, we can assume that the\n",
+    "probability distribution of our targets is also a normal distribution\n",
+    "but now with mean value $\\boldsymbol{X}\\hat{\\boldsymbol{\\beta}}$. This means that a\n",
+    "single output $y_i$ is given by the Gaussian distribution"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e6b4e7dd",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "y_i\\sim \\mathcal{N}(\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta}, \\sigma^2)=\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta})^2}{2\\sigma^2}\\right]}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8169d91a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Independent and Identically Distrubuted (iid)\n",
+    "\n",
+    "We assume now that the various $y_i$ values are stochastically distributed according to the above Gaussian distribution. \n",
+    "We define this distribution as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "99e90d11",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "p(y_i, \\boldsymbol{X}\\vert\\boldsymbol{\\beta})=\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta})^2}{2\\sigma^2}\\right]},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0b4adc26",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "which reads as finding the likelihood of an event $y_i$ with the input variables $\\boldsymbol{X}$ given the parameters (to be determined) $\\boldsymbol{\\beta}$.\n",
+    "\n",
+    "Since these events are assumed to be independent and identicall distributed we can build the probability distribution function (PDF) for all possible event $\\boldsymbol{y}$ as the product of the single events, that is we have"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9ca9e238",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "p(\\boldsymbol{y},\\boldsymbol{X}\\vert\\boldsymbol{\\beta})=\\prod_{i=0}^{n-1}\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta})^2}{2\\sigma^2}\\right]}=\\prod_{i=0}^{n-1}p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\beta}).\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "23dcb3a5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "We will write this in a more compact form reserving $\\boldsymbol{D}$ for the domain of events, including the ouputs (targets) and the inputs. That is\n",
+    "in case we have a simple one-dimensional input and output case"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "67cb2d01",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{D}=[(x_0,y_0), (x_1,y_1),\\dots, (x_{n-1},y_{n-1})].\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "80d807da",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "In the more general case the various inputs should be replaced by the possible features represented by the input data set $\\boldsymbol{X}$. \n",
+    "We can now rewrite the above probability as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "14b1cbfd",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "p(\\boldsymbol{D}\\vert\\boldsymbol{\\beta})=\\prod_{i=0}^{n-1}\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta})^2}{2\\sigma^2}\\right]}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "cf86395e",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "It is a conditional probability (see below) and reads as the likelihood of a domain of events $\\boldsymbol{D}$ given a set of parameters $\\boldsymbol{\\beta}$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4eee417a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Maximum Likelihood Estimation (MLE)\n",
+    "\n",
+    "In statistics, maximum likelihood estimation (MLE) is a method of\n",
+    "estimating the parameters of an assumed probability distribution,\n",
+    "given some observed data. This is achieved by maximizing a likelihood\n",
+    "function so that, under the assumed statistical model, the observed\n",
+    "data is the most probable. \n",
+    "\n",
+    "We will assume here that our events are given by the above Gaussian\n",
+    "distribution and we will determine the optimal parameters $\\beta$ by\n",
+    "maximizing the above PDF. However, computing the derivatives of a\n",
+    "product function is cumbersome and can easily lead to overflow and/or\n",
+    "underflowproblems, with potentials for loss of numerical precision.\n",
+    "\n",
+    "In practice, it is more convenient to maximize the logarithm of the\n",
+    "PDF because it is a monotonically increasing function of the argument.\n",
+    "Alternatively, and this will be our option, we will minimize the\n",
+    "negative of the logarithm since this is a monotonically decreasing\n",
+    "function.\n",
+    "\n",
+    "Note also that maximization/minimization of the logarithm of the PDF\n",
+    "is equivalent to the maximization/minimization of the function itself."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "02893846",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## A new Cost Function\n",
+    "\n",
+    "We could now define a new cost function to minimize, namely the negative logarithm of the above PDF"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "098674aa",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "C(\\boldsymbol{\\beta}=-\\log{\\prod_{i=0}^{n-1}p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\beta})}=-\\sum_{i=0}^{n-1}\\log{p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\beta})},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "76b18e95",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "which becomes"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "52c82f5e",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "C(\\boldsymbol{\\beta}=\\frac{n}{2}\\log{2\\pi\\sigma^2}+\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})\\vert\\vert_2^2}{2\\sigma^2}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "46e101f5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Taking the derivative of the *new* cost function with respect to the parameters $\\beta$ we recognize our familiar OLS equation, namely"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e8527450",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{X}^T\\left(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right) =0,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a421d3d5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "which leads to the well-known OLS equation for the optimal paramters $\\beta$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "22137f8a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\hat{\\boldsymbol{\\beta}}^{\\mathrm{OLS}}=\\left(\\boldsymbol{X}^T\\boldsymbol{X}\\right)^{-1}\\boldsymbol{X}^T\\boldsymbol{y}!\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4eb8b2fa",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Before we make a similar analysis for Ridge and Lasso regression, we need a short reminder on statistics."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8752defc",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## More basic Statistics and Bayes' theorem\n",
+    "\n",
+    "A central theorem in statistics is Bayes' theorem. This theorem plays a similar role as the good old Pythagoras' theorem in geometry.\n",
+    "Bayes' theorem is extremely simple to derive. But to do so we need some basic axioms from statistics.\n",
+    "\n",
+    "Assume we have two domains of events $X=[x_0,x_1,\\dots,x_{n-1}]$ and $Y=[y_0,y_1,\\dots,y_{n-1}]$.\n",
+    "\n",
+    "We define also the likelihood for $X$ and $Y$ as $p(X)$ and $p(Y)$ respectively.\n",
+    "The likelihood of a specific event $x_i$ (or $y_i$) is then written as $p(X=x_i)$ or just $p(x_i)=p_i$. \n",
+    "\n",
+    "**Union of events is given by.**"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4befff39",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "p(X \\cup Y)= p(X)+p(Y)-p(X \\cap Y).\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d18ce941",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "**The product rule (aka joint probability) is given by.**"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0a4fd449",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "p(X \\cup Y)= p(X,Y)= p(X\\vert Y)p(Y)=p(Y\\vert X)p(X),\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ec27160e",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where we read $p(X\\vert Y)$ as the likelihood of obtaining $X$ given $Y$.\n",
+    "\n",
+    "If we have independent events then $p(X,Y)=p(X)p(Y)$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "cd11746f",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Marginal Probability\n",
+    "\n",
+    "The marginal probability is defined in terms of only one of the set of variables $X,Y$. For a discrete probability we have"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b966cbbf",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "p(X)=\\sum_{i=0}^{n-1}p(X,Y=y_i)=\\sum_{i=0}^{n-1}p(X\\vert Y=y_i)p(Y=y_i)=\\sum_{i=0}^{n-1}p(X\\vert y_i)p(y_i).\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "bccd1443",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Conditional  Probability\n",
+    "\n",
+    "The conditional  probability, if $p(Y) > 0$, is"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7b6361b1",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "p(X\\vert Y)= \\frac{p(X,Y)}{p(Y)}=\\frac{p(X,Y)}{\\sum_{i=0}^{n-1}p(Y\\vert X=x_i)p(x_i)}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f1ff2fe1",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Bayes' Theorem\n",
+    "\n",
+    "If we combine the conditional probability with the marginal probability and the standard product rule, we have"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ccc6b096",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "p(X\\vert Y)= \\frac{p(X,Y)}{p(Y)},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "86507503",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "which we can rewrite as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "bee1fbb6",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "p(X\\vert Y)= \\frac{p(X,Y)}{\\sum_{i=0}^{n-1}p(Y\\vert X=x_i)p(x_i)}=\\frac{p(Y\\vert X)p(X)}{\\sum_{i=0}^{n-1}p(Y\\vert X=x_i)p(x_i)},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ae2e7deb",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "which is Bayes' theorem. It allows us to evaluate the uncertainty in in $X$ after we have observed $Y$. We can easily interchange $X$ with $Y$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8e262661",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Interpretations of Bayes' Theorem\n",
+    "\n",
+    "The quantity $p(Y\\vert X)$ on the right-hand side of the theorem is\n",
+    "evaluated for the observed data $Y$ and can be viewed as a function of\n",
+    "the parameter space represented by $X$. This function is not\n",
+    "necesseraly normalized and is normally called the likelihood function.\n",
+    "\n",
+    "The function $p(X)$ on the right hand side is called the prior while the function on the left hand side is the called the posterior probability. The denominator on the right hand side serves as a normalization factor for the posterior distribution.\n",
+    "\n",
+    "Let us try to illustrate Bayes' theorem through an example."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5de65e5b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Example of Usage of Bayes' theorem\n",
+    "\n",
+    "Let us suppose that you are undergoing a series of mammography scans in\n",
+    "order to rule out possible breast cancer cases.  We define the\n",
+    "sensitivity for a positive event by the variable $X$. It takes binary\n",
+    "values with $X=1$ representing a positive event and $X=0$ being a\n",
+    "negative event. We reserve $Y$ as a classification parameter for\n",
+    "either a negative or a positive breast cancer confirmation. (Short note on wordings: positive here means having breast cancer, although none of us would consider this being a  positive thing).\n",
+    "\n",
+    "We let $Y=1$ represent the the case of having breast cancer and $Y=0$ as not.\n",
+    "\n",
+    "Let us assume that if you have breast cancer, the test will be positive with a probability of $0.8$, that is we have"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6f1ba40c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "p(X=1\\vert Y=1) =0.8.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0e4cdf38",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "This obviously sounds  scary since many would conclude that if the test is positive, there is a likelihood of $80\\%$ for having cancer.\n",
+    "It is however not correct, as the following Bayesian analysis shows."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "76584b5c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Doing it correctly\n",
+    "\n",
+    "If we look at various national surveys on breast cancer, the general likelihood of developing breast cancer is a very small number.\n",
+    "Let us assume that the prior probability in the population as a whole is"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a879a6bd",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "p(Y=1) =0.004.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "dd0274e0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "We need also to account for the fact that the test may produce a false positive result (false alarm). Let us here assume that we have"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "684fbc25",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "p(X=1\\vert Y=0) =0.1.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "54cd9a76",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Using Bayes' theorem we can then find the posterior probability that the person has breast cancer in case of a positive test, that is we can compute"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "051338d6",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "p(Y=1\\vert X=1)=\\frac{p(X=1\\vert Y=1)p(Y=1)}{p(X=1\\vert Y=1)p(Y=1)+p(X=1\\vert Y=0)p(Y=0)}=\\frac{0.8\\times 0.004}{0.8\\times 0.004+0.1\\times 0.996}=0.031.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e5f3d505",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "That is, in case of a positive test, there is only a $3\\%$ chance of having breast cancer!"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ef60f6e2",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Bayes' Theorem and Ridge and Lasso Regression\n",
+    "\n",
+    "Using Bayes' theorem we can gain a better intuition about Ridge and Lasso regression. \n",
+    "\n",
+    "For ordinary least squares we postulated that the maximum likelihood for the doamin of events $\\boldsymbol{D}$ (one-dimensional case)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "dde5ce68",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{D}=[(x_0,y_0), (x_1,y_1),\\dots, (x_{n-1},y_{n-1})],\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "428b7cfc",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "is given by"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "95ad5eba",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "p(\\boldsymbol{D}\\vert\\boldsymbol{\\beta})=\\prod_{i=0}^{n-1}\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta})^2}{2\\sigma^2}\\right]}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6e6b706c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "In Bayes' theorem this function plays the role of the so-called likelihood. We could now ask the question what is the posterior probability of a parameter set $\\boldsymbol{\\beta}$ given a domain of events $\\boldsymbol{D}$?  That is, how can we define the posterior probability"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6e6a60cb",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "p(\\boldsymbol{\\beta}\\vert\\boldsymbol{D}).\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c7127db8",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Bayes' theorem comes to our rescue here since (omitting the normalization constant)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "60288e6d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "p(\\boldsymbol{\\beta}\\vert\\boldsymbol{D})\\propto p(\\boldsymbol{D}\\vert\\boldsymbol{\\beta})p(\\boldsymbol{\\beta}).\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0e8d9dfd",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "We have a model for $p(\\boldsymbol{D}\\vert\\boldsymbol{\\beta})$ but need one for the **prior** $p(\\boldsymbol{\\beta}$!"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c0450362",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Ridge and Bayes\n",
+    "\n",
+    "With the posterior probability defined by a likelihood which we have\n",
+    "already modeled and an unknown prior, we are now ready to make\n",
+    "additional models for the prior.\n",
+    "\n",
+    "We can, based on our discussions of the variance of $\\boldsymbol{\\beta}$ and the mean value, assume that the prior for the values $\\boldsymbol{\\beta}$ is given by a Gaussian with mean value zero and variance $\\tau^2$, that is"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5911b76d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "p(\\boldsymbol{\\beta})=\\prod_{j=0}^{p-1}\\exp{\\left(-\\frac{\\beta_j^2}{2\\tau^2}\\right)}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6029916b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Our posterior probability becomes then (omitting the normalization factor which is just a constant)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b704a6fd",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "p(\\boldsymbol{\\beta\\vert\\boldsymbol{D})}=\\prod_{i=0}^{n-1}\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta})^2}{2\\sigma^2}\\right]}\\prod_{j=0}^{p-1}\\exp{\\left(-\\frac{\\beta_j^2}{2\\tau^2}\\right)}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "60c7948c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "We can now optimize this quantity with respect to $\\boldsymbol{\\beta}$. As we\n",
+    "did for OLS, this is most conveniently done by taking the negative\n",
+    "logarithm of the posterior probability. Doing so and leaving out the\n",
+    "constants terms that do not depend on $\\beta$, we have"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "51dcd9c3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "C(\\boldsymbol{\\beta})=\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})\\vert\\vert_2^2}{2\\sigma^2}+\\frac{1}{2\\tau^2}\\vert\\vert\\boldsymbol{\\beta}\\vert\\vert_2^2,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c6512c09",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "and replacing $1/2\\tau^2$ with $\\lambda$ we have"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2c5ca7b5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "C(\\boldsymbol{\\beta})=\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})\\vert\\vert_2^2}{2\\sigma^2}+\\lambda\\vert\\vert\\boldsymbol{\\beta}\\vert\\vert_2^2,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1c530682",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "which is our Ridge cost function!  Nice, isn't it?"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "81771a49",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Lasso and Bayes\n",
+    "\n",
+    "To derive the Lasso cost function, we simply replace the Gaussian prior with an exponential distribution ([Laplace in this case](https://en.wikipedia.org/wiki/Laplace_distribution)) with zero mean value,  that is"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c2aac5ba",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "p(\\boldsymbol{\\beta})=\\prod_{j=0}^{p-1}\\exp{\\left(-\\frac{\\vert\\beta_j\\vert}{\\tau}\\right)}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d2e548d7",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Our posterior probability becomes then (omitting the normalization factor which is just a constant)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2901f9c7",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "p(\\boldsymbol{\\beta}\\vert\\boldsymbol{D})=\\prod_{i=0}^{n-1}\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta})^2}{2\\sigma^2}\\right]}\\prod_{j=0}^{p-1}\\exp{\\left(-\\frac{\\vert\\beta_j\\vert}{\\tau}\\right)}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8b0dc761",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Taking the negative\n",
+    "logarithm of the posterior probability and leaving out the\n",
+    "constants terms that do not depend on $\\beta$, we have"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "81709208",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "C(\\boldsymbol{\\beta}=\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})\\vert\\vert_2^2}{2\\sigma^2}+\\frac{1}{\\tau}\\vert\\vert\\boldsymbol{\\beta}\\vert\\vert_1,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "757cbc8c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "and replacing $1/\\tau$ with $\\lambda$ we have"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "337a92ec",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "C(\\boldsymbol{\\beta}=\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})\\vert\\vert_2^2}{2\\sigma^2}+\\lambda\\vert\\vert\\boldsymbol{\\beta}\\vert\\vert_1,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "170ec18c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "which is our Lasso cost function!"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1919001a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Why resampling methods\n",
+    "\n",
+    "Before we proceed, we need to rethink what we have been doing. In our\n",
+    "eager to fit the data, we have omitted several important elements in\n",
+    "our regression analysis. In what follows we will\n",
+    "1. look at statistical properties, including a discussion of mean values, variance and the so-called bias-variance tradeoff\n",
+    "\n",
+    "2. introduce resampling techniques like cross-validation, bootstrapping and jackknife and more\n",
+    "\n",
+    "and discuss how to select a given model (one of the difficult parts in machine learning)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "861c96a1",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Resampling methods\n",
+    "Resampling methods are an indispensable tool in modern\n",
+    "statistics. They involve repeatedly drawing samples from a training\n",
+    "set and refitting a model of interest on each sample in order to\n",
+    "obtain additional information about the fitted model. For example, in\n",
+    "order to estimate the variability of a linear regression fit, we can\n",
+    "repeatedly draw different samples from the training data, fit a linear\n",
+    "regression to each new sample, and then examine the extent to which\n",
+    "the resulting fits differ. Such an approach may allow us to obtain\n",
+    "information that would not be available from fitting the model only\n",
+    "once using the original training sample.\n",
+    "\n",
+    "Two resampling methods are often used in Machine Learning analyses,\n",
+    "1. The **bootstrap method**\n",
+    "\n",
+    "2. and **Cross-Validation**\n",
+    "\n",
+    "In addition there are several other methods such as the Jackknife and the Blocking methods. We will discuss in particular\n",
+    "cross-validation and the bootstrap method."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9e8d9abb",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Resampling approaches can be computationally expensive\n",
+    "\n",
+    "Resampling approaches can be computationally expensive, because they\n",
+    "involve fitting the same statistical method multiple times using\n",
+    "different subsets of the training data. However, due to recent\n",
+    "advances in computing power, the computational requirements of\n",
+    "resampling methods generally are not prohibitive. In this chapter, we\n",
+    "discuss two of the most commonly used resampling methods,\n",
+    "cross-validation and the bootstrap. Both methods are important tools\n",
+    "in the practical application of many statistical learning\n",
+    "procedures. For example, cross-validation can be used to estimate the\n",
+    "test error associated with a given statistical learning method in\n",
+    "order to evaluate its performance, or to select the appropriate level\n",
+    "of flexibility. The process of evaluating a model’s performance is\n",
+    "known as model assessment, whereas the process of selecting the proper\n",
+    "level of flexibility for a model is known as model selection. The\n",
+    "bootstrap is widely used."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "cca36e61",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Why resampling methods ?\n",
+    "**Statistical analysis.**\n",
+    "\n",
+    "* Our simulations can be treated as *computer experiments*. This is particularly the case for Monte Carlo methods which are widely used in statistical analyses.\n",
+    "\n",
+    "* The results can be analysed with the same statistical tools as we would use when analysing experimental data.\n",
+    "\n",
+    "* As in all experiments, we are looking for expectation values and an estimate of how accurate they are, i.e., possible sources for errors."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "060a4427",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Statistical analysis\n",
+    "\n",
+    "* As in other experiments, many numerical  experiments have two classes of errors:\n",
+    "\n",
+    "  * Statistical errors\n",
+    "\n",
+    "  * Systematical errors\n",
+    "\n",
+    "* Statistical errors can be estimated using standard tools from statistics\n",
+    "\n",
+    "* Systematical errors are method specific and must be treated differently from case to case."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "bc631501",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Resampling methods\n",
+    "\n",
+    "With all these analytical equations for both the OLS and Ridge\n",
+    "regression, we will now outline how to assess a given model. This will\n",
+    "lead to a discussion of the so-called bias-variance tradeoff (see\n",
+    "below) and so-called resampling methods.\n",
+    "\n",
+    "One of the quantities we have discussed as a way to measure errors is\n",
+    "the mean-squared error (MSE), mainly used for fitting of continuous\n",
+    "functions. Another choice is the absolute error.\n",
+    "\n",
+    "In the discussions below we will focus on the MSE and in particular since we will split the data into test and training data,\n",
+    "we discuss the\n",
+    "1. prediction error or simply the **test error** $\\mathrm{Err_{Test}}$, where we have a fixed training set and the test error is the MSE arising from the data reserved for testing. We discuss also the \n",
+    "\n",
+    "2. training error $\\mathrm{Err_{Train}}$, which is the average loss over the training data.\n",
+    "\n",
+    "As our model becomes more and more complex, more of the training data tends to  used. The training may thence adapt to more complicated structures in the data. This may lead to a decrease in the bias (see below for code example) and a slight increase of the variance for the test error.\n",
+    "For a certain level of complexity the test error will reach minimum, before starting to increase again. The\n",
+    "training error reaches a saturation."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "65212453",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Resampling methods: Bootstrap\n",
+    "Bootstrapping is a [non-parametric approach](https://en.wikipedia.org/wiki/Nonparametric_statistics) to statistical inference\n",
+    "that substitutes computation for more traditional distributional\n",
+    "assumptions and asymptotic results. Bootstrapping offers a number of\n",
+    "advantages: \n",
+    "1. The bootstrap is quite general, although there are some cases in which it fails.  \n",
+    "\n",
+    "2. Because it does not require distributional assumptions (such as normally distributed errors), the bootstrap can provide more accurate inferences when the data are not well behaved or when the sample size is small.  \n",
+    "\n",
+    "3. It is possible to apply the bootstrap to statistics with sampling distributions that are difficult to derive, even asymptotically. \n",
+    "\n",
+    "4. It is relatively simple to apply the bootstrap to complex data-collection plans (such as stratified and clustered samples).\n",
+    "\n",
+    "The textbook by [Davison on the Bootstrap Methods and their Applications](https://www.cambridge.org/core/books/bootstrap-methods-and-their-application/ED2FD043579F27952363566DC09CBD6A) provides many more insights and proofs. In this course we will take a more practical approach and use the results and theorems provided in the literature. For those interested in reading more about the bootstrap methods, we recommend the above text and the one by [Efron and Tibshirani](https://www.routledge.com/An-Introduction-to-the-Bootstrap/Efron-Tibshirani/p/book/9780412042317).\n",
+    "\n",
+    "Before we proceed however, we need to remind ourselves about a central theorem in statistics, namely the so-called **central limit theorem**."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ce801e18",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## The Central Limit Theorem\n",
+    "\n",
+    "Suppose we have a PDF $p(x)$ from which we generate  a series $N$\n",
+    "of averages $\\mathbb{E}[x_i]$. Each mean value $\\mathbb{E}[x_i]$\n",
+    "is viewed as the average of a specific measurement, e.g., throwing \n",
+    "dice 100 times and then taking the average value, or producing a certain\n",
+    "amount of random numbers. \n",
+    "For notational ease, we set $\\mathbb{E}[x_i]=x_i$ in the discussion\n",
+    "which follows. We do the same for $\\mathbb{E}[z]=z$.\n",
+    "\n",
+    "If we compute the mean $z$ of $m$ such mean values $x_i$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "927e2be5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "z=\\frac{x_1+x_2+\\dots+x_m}{m},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fe6c7817",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "the question we pose is which is the PDF of the new variable $z$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b0ae80c3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Finding the Limit\n",
+    "\n",
+    "The probability of obtaining an average value $z$ is the product of the \n",
+    "probabilities of obtaining arbitrary individual mean values $x_i$,\n",
+    "but with the constraint that the average is $z$. We can express this through\n",
+    "the following expression"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b8bf320d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\tilde{p}(z)=\\int dx_1p(x_1)\\int dx_2p(x_2)\\dots\\int dx_mp(x_m)\n",
+    "    \\delta(z-\\frac{x_1+x_2+\\dots+x_m}{m}),\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "62def127",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where the $\\delta$-function enbodies the constraint that the mean is $z$.\n",
+    "All measurements that lead to each individual $x_i$ are expected to\n",
+    "be independent, which in turn means that we can express $\\tilde{p}$ as the \n",
+    "product of individual $p(x_i)$.  The independence assumption is important in the derivation of the central limit theorem."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "71d882fb",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Rewriting the $\\delta$-function\n",
+    "\n",
+    "If we use the integral expression for the $\\delta$-function"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "37f348c8",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\delta(z-\\frac{x_1+x_2+\\dots+x_m}{m})=\\frac{1}{2\\pi}\\int_{-\\infty}^{\\infty}\n",
+    "   dq\\exp{\\left(iq(z-\\frac{x_1+x_2+\\dots+x_m}{m})\\right)},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0b949710",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "and inserting $e^{i\\mu q-i\\mu q}$ where $\\mu$ is the mean value\n",
+    "we arrive at"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "673d5c06",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\tilde{p}(z)=\\frac{1}{2\\pi}\\int_{-\\infty}^{\\infty}\n",
+    "   dq\\exp{\\left(iq(z-\\mu)\\right)}\\left[\\int_{-\\infty}^{\\infty}\n",
+    "   dxp(x)\\exp{\\left(iq(\\mu-x)/m\\right)}\\right]^m,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "81c0beaf",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "with the integral over $x$ resulting in"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e83202fb",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\int_{-\\infty}^{\\infty}dxp(x)\\exp{\\left(iq(\\mu-x)/m\\right)}=\n",
+    "  \\int_{-\\infty}^{\\infty}dxp(x)\n",
+    "   \\left[1+\\frac{iq(\\mu-x)}{m}-\\frac{q^2(\\mu-x)^2}{2m^2}+\\dots\\right].\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "27744da9",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Identifying Terms\n",
+    "\n",
+    "The second term on the rhs disappears since this is just the mean and \n",
+    "employing the definition of $\\sigma^2$ we have"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "420c8688",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\int_{-\\infty}^{\\infty}dxp(x)e^{\\left(iq(\\mu-x)/m\\right)}=\n",
+    "  1-\\frac{q^2\\sigma^2}{2m^2}+\\dots,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "591e95ca",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "resulting in"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a044c8a4",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\left[\\int_{-\\infty}^{\\infty}dxp(x)\\exp{\\left(iq(\\mu-x)/m\\right)}\\right]^m\\approx\n",
+    "  \\left[1-\\frac{q^2\\sigma^2}{2m^2}+\\dots \\right]^m,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "22b21609",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "and in the limit $m\\rightarrow \\infty$ we obtain"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "461ba192",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\tilde{p}(z)=\\frac{1}{\\sqrt{2\\pi}(\\sigma/\\sqrt{m})}\n",
+    "    \\exp{\\left(-\\frac{(z-\\mu)^2}{2(\\sigma/\\sqrt{m})^2}\\right)},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "97d21082",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "which is the normal distribution with variance\n",
+    "$\\sigma^2_m=\\sigma^2/m$, where $\\sigma$ is the variance of the PDF $p(x)$\n",
+    "and $\\mu$ is also the mean of the PDF $p(x)$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1231f2f0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Wrapping it up\n",
+    "\n",
+    "Thus, the central limit theorem states that the PDF $\\tilde{p}(z)$ of\n",
+    "the average of $m$ random values corresponding to a PDF $p(x)$ \n",
+    "is a normal distribution whose mean is the \n",
+    "mean value of the PDF $p(x)$ and whose variance is the variance\n",
+    "of the PDF $p(x)$ divided by $m$, the number of values used to compute $z$.\n",
+    "\n",
+    "The central limit theorem leads to the well-known expression for the\n",
+    "standard deviation, given by"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "def2d3ca",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\sigma_m=\n",
+    "\\frac{\\sigma}{\\sqrt{m}}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "acdeb582",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "The latter is true only if the average value is known exactly. This is obtained in the limit\n",
+    "$m\\rightarrow \\infty$  only. Because the mean and the variance are measured quantities we obtain \n",
+    "the familiar expression in statistics (the so-called Bessel correction)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ad0ce315",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\sigma_m\\approx \n",
+    "\\frac{\\sigma}{\\sqrt{m-1}}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6be519fc",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "In many cases however the above estimate for the standard deviation,\n",
+    "in particular if correlations are strong, may be too simplistic. Keep\n",
+    "in mind that we have assumed that the variables $x$ are independent\n",
+    "and identically distributed. This is obviously not always the\n",
+    "case. For example, the random numbers (or better pseudorandom numbers)\n",
+    "we generate in various calculations do always exhibit some\n",
+    "correlations.\n",
+    "\n",
+    "The theorem is satisfied by a large class of PDFs. Note however that for a\n",
+    "finite $m$, it is not always possible to find a closed form /analytic expression for\n",
+    "$\\tilde{p}(x)$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "72497b42",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Confidence Intervals\n",
+    "\n",
+    "Confidence intervals are used in statistics and represent a type of estimate\n",
+    "computed from the observed data. This gives a range of values for an\n",
+    "unknown parameter such as the parameters $\\boldsymbol{\\beta}$ from linear regression.\n",
+    "\n",
+    "With the OLS expressions for the parameters $\\boldsymbol{\\beta}$ we found \n",
+    "$\\mathbb{E}(\\boldsymbol{\\beta}) = \\boldsymbol{\\beta}$, which means that the estimator of the regression parameters is unbiased.\n",
+    "\n",
+    "We found also that the variance of the estimate of the $j$-th regression coefficient is\n",
+    "$\\boldsymbol{\\sigma}^2 (\\boldsymbol{\\beta}_j ) = \\boldsymbol{\\sigma}^2 [(\\mathbf{X}^{T} \\mathbf{X})^{-1}]_{jj} $.\n",
+    "\n",
+    "This quantity will be used to\n",
+    "construct a confidence interval for the estimates."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7d663e8f",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Standard Approach based on the Normal Distribution\n",
+    "\n",
+    "We will assume that the parameters $\\beta$ follow a normal\n",
+    "distribution.  We can then define the confidence interval.  Here we will be using as\n",
+    "shorthands $\\mu_{\\beta}$ for the above mean value and $\\sigma_{\\beta}$\n",
+    "for the standard deviation. We have then a confidence interval"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4925ba6e",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\left(\\mu_{\\beta}\\pm \\frac{z\\sigma_{\\beta}}{\\sqrt{n}}\\right),\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9fbe8108",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where $z$ defines the level of certainty (or confidence). For a normal\n",
+    "distribution typical parameters are $z=2.576$ which corresponds to a\n",
+    "confidence of $99\\%$ while $z=1.96$ corresponds to a confidence of\n",
+    "$95\\%$.  A confidence level of $95\\%$ is commonly used and it is\n",
+    "normally referred to as a *two-sigmas* confidence level, that is we\n",
+    "approximate $z\\approx 2$.\n",
+    "\n",
+    "For more discussions of confidence intervals (and in particular linked with a discussion of the bootstrap method), see chapter 5 of the textbook by [Davison on the Bootstrap Methods and their Applications](https://www.cambridge.org/core/books/bootstrap-methods-and-their-application/ED2FD043579F27952363566DC09CBD6A)\n",
+    "\n",
+    "In this text you will also find an in-depth discussion of the\n",
+    "Bootstrap method, why it works and various theorems related to it."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b6b2b234",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Resampling methods: Bootstrap background\n",
+    "\n",
+    "Since $\\widehat{\\beta} = \\widehat{\\beta}(\\boldsymbol{X})$ is a function of random variables,\n",
+    "$\\widehat{\\beta}$ itself must be a random variable. Thus it has\n",
+    "a pdf, call this function $p(\\boldsymbol{t})$. The aim of the bootstrap is to\n",
+    "estimate $p(\\boldsymbol{t})$ by the relative frequency of\n",
+    "$\\widehat{\\beta}$. You can think of this as using a histogram\n",
+    "in the place of $p(\\boldsymbol{t})$. If the relative frequency closely\n",
+    "resembles $p(\\vec{t})$, then using numerics, it is straight forward to\n",
+    "estimate all the interesting parameters of $p(\\boldsymbol{t})$ using point\n",
+    "estimators."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "82bd2034",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Resampling methods: More Bootstrap background\n",
+    "\n",
+    "In the case that $\\widehat{\\beta}$ has\n",
+    "more than one component, and the components are independent, we use the\n",
+    "same estimator on each component separately.  If the probability\n",
+    "density function of $X_i$, $p(x)$, had been known, then it would have\n",
+    "been straightforward to do this by: \n",
+    "1. Drawing lots of numbers from $p(x)$, suppose we call one such set of numbers $(X_1^*, X_2^*, \\cdots, X_n^*)$. \n",
+    "\n",
+    "2. Then using these numbers, we could compute a replica of $\\widehat{\\beta}$ called $\\widehat{\\beta}^*$. \n",
+    "\n",
+    "By repeated use of the above two points, many\n",
+    "estimates of $\\widehat{\\beta}$ can  be obtained. The\n",
+    "idea is to use the relative frequency of $\\widehat{\\beta}^*$\n",
+    "(think of a histogram) as an estimate of $p(\\boldsymbol{t})$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "61a94d24",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Resampling methods: Bootstrap approach\n",
+    "\n",
+    "But\n",
+    "unless there is enough information available about the process that\n",
+    "generated $X_1,X_2,\\cdots,X_n$, $p(x)$ is in general\n",
+    "unknown. Therefore, [Efron in 1979](https://projecteuclid.org/euclid.aos/1176344552)  asked the\n",
+    "question: What if we replace $p(x)$ by the relative frequency\n",
+    "of the observation $X_i$?\n",
+    "\n",
+    "If we draw observations in accordance with\n",
+    "the relative frequency of the observations, will we obtain the same\n",
+    "result in some asymptotic sense? The answer is yes."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fd22fd14",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Resampling methods: Bootstrap steps\n",
+    "\n",
+    "The independent bootstrap works like this: \n",
+    "\n",
+    "1. Draw with replacement $n$ numbers for the observed variables $\\boldsymbol{x} = (x_1,x_2,\\cdots,x_n)$. \n",
+    "\n",
+    "2. Define a vector $\\boldsymbol{x}^*$ containing the values which were drawn from $\\boldsymbol{x}$. \n",
+    "\n",
+    "3. Using the vector $\\boldsymbol{x}^*$ compute $\\widehat{\\beta}^*$ by evaluating $\\widehat \\beta$ under the observations $\\boldsymbol{x}^*$. \n",
+    "\n",
+    "4. Repeat this process $k$ times. \n",
+    "\n",
+    "When you are done, you can draw a histogram of the relative frequency\n",
+    "of $\\widehat \\beta^*$. This is your estimate of the probability\n",
+    "distribution $p(t)$. Using this probability distribution you can\n",
+    "estimate any statistics thereof. In principle you never draw the\n",
+    "histogram of the relative frequency of $\\widehat{\\beta}^*$. Instead\n",
+    "you use the estimators corresponding to the statistic of interest. For\n",
+    "example, if you are interested in estimating the variance of $\\widehat\n",
+    "\\beta$, apply the etsimator $\\widehat \\sigma^2$ to the values\n",
+    "$\\widehat \\beta^*$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3497401f",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Code example for the Bootstrap method\n",
+    "\n",
+    "The following code starts with a Gaussian distribution with mean value\n",
+    "$\\mu =100$ and variance $\\sigma=15$. We use this to generate the data\n",
+    "used in the bootstrap analysis. The bootstrap analysis returns a data\n",
+    "set after a given number of bootstrap operations (as many as we have\n",
+    "data points). This data set consists of estimated mean values for each\n",
+    "bootstrap operation. The histogram generated by the bootstrap method\n",
+    "shows that the distribution for these mean values is also a Gaussian,\n",
+    "centered around the mean value $\\mu=100$ but with standard deviation\n",
+    "$\\sigma/\\sqrt{n}$, where $n$ is the number of bootstrap samples (in\n",
+    "this case the same as the number of original data points). The value\n",
+    "of the standard deviation is what we expect from the central limit\n",
+    "theorem."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "3ef8772f",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Bootstrap Statistics :\n",
+      "original           bias      std. error\n",
+      " 100.232  14.9426        100.231        0.148895\n"
+     ]
+    }
+   ],
+   "source": [
+    "%matplotlib inline\n",
+    "\n",
+    "import numpy as np\n",
+    "from time import time\n",
+    "from scipy.stats import norm\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "# Returns mean of bootstrap samples \n",
+    "# Bootstrap algorithm\n",
+    "def bootstrap(data, datapoints):\n",
+    "    t = np.zeros(datapoints)\n",
+    "    n = len(data)\n",
+    "    # non-parametric bootstrap         \n",
+    "    for i in range(datapoints):\n",
+    "        t[i] = np.mean(data[np.random.randint(0,n,n)])\n",
+    "    # analysis    \n",
+    "    print(\"Bootstrap Statistics :\")\n",
+    "    print(\"original           bias      std. error\")\n",
+    "    print(\"%8g %8g %14g %15g\" % (np.mean(data), np.std(data),np.mean(t),np.std(t)))\n",
+    "    return t\n",
+    "\n",
+    "# We set the mean value to 100 and the standard deviation to 15\n",
+    "mu, sigma = 100, 15\n",
+    "datapoints = 10000\n",
+    "# We generate random numbers according to the normal distribution\n",
+    "x = mu + sigma*np.random.randn(datapoints)\n",
+    "# bootstrap returns the data sample                                    \n",
+    "t = bootstrap(x, datapoints)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ffe9e08b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "We see that our new variance and from that the standard deviation, agrees with the central limit theorem."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c8770096",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Plotting the Histogram"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "ac35a65b",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [
+    {
+     "data": {
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\n",
+      "text/plain": [
+       "
    "
+      ]
+     },
+     "metadata": {
+      "filenames": {
+       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week37_144_0.png"
+      }
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# the histogram of the bootstrapped data (normalized data if density = True)\n",
+    "n, binsboot, patches = plt.hist(t, 50, density=True, facecolor='red', alpha=0.75)\n",
+    "# add a 'best fit' line  \n",
+    "y = norm.pdf(binsboot, np.mean(t), np.std(t))\n",
+    "lt = plt.plot(binsboot, y, 'b', linewidth=1)\n",
+    "plt.xlabel('x')\n",
+    "plt.ylabel('Probability')\n",
+    "plt.grid(True)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e4ad71a5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## The bias-variance tradeoff\n",
+    "\n",
+    "We will discuss the bias-variance tradeoff in the context of\n",
+    "continuous predictions such as regression. However, many of the\n",
+    "intuitions and ideas discussed here also carry over to classification\n",
+    "tasks. Consider a dataset $\\mathcal{D}$ consisting of the data\n",
+    "$\\mathbf{X}_\\mathcal{D}=\\{(y_j, \\boldsymbol{x}_j), j=0\\ldots n-1\\}$. \n",
+    "\n",
+    "Let us assume that the true data is generated from a noisy model"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "edcf8b5c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{y}=f(\\boldsymbol{x}) + \\boldsymbol{\\epsilon}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "77b70dca",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where $\\epsilon$ is normally distributed with mean zero and standard deviation $\\sigma^2$.\n",
+    "\n",
+    "In our derivation of the ordinary least squares method we defined then\n",
+    "an approximation to the function $f$ in terms of the parameters\n",
+    "$\\boldsymbol{\\beta}$ and the design matrix $\\boldsymbol{X}$ which embody our model,\n",
+    "that is $\\boldsymbol{\\tilde{y}}=\\boldsymbol{X}\\boldsymbol{\\beta}$. \n",
+    "\n",
+    "Thereafter we found the parameters $\\boldsymbol{\\beta}$ by optimizing the means squared error via the so-called cost function"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "07cccff6",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "C(\\boldsymbol{X},\\boldsymbol{\\beta}) =\\frac{1}{n}\\sum_{i=0}^{n-1}(y_i-\\tilde{y}_i)^2=\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right].\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b04fa9bd",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "We can rewrite this as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c79570c2",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\frac{1}{n}\\sum_i(f_i-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2+\\frac{1}{n}\\sum_i(\\tilde{y}_i-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2+\\sigma^2.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9a8a6a3b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "The three terms represent the square of the bias of the learning\n",
+    "method, which can be thought of as the error caused by the simplifying\n",
+    "assumptions built into the method. The second term represents the\n",
+    "variance of the chosen model and finally the last terms is variance of\n",
+    "the error $\\boldsymbol{\\epsilon}$.\n",
+    "\n",
+    "To derive this equation, we need to recall that the variance of $\\boldsymbol{y}$ and $\\boldsymbol{\\epsilon}$ are both equal to $\\sigma^2$. The mean value of $\\boldsymbol{\\epsilon}$ is by definition equal to zero. Furthermore, the function $f$ is not a stochastics variable, idem for $\\boldsymbol{\\tilde{y}}$.\n",
+    "We use a more compact notation in terms of the expectation value"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a9a892c2",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\mathbb{E}\\left[(\\boldsymbol{f}+\\boldsymbol{\\epsilon}-\\boldsymbol{\\tilde{y}})^2\\right],\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0057120a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "and adding and subtracting $\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right]$ we get"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9e9b0c0f",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\mathbb{E}\\left[(\\boldsymbol{f}+\\boldsymbol{\\epsilon}-\\boldsymbol{\\tilde{y}}+\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right]-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2\\right],\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4b28d5f5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "which, using the abovementioned expectation values can be rewritten as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3fbb0a03",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\mathbb{E}\\left[(\\boldsymbol{y}-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2\\right]+\\mathrm{Var}\\left[\\boldsymbol{\\tilde{y}}\\right]+\\sigma^2,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c367d950",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "that is the rewriting in terms of the so-called bias, the variance of the model $\\boldsymbol{\\tilde{y}}$ and the variance of $\\boldsymbol{\\epsilon}$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e71acf60",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## A way to Read the Bias-Variance Tradeoff\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "
    Figure 1: 
    \n",
+    ""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "93070f01",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Example code for Bias-Variance tradeoff"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "a46b37f7",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Error: 0.013121574062587286\n",
+      "Bias^2: 0.012073649469946107\n",
+      "Var: 0.0010479245926411787\n",
+      "0.013121574062587286 >= 0.012073649469946107 + 0.0010479245926411787 = 0.013121574062587286\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "
    "
+      ]
+     },
+     "metadata": {
+      "filenames": {
+       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week37_160_1.png"
+      }
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "from sklearn.linear_model import LinearRegression, Ridge, Lasso\n",
+    "from sklearn.preprocessing import PolynomialFeatures\n",
+    "from sklearn.model_selection import train_test_split\n",
+    "from sklearn.pipeline import make_pipeline\n",
+    "from sklearn.utils import resample\n",
+    "\n",
+    "np.random.seed(2018)\n",
+    "\n",
+    "n = 500\n",
+    "n_boostraps = 100\n",
+    "degree = 18  # A quite high value, just to show.\n",
+    "noise = 0.1\n",
+    "\n",
+    "# Make data set.\n",
+    "x = np.linspace(-1, 3, n).reshape(-1, 1)\n",
+    "y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2) + np.random.normal(0, 0.1, x.shape)\n",
+    "\n",
+    "# Hold out some test data that is never used in training.\n",
+    "x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2)\n",
+    "\n",
+    "# Combine x transformation and model into one operation.\n",
+    "# Not neccesary, but convenient.\n",
+    "model = make_pipeline(PolynomialFeatures(degree=degree), LinearRegression(fit_intercept=False))\n",
+    "\n",
+    "# The following (m x n_bootstraps) matrix holds the column vectors y_pred\n",
+    "# for each bootstrap iteration.\n",
+    "y_pred = np.empty((y_test.shape[0], n_boostraps))\n",
+    "for i in range(n_boostraps):\n",
+    "    x_, y_ = resample(x_train, y_train)\n",
+    "\n",
+    "    # Evaluate the new model on the same test data each time.\n",
+    "    y_pred[:, i] = model.fit(x_, y_).predict(x_test).ravel()\n",
+    "\n",
+    "# Note: Expectations and variances taken w.r.t. different training\n",
+    "# data sets, hence the axis=1. Subsequent means are taken across the test data\n",
+    "# set in order to obtain a total value, but before this we have error/bias/variance\n",
+    "# calculated per data point in the test set.\n",
+    "# Note 2: The use of keepdims=True is important in the calculation of bias as this \n",
+    "# maintains the column vector form. Dropping this yields very unexpected results.\n",
+    "error = np.mean( np.mean((y_test - y_pred)**2, axis=1, keepdims=True) )\n",
+    "bias = np.mean( (y_test - np.mean(y_pred, axis=1, keepdims=True))**2 )\n",
+    "variance = np.mean( np.var(y_pred, axis=1, keepdims=True) )\n",
+    "print('Error:', error)\n",
+    "print('Bias^2:', bias)\n",
+    "print('Var:', variance)\n",
+    "print('{} >= {} + {} = {}'.format(error, bias, variance, bias+variance))\n",
+    "\n",
+    "plt.plot(x[::5, :], y[::5, :], label='f(x)')\n",
+    "plt.scatter(x_test, y_test, label='Data points')\n",
+    "plt.scatter(x_test, np.mean(y_pred, axis=1), label='Pred')\n",
+    "plt.legend()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "152a6857",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Understanding what happens"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "c385948e",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Polynomial degree: 0\n",
+      "Error: 0.32149601703519115\n",
+      "Bias^2: 0.3123314713548606\n",
+      "Var: 0.009164545680330616\n",
+      "0.32149601703519115 >= 0.3123314713548606 + 0.009164545680330616 = 0.3214960170351912\n",
+      "Polynomial degree: 1\n",
+      "Error: 0.08426840630693412\n",
+      "Bias^2: 0.0796891867672603\n",
+      "Var: 0.004579219539673834\n",
+      "0.08426840630693412 >= 0.0796891867672603 + 0.004579219539673834 = 0.08426840630693413\n",
+      "Polynomial degree: 2\n",
+      "Error: 0.10398646080125037\n",
+      "Bias^2: 0.10077114273548984\n",
+      "Var: 0.0032153180657605116\n",
+      "0.10398646080125037 >= 0.10077114273548984 + 0.0032153180657605116 = 0.10398646080125036\n",
+      "Polynomial degree: 3\n",
+      "Error: 0.06547790180152352\n",
+      "Bias^2: 0.062082386342319454\n",
+      "Var: 0.0033955154592040923\n",
+      "0.06547790180152352 >= 0.062082386342319454 + 0.0033955154592040923 = 0.06547790180152355\n",
+      "Polynomial degree: 4\n",
+      "Error: 0.06844519414009445\n",
+      "Bias^2: 0.06453579006728322\n",
+      "Var: 0.003909404072811221\n",
+      "0.06844519414009445 >= 0.06453579006728322 + 0.003909404072811221 = 0.06844519414009444\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Polynomial degree: 5\n",
+      "Error: 0.05227921801205679\n",
+      "Bias^2: 0.04818727730430286\n",
+      "Var: 0.004091940707753925\n",
+      "0.05227921801205679 >= 0.04818727730430286 + 0.004091940707753925 = 0.05227921801205679\n",
+      "Polynomial degree: 6\n",
+      "Error: 0.03781367141738902\n",
+      "Bias^2: 0.03365768507152769\n",
+      "Var: 0.0041559863458613296\n",
+      "0.03781367141738902 >= 0.03365768507152769 + 0.0041559863458613296 = 0.03781367141738902\n",
+      "Polynomial degree: 7\n",
+      "Error: 0.027609773491022394\n",
+      "Bias^2: 0.022999498260366198\n",
+      "Var: 0.004610275230656182\n",
+      "0.027609773491022394 >= 0.022999498260366198 + 0.004610275230656182 = 0.02760977349102238\n",
+      "Polynomial degree: 8\n",
+      "Error: 0.017355848195593312\n",
+      "Bias^2: 0.010331721306655165\n",
+      "Var: 0.007024126888938144\n",
+      "0.017355848195593312 >= 0.010331721306655165 + 0.007024126888938144 = 0.01735584819559331\n",
+      "Polynomial degree: 9\n",
+      "Error: 0.026605727637184558\n",
+      "Bias^2: 0.010018312644139219\n",
+      "Var: 0.016587414993045335\n",
+      "0.026605727637184558 >= 0.010018312644139219 + 0.016587414993045335 = 0.026605727637184554\n",
+      "Polynomial degree: 10\n",
+      "Error: 0.021592704588021178\n",
+      "Bias^2: 0.010516485576646504\n",
+      "Var: 0.01107621901137467\n",
+      "0.021592704588021178 >= 0.010516485576646504 + 0.01107621901137467 = 0.021592704588021174\n",
+      "Polynomial degree: 11\n",
+      "Error: 0.07160048164232538\n",
+      "Bias^2: 0.014436800088896381\n",
+      "Var: 0.05716368155342902\n",
+      "0.07160048164232538 >= 0.014436800088896381 + 0.05716368155342902 = 0.0716004816423254\n",
+      "Polynomial degree: 12\n",
+      "Error: 0.11547777218876518\n",
+      "Bias^2: 0.016285782696017142\n",
+      "Var: 0.09919198949274803\n",
+      "0.11547777218876518 >= 0.016285782696017142 + 0.09919198949274803 = 0.11547777218876518\n",
+      "Polynomial degree: 13\n",
+      "Error: 0.2284246870217162\n",
+      "Bias^2: 0.01975416527168255\n",
+      "Var: 0.20867052175003364\n",
+      "0.2284246870217162 >= 0.01975416527168255 + 0.20867052175003364 = 0.2284246870217162\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "
    "
+      ]
+     },
+     "metadata": {
+      "filenames": {
+       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week37_162_2.png"
+      }
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "from sklearn.linear_model import LinearRegression, Ridge, Lasso\n",
+    "from sklearn.preprocessing import PolynomialFeatures\n",
+    "from sklearn.model_selection import train_test_split\n",
+    "from sklearn.pipeline import make_pipeline\n",
+    "from sklearn.utils import resample\n",
+    "\n",
+    "np.random.seed(2018)\n",
+    "\n",
+    "n = 40\n",
+    "n_boostraps = 100\n",
+    "maxdegree = 14\n",
+    "\n",
+    "\n",
+    "# Make data set.\n",
+    "x = np.linspace(-3, 3, n).reshape(-1, 1)\n",
+    "y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)+ np.random.normal(0, 0.1, x.shape)\n",
+    "error = np.zeros(maxdegree)\n",
+    "bias = np.zeros(maxdegree)\n",
+    "variance = np.zeros(maxdegree)\n",
+    "polydegree = np.zeros(maxdegree)\n",
+    "x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2)\n",
+    "\n",
+    "for degree in range(maxdegree):\n",
+    "    model = make_pipeline(PolynomialFeatures(degree=degree), LinearRegression(fit_intercept=False))\n",
+    "    y_pred = np.empty((y_test.shape[0], n_boostraps))\n",
+    "    for i in range(n_boostraps):\n",
+    "        x_, y_ = resample(x_train, y_train)\n",
+    "        y_pred[:, i] = model.fit(x_, y_).predict(x_test).ravel()\n",
+    "\n",
+    "    polydegree[degree] = degree\n",
+    "    error[degree] = np.mean( np.mean((y_test - y_pred)**2, axis=1, keepdims=True) )\n",
+    "    bias[degree] = np.mean( (y_test - np.mean(y_pred, axis=1, keepdims=True))**2 )\n",
+    "    variance[degree] = np.mean( np.var(y_pred, axis=1, keepdims=True) )\n",
+    "    print('Polynomial degree:', degree)\n",
+    "    print('Error:', error[degree])\n",
+    "    print('Bias^2:', bias[degree])\n",
+    "    print('Var:', variance[degree])\n",
+    "    print('{} >= {} + {} = {}'.format(error[degree], bias[degree], variance[degree], bias[degree]+variance[degree]))\n",
+    "\n",
+    "plt.plot(polydegree, error, label='Error')\n",
+    "plt.plot(polydegree, bias, label='bias')\n",
+    "plt.plot(polydegree, variance, label='Variance')\n",
+    "plt.legend()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a6ddc62c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Summing up\n",
+    "\n",
+    "The bias-variance tradeoff summarizes the fundamental tension in\n",
+    "machine learning, particularly supervised learning, between the\n",
+    "complexity of a model and the amount of training data needed to train\n",
+    "it.  Since data is often limited, in practice it is often useful to\n",
+    "use a less-complex model with higher bias, that is  a model whose asymptotic\n",
+    "performance is worse than another model because it is easier to\n",
+    "train and less sensitive to sampling noise arising from having a\n",
+    "finite-sized training dataset (smaller variance). \n",
+    "\n",
+    "The above equations tell us that in\n",
+    "order to minimize the expected test error, we need to select a\n",
+    "statistical learning method that simultaneously achieves low variance\n",
+    "and low bias. Note that variance is inherently a nonnegative quantity,\n",
+    "and squared bias is also nonnegative. Hence, we see that the expected\n",
+    "test MSE can never lie below $Var(\\epsilon)$, the irreducible error.\n",
+    "\n",
+    "What do we mean by the variance and bias of a statistical learning\n",
+    "method? The variance refers to the amount by which our model would change if we\n",
+    "estimated it using a different training data set. Since the training\n",
+    "data are used to fit the statistical learning method, different\n",
+    "training data sets  will result in a different estimate. But ideally the\n",
+    "estimate for our model should not vary too much between training\n",
+    "sets. However, if a method has high variance  then small changes in\n",
+    "the training data can result in large changes in the model. In general, more\n",
+    "flexible statistical methods have higher variance.\n",
+    "\n",
+    "You may also find this recent [article](https://www.pnas.org/content/116/32/15849) of interest."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3ff69bcd",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Another Example from Scikit-Learn's Repository"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "16bd46aa",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "============================\n",
+      "Underfitting vs. Overfitting\n",
+      "============================\n",
+      "\n",
+      "This example demonstrates the problems of underfitting and overfitting and\n",
+      "how we can use linear regression with polynomial features to approximate\n",
+      "nonlinear functions. The plot shows the function that we want to approximate,\n",
+      "which is a part of the cosine function. In addition, the samples from the\n",
+      "real function and the approximations of different models are displayed. The\n",
+      "models have polynomial features of different degrees. We can see that a\n",
+      "linear function (polynomial with degree 1) is not sufficient to fit the\n",
+      "training samples. This is called **underfitting**. A polynomial of degree 4\n",
+      "approximates the true function almost perfectly. However, for higher degrees\n",
+      "the model will **overfit** the training data, i.e. it learns the noise of the\n",
+      "training data.\n",
+      "We evaluate quantitatively **overfitting** / **underfitting** by using\n",
+      "cross-validation. We calculate the mean squared error (MSE) on the validation\n",
+      "set, the higher, the less likely the model generalizes correctly from the\n",
+      "training data.\n",
+      "\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "
    "
+      ]
+     },
+     "metadata": {
+      "filenames": {
+       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week37_165_1.png"
+      }
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "\"\"\"\n",
+    "============================\n",
+    "Underfitting vs. Overfitting\n",
+    "============================\n",
+    "\n",
+    "This example demonstrates the problems of underfitting and overfitting and\n",
+    "how we can use linear regression with polynomial features to approximate\n",
+    "nonlinear functions. The plot shows the function that we want to approximate,\n",
+    "which is a part of the cosine function. In addition, the samples from the\n",
+    "real function and the approximations of different models are displayed. The\n",
+    "models have polynomial features of different degrees. We can see that a\n",
+    "linear function (polynomial with degree 1) is not sufficient to fit the\n",
+    "training samples. This is called **underfitting**. A polynomial of degree 4\n",
+    "approximates the true function almost perfectly. However, for higher degrees\n",
+    "the model will **overfit** the training data, i.e. it learns the noise of the\n",
+    "training data.\n",
+    "We evaluate quantitatively **overfitting** / **underfitting** by using\n",
+    "cross-validation. We calculate the mean squared error (MSE) on the validation\n",
+    "set, the higher, the less likely the model generalizes correctly from the\n",
+    "training data.\n",
+    "\"\"\"\n",
+    "\n",
+    "print(__doc__)\n",
+    "\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from sklearn.pipeline import Pipeline\n",
+    "from sklearn.preprocessing import PolynomialFeatures\n",
+    "from sklearn.linear_model import LinearRegression\n",
+    "from sklearn.model_selection import cross_val_score\n",
+    "\n",
+    "\n",
+    "def true_fun(X):\n",
+    "    return np.cos(1.5 * np.pi * X)\n",
+    "\n",
+    "np.random.seed(0)\n",
+    "\n",
+    "n_samples = 30\n",
+    "degrees = [1, 4, 15]\n",
+    "\n",
+    "X = np.sort(np.random.rand(n_samples))\n",
+    "y = true_fun(X) + np.random.randn(n_samples) * 0.1\n",
+    "\n",
+    "plt.figure(figsize=(14, 5))\n",
+    "for i in range(len(degrees)):\n",
+    "    ax = plt.subplot(1, len(degrees), i + 1)\n",
+    "    plt.setp(ax, xticks=(), yticks=())\n",
+    "\n",
+    "    polynomial_features = PolynomialFeatures(degree=degrees[i],\n",
+    "                                             include_bias=False)\n",
+    "    linear_regression = LinearRegression()\n",
+    "    pipeline = Pipeline([(\"polynomial_features\", polynomial_features),\n",
+    "                         (\"linear_regression\", linear_regression)])\n",
+    "    pipeline.fit(X[:, np.newaxis], y)\n",
+    "\n",
+    "    # Evaluate the models using crossvalidation\n",
+    "    scores = cross_val_score(pipeline, X[:, np.newaxis], y,\n",
+    "                             scoring=\"neg_mean_squared_error\", cv=10)\n",
+    "\n",
+    "    X_test = np.linspace(0, 1, 100)\n",
+    "    plt.plot(X_test, pipeline.predict(X_test[:, np.newaxis]), label=\"Model\")\n",
+    "    plt.plot(X_test, true_fun(X_test), label=\"True function\")\n",
+    "    plt.scatter(X, y, edgecolor='b', s=20, label=\"Samples\")\n",
+    "    plt.xlabel(\"x\")\n",
+    "    plt.ylabel(\"y\")\n",
+    "    plt.xlim((0, 1))\n",
+    "    plt.ylim((-2, 2))\n",
+    "    plt.legend(loc=\"best\")\n",
+    "    plt.title(\"Degree {}\\nMSE = {:.2e}(+/- {:.2e})\".format(\n",
+    "        degrees[i], -scores.mean(), scores.std()))\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d898e22e",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Various steps in cross-validation\n",
+    "\n",
+    "When the repetitive splitting of the data set is done randomly,\n",
+    "samples may accidently end up in a fast majority of the splits in\n",
+    "either training or test set. Such samples may have an unbalanced\n",
+    "influence on either model building or prediction evaluation. To avoid\n",
+    "this $k$-fold cross-validation structures the data splitting. The\n",
+    "samples are divided into $k$ more or less equally sized exhaustive and\n",
+    "mutually exclusive subsets. In turn (at each split) one of these\n",
+    "subsets plays the role of the test set while the union of the\n",
+    "remaining subsets constitutes the training set. Such a splitting\n",
+    "warrants a balanced representation of each sample in both training and\n",
+    "test set over the splits. Still the division into the $k$ subsets\n",
+    "involves a degree of randomness. This may be fully excluded when\n",
+    "choosing $k=n$. This particular case is referred to as leave-one-out\n",
+    "cross-validation (LOOCV)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b3c4bc74",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Cross-validation in brief\n",
+    "\n",
+    "For the various values of $k$\n",
+    "\n",
+    "1. shuffle the dataset randomly.\n",
+    "\n",
+    "2. Split the dataset into $k$ groups.\n",
+    "\n",
+    "3. For each unique group:\n",
+    "\n",
+    "a. Decide which group to use as set for test data\n",
+    "\n",
+    "b. Take the remaining groups as a training data set\n",
+    "\n",
+    "c. Fit a model on the training set and evaluate it on the test set\n",
+    "\n",
+    "d. Retain the evaluation score and discard the model\n",
+    "\n",
+    "5. Summarize the model using the sample of model evaluation scores"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "35277af5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Code Example for Cross-validation and $k$-fold Cross-validation\n",
+    "\n",
+    "The code here uses Ridge regression with cross-validation (CV)  resampling and $k$-fold CV in order to fit a specific polynomial."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "6e8a01e6",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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Uv3OZ+exxqY+X4ylCHhtZ5fsf4VXM08+Nx9OQS+ndqVjbmkSPA2FGZFLCWmjUqFHccccd11yna9euTJw4sUbyCCHUWRZ/npd6j2Xs+3/gE3HloSFuRkyX5vhnX8An6wIJ83+v8v0LyyeFigm6UiGxcOFC7O3tmTp1Kq+99ho6ne6yx9q10rNeCHFjlh5IBaBvc/9q2b/e2YlDncsGbSyY/2O1HENYNilUzMCXX37J8OHDmTlzJs8++ywATZs25ezZsxUenTt3VpxUCGFOLpxMpXTHTnSakX6RvtV2HKfhwwBouHUtJYaiajuOsEy1s1DJy7v6o7Dw+tctKPjvdW/S1KlTGTduHD/88AMPPfRQ+XIbGxvq1atX4WFnZwdAXFwc3bt3x8HBAU9PTx555BFyc6/e4z4vL4/7778fZ2dnfH19+fDDD286txDC9CV9OY8l3z3FL0vfwdu1+gYoDB96G5mOrtTJz+LwT0ur7TjCMtXOQsXZ+eqPu++uuK6399XX/fccNMHBl69zE55//nnefPNNli5dyt3/znUV+fn59OnThzp16rBr1y5++eUX1q5dy7hx4666zaRJk/jrr79YvHgxq1evZv369ezZs+emsgshTJ/tihUAFLdtV63HsdHbkRjTA4C8HxZU67GE5ZHu1yZqxYoV/P7776xbt47u3btf9npcXFyFyQEjIiLYuXMn8+fPp6CggO+++w4np7LRJWfOnMmAAQN477338PHxqbCf3NxcvvrqK7777jt69iwbkunbb7/F3796rlcLIUxDYU4ejeO2A+A1rGpvS74S+3uGwLpfCdu8htLiErn7R1y32vlJucZlEKytKz5PS7v6ulb/apA6ebLSkf4tKiqKixcv8sorr9CmTRtcXFwqvN64cWOWLFlS/lyv1wNw6NAhmjdvXl6kAHTs2BGj0ciRI0cuK1SOHz9OUVERMTEx5cs8PDxo3LhxlZ2LEML0HP15KVHFhaS5eBLas1O1H6/J8DtY9FkfVgVF82BSOu0a+fz3RkJQWwsVpxuYx6K61v0P9evXZ9GiRXTr1o0+ffqwcuXKCsWKnZ0dYWFhl22nadpVZz290nKFc1IKIRQq+LXsVuGk9t3w/vcfXdXA1l7PpknvsDo2lZDjGVKoiOtWO/uomInAwEA2bNhAWloavXr1Ijs7+z+3iYiIIDY2lrx/dOTdsmULVlZWNGrU6LL1w8LCsLW1Zfv27eXLMjMzOXr0aNWchBDCJNXfsQEA/e0DauyY3cK9Afjr8DVaqoX4FylUTJy/vz/r168nPT2dXr16kZWVdc31hw8fjr29PSNHjuTgwYP89ddfjB8/nhEjRlx22QfA2dmZBx98kEmTJrFu3ToOHjzIqFGjsKqBv7CEEGqk7kvAPz2VEp0VYcNqrlDp0siLyPPH6LtoNmfj5I8hcX3k28gM1K9fnw0bNnDp0iV69uzJpUuXrrquo6Mjq1atIiMjgzZt2jBo0CBuvfVWZs6cedVt3n//fTp37sztt99Ojx496NSpE9HR0dVwJkIIU7A5346h90zhq2FP41y3To0d193RjqmbvubJLT+Q/O1PNXZcYd50mhl3UsjOzsbNzY2srCxcXV0rvFZYWEhSUhIhISHY21ff+ABC/JN87oQ5GPfDXpYeOMuEWxvyZM/LLwlXp22PTCJmzgcciIwh6sDWGj22MB3X+v7+N2lREUKIWsRo1Nh6PB2ATg3r1vjx6907CIBGh/ZQcCmnxo8vzI8UKkIIUYuc2LiT8b9/Qu/kfbQIcK/x4wd3bsM5d2/sS4o48uNvNX58YX6kUBFCiFrk4s+/MXrPHzyesBJb65r/CtBZWXGqfVcADL//UePHF+bH4gsVM+6CI8yQfN6EqXPYugmAgk5dlGWwH1h2p1HQjg1oRqOyHMI8WGyhYmtrC5TNfSNETfn78/b3508IU2IsKSXkyH4APPrcqixHo2EDKbK2wSk/h+SEE8pyCPNgsSPTWltb4+7uTtr/hsB3dHS86oitQtwsTdPIz88nLS0Nd3d3rP89FYMQJuDUpp2EFOaSb2tPgxoYNv9qHNxdeOalb1ic78JrubaMUJZEmAOLLVQA6tWrB1BerAhR3dzd3cs/d0KYmrQV6wgBjodFEqm3U5oluHNbSlcfZUviRUa0D1KaRZg2iy5UdDodvr6+eHt7U1xcrDqOsHC2trbSkiJMmvWWLQDktmmvOAl0DKvLB6uPsvX4RUpLjVgr6NgrzINFFyp/s7a2li8QIUStZ59yEgCXHt3UBgEi67vxyqZv6J6wheOt59Hotu6qIwkTJSWsEELUAqcz87ntnvfp8tjXNBjYU3UcbKytaFl4keBLZ0n/fbnqOMKESaEihBC1wO6TmaDT4d60EY6uzqrjAFDUpSsALpvXK80hTJsUKkIIUQvsPJkBQJugmpuE8L/Uu/s2ABomHqAwO1dxGmGqpFARQohaYOikEcz+9S06W2erjlIuMKYlaa510ZcWk/jrKtVxxL+czy5kw9ELZOQVKc0hhYoQQli4S8lnaX58P70St9Ms3F91nHI6KytOtYwBIHf5SsVpxL/tXr6ZGW9+x9PfblOaQwoVIYSwcCeXrQUg2SsAjxDTKVQA6FZ2t0+dXWq/DMXl6n49i8XznuGR9fOU5pBCRQghLFzh5rIi4FzTVoqTXM7/zj4c8/Bnl0cIeYUy3pUp8TgcB4C+XVulOWrFOCpCCFGbOe7fC4DWpo3iJJfzjQqn46RvOXOpgJCULDo1rKs6kgAMRcVQUABAve4dlWaRFhUhhLBgmtFI8PF4ADy7q5vf51rahngAsCMpXXES8bejafn0fPAzbnl+Ib7Nw5VmkUJFCCEs2OldcbgW5mKwtiWoq/qh86+kXYgHNqUlnNmyW3UU8T8HzlwCIDjMH52V2lJBLv0IIYQFO3b8LOfqR2Dn7EBze73qOFcUY1/IgY+GYm00UvjMHdi7OKmOVOvFnc4CyqY6UE1aVIQQwoJtcA5g8H1T+W3qN6qjXFVgszDy9Y7oS4s5sfwv1XEEcO/zo/jhxxfoUHBWdRS1hUpJSQkvvfQSISEhODg40KBBA9544w2MRqPKWEIIYTH2n74EQItA0xmR9t90VlacatoagKyV6xSnEYU5eTQ5cYAOyQcIDfNTHUftpZ/33nuPL774gm+//ZamTZuye/duRo8ejZubGxMmTFAZTQghzF6RoZiTSefA2p7m/u6q41xTSadOsGMNzju3qo5S6yVv2EEjYymZjm7Ua9pQdRy1LSrbtm1j4MCB9O/fn+DgYAYNGkSvXr3YvVs6VAkhxM06tW4rez4YzMIFkwnydFQd55q8+5fN6ByaeIDiQoPiNLVb5p+bAEgOjVDekRYUFyqdOnVi3bp1HD16FID9+/ezefNm+vXrd8X1DQYD2dnZFR5CCCGuLGP9JqzQsHNxRqfTqY5zTUG3tOWSgwuOxYWcWLVRdZxazWr3LgDyW7ZWnKSM0kLlueee45577iE8PBxbW1tatmzJxIkTueeee664/pQpU3Bzcyt/BAQE1HBiIYQwH1a7yr5w8lqY3oi0/2ZlY01Sk7KcmdJPRal6hw8A4NgpRnGSMkoLlZ9++ol58+bxww8/sHfvXr799ls++OADvv322yuuP3nyZLKyssofKSkpNZxYCCHMh9eh/33hdDTN8VP+7eJdQ5na+X6W1W+hOkqtlXUmjYALZd+tQb26KE5TRmln2kmTJvH8888zbNgwACIjIzl16hRTpkxh5MiRl62v1+vR601zHAAhhDAluRczCTx/CgD/3qbxhfNf6o28l89yAnEpseE1o4a1lWlfrrJERw6fIj8kGp+SXJoEqb/jBxS3qOTn52P1r4461tbWcnuyEELcpJS/tmGFxnk3LzxDzOMyeRNfF5z1NuQUlnDorPRBVGE77owa8jpfTP1RdZRySguVAQMG8Pbbb7Ns2TJOnjzJ4sWLmTZtGnfeeafKWEIIYfaytuwA4GyI2nlaboSNtRXd3I3cdmgjp39fqTpOrbQ/5RKASd3OrvTSzyeffMLLL7/M448/TlpaGn5+fjz66KO88sorKmMJIYTZ2+/iy+lmt+LeubPqKDdk+P6VtF/yMbsv9oHHh6qOU6toRiOnDiWBzokWge6q45TTaZqmqQ5RWdnZ2bi5uZGVlYWrq6vqOEIIYTL6zNjI4XM5zB4RTa+m9VTHuW4Hv/uVZiPv5py7N/Uyz6uOU6ukxh7Cr2UESR5++J5Jwt7ertqOdSPf3+pHchFCCFGlDCWlHEvLBaCZCUwqdyNC+nenRGdFvUtpnE9IVB2nVjm7ej0AJc6u1Vqk3CgpVIQQwsIcjz9J6Pkk6uqt8HWzVx3nhjh5unOyfhgAp5euVZymdineuh2AjKbNFSepSAoVIYSwMLk/LWTV1+P46tc3TX5E2itJj4oGoGTjZsVJahe3g7EAWLUzrXF3pFARQggLo+3dA0B+eITiJJVj3fkWADz3y7xvNaUov5CQU4cB8OllWh2wpVARQggL434kHgC7NtGKk1SOf/8eAASfOUZe+iW1YWqJk+u2YF9SxCUHFwLayqUfIYQQ1aTEUETQ6WMAeHc2rSb861WvWUMm3/sqt4z5iv2ZJarj1AoZq/8C4GSj5uisrRWnqUgKFSGEsCCnt8diX1JEnp0D9VtHqY5TaTn9b+esqxd7TmWqjlIrbHEP5ruW/Unvc5vqKJeRQkUIISzIxY3bAEgOaIiVjWn9ZXwjWgfVAWC3FCrVTtM0frIP5pVej+H8yEOq41xG6ci0QgghqlbJnr0AZIc3U5zk5rTxseex7b/Q4o8TGO//y6yLLlN3OrOAtBwDNlY6mge4q45zGSlUhBDCgiwLv4XNGUaibzO9Jvwb0TjAk5CtP+FYXMiJzbto0NU8+9uYg6N/7SD6dAK61tHY25peQSiXfoQQwkJomsZSx0BmdhiG14A+quPcFBu9HSdCy1qFLqz8U3Eay+b05SwWzX+WZ9Z/qzrKFUmhIoQQFiItx0BmfjFWOgjzdlYd56bltmoLgNXWrYqTWDavA2Xj7tjd0klxkiuTQkUIISzEye376XV0G+2tc02yCf9GOXYvG3jML36v4iSWKyctneCzJwAIuO1WxWmuTAoVIYSwENrixcxe/DZPr/1KdZQqEXzbrRjRUT/jLBePnVQdxyKdXP4n1pqR1Dr18GrcQHWcK5JCRQghLITNwYMAFDU17zt+/ubqU5eTfmVfnil/yASF1SF33UYAUiNaKk5ydVKoCCGEhfA4UTZXi0Mr0/3SuVEXIltRaGPH+cNJqqNYJJc9ZTMml7aPUZzk6uT2ZCGEsADFhQb8z50CwKdTa8Vpqs6F518mMvJemgZ7Yd73MZmeovxCQhPjAPC5rZfiNFcnLSpCCGEBTm+Pxc5YQq6dI/UiG6uOU2WiIkMptrYlPjWLwuJS1XEsSty5HO655x0+7P0IQbeYbnErhYoQQliA9G27AEgJCENnZTn/tQd4OODloqe4VONAyiXVcSzK9lNZxPo1JnH4IyY3EeE/Wc6nWQgharHiffsByA6znNYUAJ1Ox8Tjf7Hqq8cpfe9d1XEsyo6kDADaNfBQnOTapI+KEEJYgEVt+jPf4EH/2023U2RlhTrpaHwxmdgd21VHsRglhiL6fv4mdeo1pt1jpj09gbSoCCGEBdhS4sLSJp3xurWz6ihVrk6PLgAEH92PsUT6qVSFE6s3cc/upby5dhbhfm6q41yTFCpCCGHmLuUXcTarEIBG9VwUp6l6IT1vodDGDveCHFK271MdxyJkLF8DwInwlljZmvbFFSlUhBDCzJ3cvIeHd/xK30vHcLW3VR2nytk52nMiJAKA8yvWKU5jGRy2bQagsOMtipP8NylUhBDCzBlWrubF9V/z6I5FqqNUm6z/TVCokwkKb1ppcQkNDpe1THn2M93xU/4mhYoQQpg5XVzZoF0F4U0VJ6k+jl3L/vKvd1AmKLxZSeu24GLIJ0fvSIOeHVXH+U9SqAghhJlzO3YIALuWUYqTVJ/gAT057lGfbb7hXLyUpzqOWUv/YxUAJxq3wNrE+6eA3J4shBBmzVhSSsCZEwDU7dBGcZrq41bfh0EvzicxLZdZZ3Lo7e6kOpLZyo8vK2wLOndTnOT6SIuKEEKYsbOxCTgWF2KwtqV+G8ttUQFoHVwHgD2nMhUnMV+GklIev+VR2j7+LR6PPaQ6znWRQkUIIczY+S3/GzrfNxgbvZ3iNNUrOsgDK2MpqTv3q45itvYlX6KguBSjry8NmwSpjnNd5NKPEEKYMcOBgwBkhjRSnKT6tdMbOPDRMOxKiyl8egD2LnL550ZtSbwAQMewuuh0OsVpro8UKkIIYcYW3zKIt0uDGN65EZbbQ6WMf0QIGbZ6nIsKOLxyA+GD+6mOZHZ6PnEfrYs1Clq8pzrKdZNLP0IIYcbis0s5WC8Mz3YtVUepdjorK5LDWwBwad0GtWHMUPb5izRN3EeXpL20aBqoOs51U1qoBAcHo9PpLnuMHTtWZSwhhDALRqPG8Qu5AIR5OytOUzMM7comXdTvlAkKb9Txn5dirRlJ8QqgXqT5XCpUWqjs2rWLs2fPlj/WrCmbe2Dw4MEqYwkhhFk4l3CcF5fNZMT+lQR6OKqOUyPce3YFIPjIfjSjUW0YM1O0cjUAZ1qb/iBv/6S0j4qXl1eF5++++y6hoaF06dLliusbDAYMBkP58+zs7GrNJ4QQpuzi5h2M2LecpHoh2Fh/ojpOjWjQqzOFNnbUyc8ieUcsgTGtVEcyG767yub30fcx/WHz/8lk+qgUFRUxb948Hnjggav2RJ4yZQpubm7lj4CAgBpOKYQQpiP/f3f8ZASFKU5Sc+wc7TkR3ASA88v/VJzGfJyLO0rghRRKdVY0GHyb6jg3xGQKld9++41Lly4xatSoq64zefJksrKyyh8pKSk1F1AIIUyM1eHDABQ1ClecpGYl3T6UaZ2Gs9EjRHUUs3Fq/kIAjjZohpuv13+sbVpM5vbkr776ir59++Ln53fVdfR6PXq9vgZTCSGE6XI7mQiAbbMIxUlqlv1DD/Cx7W4aGJ14WnUYM7Gz0J6ioBZY9eitOsoNM4lC5dSpU6xdu5Zff/1VdRQhhDALmtGIb+pJADzatlCapaZFB5UNpX/iQh4ZeUV4OFn2iLw3y1BSyueuEeQPe4ul4zupjnPDTOLSz9y5c/H29qZ///6qowghhFm4mHgSV0MepTori5/j59/cHe1o7VBE7yNbObx2q+o4Jm9XUib5RaV4u+hp6ueqOs4NU16oGI1G5s6dy8iRI7GxMYkGHiGEMHnndscBcKZuffROtePW5H96dtM8Zv32Drp581RHMXmH/1iHV24GXRp5mc2w+f+kvFBZu3YtycnJPPDAA6qjCCGE2dgb0pyoCQuY9dQ01VHU6Fg2Foj7vl2Kg5i+nu89y65P72dweoLqKJWivFDp1asXmqbRqJH5jJInhBCqJablkG3vjGuLZqqjKOHbtxsADU4ewpCXrziN6TqzJ56gtGRKdFaE39lTdZxKUV6oCCGEuHHH0v43dL5X7Rg6/9/82zYn3ckdfWkxJ5avVx3HZJ3+cREAR8Ka4+pTV3GaypFCRQghzNBDHz/Hq2tnEW5r+O+VLZDOyopTTaMBuLRyreI0pst+zSoAcrqbZ2sKmMjtyUIIIa7fpeSz9IjfBEBe/e8Up1GnuOMtsHMdTjvkzp8ryb2YSXh8WR8en2F3KU5TedKiIoQQZubsjn0AnHP3xsnTXW0Yhbz6l7UShB3dT3Fh7WxZupaj3y5EX1rMGU8/gju3UR2n0qRQEUIIM5Oz9wAA5/1DFSdRK7hLO168cxK9HvyUg+fzVMcxOaW//QZASude6KzM9+teLv0IIYSZMSaU3WZaENpQcRK1rGysOT9wCKcPnWfnyUxaBnmojmQyikuNPNlhNG3cwnnwUfO97APSoiKEEGbH8UTZHD+6prVrjp8rad+grDjZkZShOIlp2ZmUwWmdAxvb9aFJzw6q49wUKVSEEMLMeKccB8C1Ze0aOv9K2tdz5MGdixnywTOUFpeojmMyVsefA6BHEx+srcxvNNp/kks/QghhRnKzcrEtKus46tuupeI06oUHevDklh9xLsrn2J9bCevdWXUk5TSjke4vjMHeuyExg15SHeemSYuKEEKYkePZJUSPn0+P53/GPaCe6jjK2ejtON64OQAXl61RnMY0HFu5iS4JW5iwZQHtG/mojnPTpFARQggzciwtF3Q66ob4q45iMvJjOgGg37pZcRLTcPH7HwE43DwGe1fzH7lYChUhhDAjiX8Pne9t/l9AVaVO71sBCD60F2NJqeI0amlGIwFrlgJgvOtuxWmqhhQqQghhRtp98BJfLXydDueOqI5iMhr06UK+rZ46+dkkb9mjOo5Sx9dsxj/9DIU2doQ/fK/qOFVCChUhhDAjYQd2cOvxXQQ6WauOYjLsHO05ERYJwPk/VilOo9aFr74HIKFlJ5zr1lGcpmpIoSKEEGaiMCcPv/RUAOq1a6E2jInJadcRg7UNF5POqI6ijGY0ErS27LKPNmSo4jRVR25PFkIIM3F29wFCNCPZeic8w4JUxzEp+icn0NzjFhzdXelr1LAy87FDKiPu8GlOezXA3pBPxIPDVMepMtKiIoQQZiJjVywAqX4hZj13S3VoFhGElZMTGXlFHD6XozqOEktO5PL4nS/w+uercajjqjpOlZFPuhBCmImiuLI5frKDwxQnMT12Nla0CykbTn/r4XOK09Q8o1FjedxZAPq2sqzWNilUhBDCTOiPHgbA2KSJ4iSm6e7cEyyb+wRtnhytOkqNO7h5Hw4nEnHW29C1sZfqOFVK+qgIIYSZyCzRkWPngENUM9VRTFJERCAN0k6Qn3mGovxC7BztVUeqMQVvTWHdmoWsGvQo9ra9VcepUtKiIoQQZqCk1MiYPhOJnPgzHncNUB3HJAV3aUeGkxuOxQaO/bFWdZwaU5iTR5ONKwCoP9CyihSQQkUIIcxCckY+xaUaDnY21PeUUWmvxMrGmqSo9gBkLV2pOE3NiZ81H1dDHufcvIgYdrvqOFVOChUhhDADfw+d38DLqVbeenu9Srt3B6DO1o2Kk9Qc63llg7wl9b0LKxvLGwhQChUhhDADzp/MYO2cMTy4Z4nqKCbNf1DZZbGwpHhy0tIVp6l+F48n0+zAVgD8xj2sOE31kEJFCCHMgF3CQcIyTuNrU7sn3fsvfi2acNrTDxvNyPFFy1XHqXbHPpqDjWbkaFATgjpGq45TLeSuHyGEMAPuJ48BoJc7fv7TsS592XnkBBfybGmhOkw1068q64uTOchyRqL9NylUhBDCxBlLSvE7dwoAzzYt1IYxA8Vvvs1T3+0m0OjII5qGTmeZfXriTmcx5PYX6XdsB68/YZmXfUAu/QghhMk7n5CIU3EhRVY2+EVLi8p/6RDqiZ21FckZ+Zy4mKc6TrX5YWcyxda2MHQI7oG+quNUGylUhBDCxKXtjAUg1csfW72d2jBmwElvQ9vgOjRJO8HBxZY5nkpubgF/7EsB4J62gYrTVC8pVIQQwsQVxMYBkBEUqjiJ+XgsYRUr5j5Bg4+mqI5SLeLf/ojlnzzA40kbyuc4slRSqAghhIk7U2JDvHcD8iMiVUcxG/6DbgOg8ZG95KVfUhumGnjM/4bArPN09rK12D44f5NCRQghTNwPzXvTf/THZEycpDqK2QiMaUmqhy92pSUkLvhDdZwqlbh8Aw1TjlBkbUPjSWNVx6l2yguVM2fOcN999+Hp6YmjoyMtWrRgz549qmMJIYRJ0DSNY/8blTbMS4bOv146KytS2nYGwPCHZRUqmdM+BuBA+57UCfJTnKb6KS1UMjMz6dixI7a2tqxYsYKEhAQ+/PBD3N3dVcYSQgiTcSErn5y8Qqx0ZcPni+tnP7Ds8k/Qjg1oRqPiNFUj81QqURuWAuA43vJbU0DxOCrvvfceAQEBzJ07t3xZcHCwukBCCGFi0pau4dC0Iexu1Br7Kf1VxzErjYYNxDDOlnqX0jixfgcNuseojnTTDr81jZiSIo75N6LJ4L6q49QIpS0qS5YsoXXr1gwePBhvb29atmzJnDlzrrq+wWAgOzu7wkMIISxZXmwc+tJinPQyPueNcnB34VBk2WzKZ7//WXGam1dsKCL0528ByHzoMXRWyntv1AilZ3nixAk+//xzGjZsyKpVqxgzZgxPPPEE33333RXXnzJlCm5ubuWPgICAGk4shBA17FACAAVhjRQHMU/p459i+NC3eKfZANVRbtqKwxd5ZOBkfm3dj6hnHlEdp8YoLVSMRiOtWrXinXfeoWXLljz66KM8/PDDfP7551dcf/LkyWRlZZU/UlJSajixEELULKfjiQBYN41QnMQ8tRraj+0NWhJ/oYCTZj5K7debk4j1a0zylOnonRxVx6kxSgsVX19fIiIq/vI1adKE5OTkK66v1+txdXWt8BBCCEtW70wSAO7RzRUnMU91nOyIaeAJwKr4c4rTVN7eUxnEplzCztqK4e2CVMepUUovenbs2JEjR45UWHb06FGCgmrXP4IQQlxJ1pk06uZmAODbvqXiNObrDm/oNmsO4auzYe+fquNUSsnQe3izyIakRyfg5aJXHadGKS1UnnzySTp06MA777zDkCFD2LlzJ7Nnz2b27NkqYwkhhEk4u2MvbsB5Ny98vCx7mPTq1DXcG4/dS7BCI+3QcbybmNdUBCc37KTtjtW0RkdKszdUx6lxSi/9tGnThsWLF/Pjjz/SrFkz3nzzTWbMmMHw4cNVxhJCCJNwKqeU5Y06EN+8o+ooZq1uoxCONiibdTppzjzFaW7chZfLipPYNt0I6hitOE3NU36/22233cZtt92mOoYQQpicXZ4hfHnnC4zuGEx31WHM3KU+t8FncTgvWwLTXlUd57ql7kug5eYVALi89rLiNGrUjpuwhRDCDCX+PXS+twydf7MCHx4BQJOj+0g7dFxxmuuX8sLr2GhGDjRtR8N+XVXHUUIKFSGEMFGXEpNA02jo7aI6itnza9GEQ6FRWKFx4pMvVce5LucTEmmxZjEA1pMnK06jjhQqQghhgvIysvj93WHETx9MQ32p6jgWIXvQUAC8lixSnOT6HJ/0GvrSYg6FRhFxj/kPWFdZUqgIIYQJSt0eC4DBTk8dPy+1YSxE+LgHSHX1YkO9JhxJTlcd55pOpefxRMMBfNH2LrS336k1w+VfSe09cyGEMGFZe/cDcNavgeIklsPNvx6vfryMN3o8wuL4C6rjXNOMtYlctHdh66PPETG0dk9GKYWKEEKYoOKD8QDkNghTnMSy3B3tD8CivacpLjUqTnNliUnn+W3faQAm9WqsOI16UqgIIYQJsk88CoAW3kRxEsvSPdwHL0cbGsXtYPdPK1XHuaLcQUP54ccXeMAtl0h/N9VxlFM+jooQQojL1U0pu4XWqUWU4iSWxc7Gig+Or6DLTx+xPyEG7u2nOlIFB79fTMu9GyjRWeHXUS77wU20qJSUlLB27VpmzZpFTk4OAKmpqeTm5lZZOCGEqI0Mefn4XjwDgE+7FmrDWKDQx0cDEBm3nXNxRxWn+X8lhiKcnnsGgD19hxLUuY3iRKahUoXKqVOniIyMZODAgYwdO5YLF8o6JU2dOpVnnnmmSgMKIURtk5yayZy2d7Ey4ha8GoeojmNx/Ns1J75xNFZoJL0zTXWccntenkrI2RNk2TvT+PMPVccxGZUqVCZMmEDr1q3JzMzEwcGhfPmdd97JunXrqiycEELURkcLrHiv6yi+eHxKrb4ttToVjXkMgCa//0DBpRzFacpmym706fsAHBrzNO6BvooTmY5K/QZs3ryZl156CTs7uwrLg4KCOHPmTJUEE0KI2ioxreyLU4bOrz5RY0eS6uGLe0EOB975WHUcDj80njr52Zz0CSZ6Su0dhfZKKlWoGI1GSksvHynx9OnTuLjIUM9CCHEzcvfuxys3k4ZeTqqjWCxrWxuSRzwMgO83szCWqBv9d9fhVJz27QEg9/1p2NrrlWUxRZUqVHr27MmMGTPKn+t0OnJzc3n11Vfp18+0elALIYS5ufejyez6dATtjuxUHcWiNXtpItl6J3J1NmzYEq8kQ2FxKc8tPcodIz7k68kzaTbiTiU5TFmlbk+ePn063bp1IyIigsLCQu69914SExOpW7cuP/74Y1VnFEKIWqOkqJj655MB8GrdXHEay+Zctw5zP/6JN44bCY/NosstGlZWuhrNMPPPY5y4mIeXuxN3P/lIjR7bXFSqRcXPz4/Y2FgmTZrEo48+SsuWLXn33XfZt28f3t7eVZ1RCCFqjbOxh9CXFlNgo6delIxKWt3uvK8nzvZ2HDqbzar4czV67MRlf6F/83XsSop5c2BT3Bxta/T45qLSA745ODgwevRoRo8eXZV5hBCiVkvfGUsAkOoTSKitjMlZ3dwd7RjdKYQ5K+I4+sYH9PrhPaxr4H3PSUvH8f7hjM84SxM3a3o0u6Paj2muKtWi8u2337Js2bLy588++yzu7u506NCBU6dOVVk4IYSobQri4gDIDApVnKT2eLBDEMu/m8iEhdPY/fLUaj+eZjRy5M77qJ9xlrPuPrSZLWOmXEulCpV33nmnfPyUbdu2MXPmTKZOnUrdunV58sknqzSgEELUJjaHDwNQ3ChccZLaw81Jz/n7HgCg0SfvkXW6ei8B7XptOq23rqREZ0XWV9/iVl+6TFxLpQqVlJQUwsLKZvT87bffGDRoEI888ghTpkxh06ZNVRpQCCFqE/eTxwDQRzZVnKR2af3eiyTVC6FOfjaHH55Qbcc5+sc6oqa8AMCuB58k/K7e1XYsS1GpQsXZ2Zn09HQAVq9eTY8ePQCwt7enoKCg6tIJIUQtomkaX7YcwJetB+LRub3qOLWKjd6O/A+mA9Bu5c/EfbOoyo9xPiERj3uHYF9SRGzzTrT7/L0qP4YlqvQ4Kg899BAPPfQQR48epX///gDEx8cTFBRUpQGFEKK2OJtVyE/hXXi35yPUbxmhOk6t03T4QHb0HgyAz4QxVXoJ6FJ+Ee/MWou+qICkeiGErV2ClY11le3fklWqUPn000+JiYnhwoULLFq0CE9PTwD27NnDvffeW6UBhRCitkhMK5t9PriuE7bWMsePCpE/ziHFKwDv7IvsGTmeUqN20/vMKSxm5Nc7+d0hkHEPvo9+xTKc69apgrS1Q6XuwXJ3d+eDDz7gwIEDpKWlsWTJEgCio6OrNJwQQtQm6dv3EH06gcDgNqqj1FqOddw48813bB73FE83vZOBSxN47fbK9xfKSErhrc9Wst/ajzqOtrz45P34+chUMzeiUoXKypUruf/++0lPT0fTKlabOp3uivMACSGEuLb6875k0ZpFbDM+BmO6qo5TazXs15Wji5eS+eM+vtl6Ejd7Gyb2aHjDM1mf2rIHqzvu4NWcTE4/NI1Xxg+lkRQpN6xSbYvjxo1j8ODBpKamYjQaKzykSBFCiMpxPZEIgG2k9E9RrX9zP17oV3aLeMGU99jZbxhF+YXXta1mNLL7rY/x6taJgIunKXBw4oPhrWlW3606I1usSrWopKWl8dRTT+Hj41PVeYQQolbSjEZ8U5MAcI+WOX5MwSOdQ/E+l8yAqd9irRk50XAvJbNm0+i27lfd5vjqTRRMfIrWh3YDEN84Gp+lC6kXFlxDqS1PpQqVQYMGsX79ekJDZeREIYSoChmnzuBZkIMRHfXbtVQdR/zPHUO6se/8VwQ/P5EGqcdhwK3EN2xJ7h134dahLbqWLcnWrNmfcommEx4kZt96AAzWtuwd8ThtZ39QI0PyWzKd9u9OJtchPz+fwYMH4+XlRWRkJLa2FSdSeuKJJ6os4LVkZ2fj5uZGVlYWrq6uNXJMIYSoDvHzf6fpfXdwxsOX+umpquOIf8lIOs2J+8fQYssKbDRj+fJbH/qc454BADy98XvG7FjI/nY98Pt0Gn5yi/lV3cj3d6XKvB9++IFVq1bh4ODA+vXr0en+f1psnU5XY4WKEEJYitz9ZXP8XAxoQH3FWcTlPEL88di0lPMJiZx4/1Ocdu+g3qlE6jjYUt/dgSa+rrjGPM2lJlNo3ShEdVyLUqlC5aWXXuKNN97g+eefx+oGe0ELIYS4gvgEAApCGykOIq7FJ6IhPnNnlD9fqC5KrVGpQqWoqIihQ4dKkSKEEFXk9+jeLC12o2t/mftFiH+qVKUxcuRIfvrpp6rOIoQQtdZafX2+b3UbdXp0UR1FCJNSqRaV0tJSpk6dyqpVq4iKirqsM+20adOuaz+vvfYar7/+eoVlPj4+nDtXvVNsCyGEKcnKLyYtxwBAQ29nxWmEMC2VKlTi4uJo2bLs9rmDBw9WeO2fHWuvR9OmTVm7dm35c2trmaRJCFG7JO89yN1x6zgf2gQXe9v/3kCIWqRShcpff/1VdQFsbKhXr16V7U8IIcxN/orVfLh8OgeatgceVh1HCJOivDdsYmIifn5+hISEMGzYME6cOHHVdQ0GA9nZ2RUeQghh7rSD8QDkh8kdP0L8m9JCpV27dnz33XesWrWKOXPmcO7cOTp06EB6evoV158yZQpubm7lj4CAgBpOLIQQVc/x+FEArJrKAGFC/FulRqatLnl5eYSGhvLss8/y1FNPXfa6wWDAYDCUP8/OziYgIEBGphVCmLXz7t74ZF3g8KIVhN/VR3UcIapdtY9MW12cnJyIjIwkMTHxiq/r9Xr0en0NpxJCiOqTnZaOT9YFAHzbRytOI4TpUd5H5Z8MBgOHDh3C19dXdRQhhKgRqdv2ApDm4ombn5fiNEKYHqWFyjPPPMOGDRtISkpix44dDBo0iOzsbEaOHKkylhBC1Jic3fsBOO/fQHESIUyT0ks/p0+f5p577uHixYt4eXnRvn17tm/fTlBQkMpYQghRYzZFdOCTwa/TPSqASNVhhDBBSguVBQsWqDy8EEIod6DQho0Nounds5nqKEKYJJPqoyKEELVN4vlcABp6uyhOIoRpMqm7foQQojbJTb/E0CWzSawbSEOvHqrjCGGSpFARQghFUrft5YltP3HRuQ51nKeqjiOESZJLP0IIoUjWnv/d8VNf7vgR4mqkUBFCCEVK4srm+MkJlTl+hLgaKVSEEEIRh2NHANDJHD9CXJUUKkIIoYh3ynEAnFtGKU4ihOmSQkUIIRTIz8yiXsY5AHzbt1KcRgjTJYWKEEIokLojFis0Mh3d8AjxVx1HCJMltycLIYQCBzyDefCR2XR2LeVN1WGEMGFSqAghhAKJ6QWcquOH1j5QdRQhTJpc+hFCCAVk6Hwhro+0qAghhAJ9vpxCuM6RJne9pDqKECZNChUhhKhhhdm53LnlN6w1Ixc831IdRwiTJpd+hBCihp3Zvg9rzcglBxfqhgSojiOESZNCRQghaljmrlgAzvqFoLOS/4aFuBb5DRFCiBpWsv8AANlhjRUnEcL0SaEihBA1zOHoobIfmkWqDSKEGZBCRQghapjPqUQAXFq3UBtECDMghYoQQtSgnPRLeGRnAFD/lnaK0whh+uT2ZCGEqEFHc40Me+oXooszWFDfW3UcIUyeFCpCCFGDjpzLpdjaFrsmzVRHEcIsyKUfIYSoQUfOZQMQXk+GzhfiekiLihBC1KCO014hMiMbl+gXgCaq4whh8qRQEUKIGqIZjbTZvY46+dkcc3lZdRwhzIJc+hFCiBqSfuwUdfKzKdVZ4d8hWnUcIcyCFCpCCFFDUrfsBuBM3frYuzorTiOEeZBCRQghakj+nlgALgY3VBtECDMihYoQQtQQ6/iDABiaNFWcRAjzIYWKEELUEPcTRwHQt2iuOIkQ5kMKFSGEqAGlpUZKDEUY0eEV00p1HCHMhtyeLIQQNSA5s4C+oz7G3VjEntZRquMIYTakRUUIIWrAkXM5APgH1MXaxlpxGiHMh8kUKlOmTEGn0zFx4kTVUYQQosr9Xag09nFVnEQI82ISl3527drF7NmziYqS5lAhhGVq/faz/HzsKBe8nwOkM60Q10t5i0pubi7Dhw9nzpw51KlT55rrGgwGsrOzKzyEEMIc+Cfspe3pBALc9KqjCGFWlBcqY8eOpX///vTo0eM/150yZQpubm7lj4CAgBpIKIQQN6cwOxf/C6cB8O3URnEaIcyL0kJlwYIF7N27lylTplzX+pMnTyYrK6v8kZKSUs0JhRDi5iVv3Im1ZiTDyY26DYNVxxHCrCjro5KSksKECRNYvXo19vb217WNXq9Hr5dmUyGEebm0dRcAZ4Ia42GlvCFbCLOirFDZs2cPaWlpREf//wyipaWlbNy4kZkzZ2IwGLC2llv4hBDmzxgbC0Bek2ZqgwhhhpQVKrfeeitxcXEVlo0ePZrw8HCee+45KVKEEBbD7WgCADYtW6gNIoQZUlaouLi40KxZxb8unJyc8PT0vGy5EEKYK6NR46TenTrOHtTt1E51HCHMjkmMoyKEEJYqOSOfxwY8i52NFQkdo/97AyFEBSZVqKxfv151BCGEqFIJZ8vGewqv54KNDJ0vxA2T7udCCFGNjpy8AECErwydL0RlSKEihBDVqNvLY9k5cwS9ju9QHUUIsySFihBCVCPfk0fwzsvEt4G/6ihCmCUpVIQQoppknkrFJ6vs0o9/F7njR4jKkEJFCCGqyZkN2wE47emHi5eH4jRCmCcpVIQQoprk7tgNQFqDcMVJhDBfUqgIIUQ1sY47AIChaZTiJEKYLylUhBCimngeOwSAQ9tWipMIYb5MasA3IYSwFIXFpfwZ0Jw0G0eCO7dXHUcIsyWFihBCVINjabm81e1B3B1t2RcRpjqOEGZLLv0IIUQ1SEgtGzo/wtcVnU6nOI0Q5ksKFSGEqAapew/iZMiniQydL8RNkUJFCCGqQZ/3niVuxlB6JW5XHUUIsyaFihBCVLESQxFBKYlYoeHbvoXqOEKYNSlUhBCiiiVv2YNDiYFcO0f82zRXHUcIsyaFihBCVLGL67cCcCo4HCsba8VphDBvUqgIIUQV03btAiC7mbSmCHGzpFARQogq5n44DgDbtm0UJxHC/EmhIoQQVai40EBwSiIA9bp1VJxGCPMnI9MKIUQVSjyTyY/dHyQq/RSDWjdTHUcIsyeFihBCVKED6UV83+o2OoR6MthKGq2FuFnyWySEEFUo7kwWAJH+boqTCGEZpEVFCCGqkOPyP2hS6kKUT6TqKEJYBJ2maZrqEJWVnZ2Nm5sbWVlZuLrKfBpCCLWK8gvB1QW70hLO7D5I/eimqiMJYZJu5PtbLv0IIUQVSd64A7vSErLsnfFr2UR1HCEsghQqQghRRdL/3ARAcoMIdNKRVogqIb9JQghRRax27AAgt5UM9CZEVZFCRQghqki9Q/sBcOwsA70JUVWkUBFCiCpwKfksARdSAAjq3VVtGCEsiBQqQghRBU6tWg9AilcA7oG+asMIYUFkHBUhhKgCG70b88GQN+ge4MRo1WGEsCDSoiKEEFVg58ViNoW0wmbQ3aqjCGFRlBYqn3/+OVFRUbi6uuLq6kpMTAwrVqxQGUkIIW6Y0agRm3IJgJYB7kqzCGFplBYq/v7+vPvuu+zevZvdu3fTvXt3Bg4cSHx8vMpYQghxQ5L3HOTxlV/S69Qewuu5qI4jhEVR2kdlwIABFZ6//fbbfP7552zfvp2mTWXoaSGEeUj7YzWP7VhIQsYxbKxfUR1HCItiMp1pS0tL+eWXX8jLyyMmJuaK6xgMBgwGQ/nz7OzsmoonhBBXpW3fDkBW82jFSYSwPMo708bFxeHs7Ixer2fMmDEsXryYiIiIK647ZcoU3Nzcyh8BAQE1nFYIIS7nFb8PAH2nDoqTCGF5lM+eXFRURHJyMpcuXWLRokV8+eWXbNiw4YrFypVaVAICAmT2ZCGEMtnnL+Lk64O1ZuTC4eN4NW6gOpIQJu9GZk9WfunHzs6OsLAwAFq3bs2uXbv46KOPmDVr1mXr6vV69Hp9TUcUQoirSlqyhuaakTMevtSXIkWIKqf80s+/aZpWodVECCFMWf669QCkRslEhEJUB6UtKi+88AJ9+/YlICCAnJwcFixYwPr161m5cqXKWEIIcd1sE/43nEKnW9QGEcJCKS1Uzp8/z4gRIzh79ixubm5ERUWxcuVKevbsqTKWEEJcl8LiUu697QXqtz/NNyP7qY4jhEVSWqh89dVXKg8vhBA3ZX/KJYqMGrlBDQgMra86jhAWyeT6qAghhLnYdTIDgLbBHuh0OsVphLBMyu/6EUIIc9XipQl8mpFNacSLqqMIYbGkUBFCiEooMRTRcs96nIoKOO4r4zgJUV3k0o8QQlTCybVbcSoqIFvvRHDXdqrjCGGxpFARQohKuLhyLQBJ4S2wtpXGaSGqixQqQghRCfqtWwDIbyfz+whRnaRQEUKIG1RiKCI0fhcAngP6KE4jhGWT9kohLFRG0mlSVm8kraCEPY3bciHHQInRyKC572FrZwP+/jg0b4Z/7y54hshM5Dfi2Ir1hBvyyLJ3JrR3Z9VxhLBoUqgIYSEKc/I4/N2vFP26GL/9O/FPP4MHsNM/gi+GTy1f78Utq/HOy6yw7Qm/UM5370vA+IfxbxtVw8nNT8LxNAp9G1ESGERr6Z8iRLWS3zAhzJimaew+mYHxgQeJ3LKKFsWFFV4/5R1IQcNwRnUIxsfVHjsbK44UTeT4mdPYJZ/CM+kowedP0iD1OA3mzeTQqqWMfncBj3VrSNsQD0VnZfoWOIey8/5pvHV7BK1VhxHCwkmhIoQZys3J5+f95/lhZzLH0nL5IjUNx+JCzrl5capTT+wH3kZwv1sJqu9NENDlnxt3eqXCvjKSTnN83iL0Py/g65BO/HX0In8dvUivMA9eamZPYPuWNXlqJi/PUMK+5LIWqU6NvBWnEcLySWdaIcxIRtJptg1/nKJ6fnw970+OpeXiYGvN4Yef5PDiVfhknKPd0vk0f/ge3Opf35eoR4g/bV6eQFTcNiZ+/Rr3tA3ExkpH/QVzqdepLdsfepoSQ1E1n5n52LfnCPr8PPzrOBDk6ag6jhAWT6dpmqY6RGVlZ2fj5uZGVlYWrq4yMqSwXOlJKSROfJHmy3/GocQAwHc9RqB7803uaOGHi71tlR7v+IVczt8+mA7bVwJwJKQp7ksX4xPRsEqPY4623zGS1kvmsfaecfSZ/5HqOEKYpRv5/pYWFSFMWPb5i2wb/jgOjRvRfsn3OJQYSAwMZ9/0Lxm+/GtGtA+q8iIFINTLmZgty9j1xgyy7Z1pnBSPTdu2JCz4o8qPZW58dm7GRjPi1aKJ6ihC1ArSoiKECSosLuX7jYn0v7sLfllpABwNbILh1ddoNmoQOqua+xvjzJ54Cm+/g9DUY5TorNjz3Nu0m/J8jR3flFw8dpK6DUMAyDx5hjpBfooTCWGepEVFCDNVbChi/o5TdHn/L95ec5yFEd045RPEvulf0jDpIJEPDKnRIgWgfnRT/OL3srtjX2w0I63fe5EfvluNGf+NU2knFywB4Jh/QylShKghctePECbAWFLK3ve/wPfDd/ij1zjOB0ZR390B/w/ewr9NMEGKx+pwcHcheuNSto0Yx28ZNvyUUMzJFYeZ3DccnU6nNFtN0i1fDsCFDl0JU5xFiNpCChUhFNKMRg589RPOr71C69RjADy+93f6jB3GPe0C0dtYK074/3RWVsTM/4z4TSdg2SFmbzyBdV4uz94dXeOtPCqUGIpouK9sfp86Q+9SnEaI2sPy/3cRwkQdXriCQ41b0fyRewlNPUaO3pFtoyYSvWUlozqGmFSR8k8P3dKAd++KxDsnnTsfG8SOkU+ojlQjji5ehWthLpmOrjQc0EN1HCFqDWlREaKGHT6XTep9D9F93S8AFNrYETvwPsKnvUVMoK/idNdnWNtA/H87R6P0ZJj3KdtdXGj/2RTVsarVajyY3+tx2vg4cIcMmy9EjZEWFSFqyIkLuTz5Uyx9P9rEEodASnRW7Oh5N1kH4mm/8CvczaRI+Vund55l20NPA9D+83fZPeVTxYmq17LUEua37If100+pjiJErSKFihDV7OSGnezu2Je59z3H4n1n0DQoGTqU1G17abd6IT5NzLdbZsycD9h+5ygAol6eSMJPy9QGqiYpGfkkpuVibaWjcyMv1XGEqFWk/VKIanJ8zRayXnqVFjv/JBgNXxcvzg+9j/G9Ioj0d1Mdr8q0/flL9sacotXuv/AbfQ8pQRsIsLD5gY7MnMv9e+K40Os23ByqfoA9IcTVSYuKEFVIMxo5+P1i9rfoRGivTrTauQ4rNPa26U7BwkXMfiDGoooUACsba5qs+Z2jQU1wL8ghY/gosguLVceqUgHffM4ba2cx6twe1VGEqHWkUBGiChhKSvlldwoLewyn2f130Xz/Fozo2BPTm6S/ttNq5zrCet2iOma1cXB3wWPdSv5q2olHez/FkwtiMRotY0C4tEPHaZwUD0CDh+9TnEaI2kcu/QhxE87sOciSg+f5KkXjYq6BFv5t6G+7mLied+L3yvNEt2uuOmKNqRsaiOfKP8j4YhvrDqfx0bpEnuzZSHWsm5Y0Zx7ewOGQZoSHh6qOI0StIy0qQtygovxC9nwwm7iIttRvHYnLjA+5mGugnqs9vR8YSFHyadot+5GAWlSk/C3K352372gGwJHPvmHfp98rTnTznJeVDZuf1XeA4iRC1E7SoiLEdTAWl3Do52XkffM9jTevIrowt2w5OhraFPHFfa24tYkPttZS+w9uHUDRb0sY/tsUcpc7ktyqKYExrVTHqpSLx04SnhgLQMBDctlHCBWkUBHiKkpKjew5lcmahPMMGDeE5qfiy19Lc/HkxG2DCZw0nnYtIxSmNE1DXnqIhJ+/JCIxlot33k1e/D6cPN1Vx7phxz7+ivaaseyyj/w7C6GEFCpC/EP2+YskfreQkmXLGX/LI6QVl024V8c3gpBzJznSqRcOI0fQZNgAvGV00quytdfjvXwxF1pFE3z+JHsGDKPV5uVmNyfQmYTjFFtZk3XXYNVRhKi1dJoZz9WenZ2Nm5sbWVlZuLq6qo4jzFBhTh7Hf19D9qq1uG3fTNiJeOyMJQCMGvQasZExdG/sTf8gRzpF+qN3clSc2LwcXriC0KEDsDWWsn3CK7Sf8brqSNftWFouPaZtwLMwh9XP9cDTt67qSEJYjBv5/pY/CUWtkpFrYP+ZLGKTL6EtWsjYL1+jaWnFMT+SvQJIvaUHT43pQ0TXNthIv5NKCx/Ul+3jXqD9x28S/cnbHO7UnvBBfVXHui6/x54BoHmLUClShFBIChVhkTSjkfRjpzi7dS95u/Zgu3cPvkfj+Cz6Dua16g9Ao2I3niot5qKzByej2mLs0pX6d/UjsHUkgYrzW5J2019jz84dRG9fzfpZP+PZuzteLnrVsa6ptLiEXau2g21dBrbwUx1HiFpNaaEyZcoUfv31Vw4fPoyDgwMdOnTgvffeo3HjxipjCTNSYiji3LlMThVbc/xCLmlxR+j3/nP4nTlB3YIc/v13cIuzR9nqNYQW/u60CmxK8kMxBLRrQV0z6zthTnRWVoQv/YmXJ33G997NWf/jXuY92M6kW6riv13IgmmjWBfekY5vblAdR4haTWmhsmHDBsaOHUubNm0oKSnhxRdfpFevXiQkJODk5KQymjARuYYSzl/MpuCvjRSeTKbk9Bl0J5NwOJ2Mx7kUfDLPsyGqJy/2HgeAkyGfZ47tB6BUZ0Vq3fpcCArD0KIVLrd0oGfPWxjk+89J5YJr/qRqISdPd0a++wS/ztzM9hMZvL/yEJP7N1Ud66pKv5gFgFPDEOxtrRWnEaJ2U1qorFy5ssLzuXPn4u3tzZ49e+jcubOiVKK6aJpGrqGES/nFZGblwZ9/UpR2kdILFzGmp2OVno71pUwcLqaxNyCC9zoMJ9dQgkNRIYemD7rqfgOyLxDq5USwpxON6rmw0+8LPJtHUD+mFQEuTgTU4DmKqwvzdub9wc15ddZauj/2PPuemkjLiQ+qjnWZC0dOELl3IwD1nh6vOI0QwqT6qGRlZQHg4eFxxdcNBgMGg6H8eXZ2do3ksnSa0UhJUTGG3HyK8wowoKPQyRVDiZGiAgO2e3ZRkl9AaUEhxoICSgsKMBYY0AoLyPAJ4FiLDuQWlVCUnUP/mW9gk5+LTUEedvl56AvzsS/Mx8FQwKpGMUzqOwEAu5Jijn447KqZLhRBbnTZ3Tc2Ls4c9m9MibMzhZ7eFAcEYd0wDKcmDanbvAmdGjVgnc0//urtE16t75eovH6RvjhnbKddykFyn3uClPatTG6m5WPvfkKMZuRQaBRNurRVHUeIWs9kChVN03jqqafo1KkTzZo1u+I6U6ZM4fXXq//2xkNns9m2dDNN/lwCmgZGDdDQGY2gaWhGjUMde3K6cQs0NDxSkmi77Afg/9f9ezudpnGgQy8SI9tj1DQ8ziXTY9Gcste1/+2z7A1AZzSyp31P9rfujoZGnbRUBs2fBhrl+9QZjejQ0JUa2d76Vv6M6UepUcP94lkmzXkZK2MJ1qWlWBlLsSotxdpY9vMfrXozq9sISowaHpcusnTmA9gYS7E2GrHWjNgCf09eP79Fn/JLKW4FOez/+J6rvle/RXThwwFlPUFsS4t5dfOyq67rmZsJgL2tFXXcXDgUFIHR3gGDmzvF7h4Y69RB5+mJjb8fHuGN+bNTDN6u9jjrbeD1wzfzTypMSMzc6STs3kpEYiwX7ryb/IR9ONYxjRmlDXn5NFz4HQB5o0yvtUeI2shkCpVx48Zx4MABNm/efNV1Jk+ezFNPPVX+PDs7m4CAqm/YP3o+h60rt/PAr7Ouus7SfEfmXyz7z7XDyf2MX/7jVdddVerOT4b6ALQ6c4TJG/646rrrbbxYpm8CQHjaKd7es/6q625xqs92n/YABGZm0ij50FXXtb2UycXcIgBsio04Fhuuuq7eWIqTnTV6W2tcHVw47VmfYls7Suz0lNjaUWpnR4mtHqOdHcYmrbinbQCOdjY46W3Ylj8ZKxdnrN1csXFxxcbdFX0dN/QebjTz8eJwgN//X/OfHH/VDMJy2ert8F76KxejWxNyLondA+4heuNSkxgMbv/UL2ibm0GaiydRTz2iOo4QAhMZ8G38+PH89ttvbNy4kZCQkOverroGfIs7ncXGX/8kes0i0OlAp0OzsgJ06KzKnh/p2JOz4S3Q6aDOuRQiV/0K/3sNndX/frYCnY6UVh240Kysedsp/TyN1ywp3w86HVhZlf98oWlL0pu2QKfTYZ+dSfCfywAdWOnQWVmDDtDp0NnaktuwCblNo7Cx0mFjKMBr91Z0NrZY2dpiZWuDla0NOhsbrGxt0Xy80QICsLHSYa1p6FNPY2Vjg7WdDVZ2ttjY2mLn4oydkwPWNtJ5UFS/hJ+W0eie27HRjGx/6nXaf/iK0jyaprE3vC3RR3ez/dFnaf/Fe0rzCGHJbuT7W2mhomka48ePZ/Hixaxfv56GDRve0PYyMq0Q5m37+JdoP/NtiqxsOLFwGeF39lKWZf2RNB6Zs5VBiZt47ovncatwd5gQoirdyPe30rbWsWPHMm/ePH744QdcXFw4d+4c586do6CgQGUsIUQNaffRG+xteyvJ7vV4bcNpLuZe/ZJkddI0jelrjlJkY4vDww9KkSKECVHaoqLT6a64fO7cuYwaNeo/t5cWFSHMX+7FTIbN2sbBHI2YBp58/2DbGh8MbtPa3YxedQZbez0bn+1m8iPnCmHuzKZFRdO0Kz6up0gRQlgG57p1mPHwLTjaWbPtRDpz5v1Vo8c3lpRSf+Qw1n05hud98qRIEcLEqO9mL4So9cK8XZg6KIoHdy7moQd6s+/juTV27N1vzKBB6nHqFORwx52dauy4QojrI4WKEMIk3BblR0+XImyNpTSaNJbEZdXfspJ1+hwNP3wTgIQHxuNW36fajymEuDFSqAghTEb0T3M42KQ1TkUF1B1yJ8nb9lbr8Q4/+AR18rM4WS+Y6GmvVeuxhBCVI4WKEMJk2NrrCd64msSAxtTJz8KuX1/OJyRWy7HivllEu9W/AJA37SNs7aVvihCmSAoVIYRJca5bB88Na0nxCqDepTSKO3cldX/VTqGQkXQa3/FlI8/u6D2YpvfcXqX7F0JUHSlUhBAmxyPEH5u1q0n18MU/PZUFL83k+IXcKtl3SamRl5YkEOsTykmfYKIWfFUl+xVCVA8pVIQQJsk3KhybzZv4dOBYPm7al6GztrEvOfOm9qlpGi8uPsjys8WMG/YaRWvX4eDuUkWJhRDVQQoVIYTJ8m4SyrB5H9LUz5WLuUU8MmMN296eWal9GUtK+f2Zqfy86xRWOvjk3mgaNWtQxYmFEFVNChUhhEnzdNaz4JH29G7syYeL3yXmpfHsbdeTjKTT172Pgks57LulH3dMe57Jf83ljYHN6BkhtyILYQ6kUBFCmDwXe1s+H9EG265dKLayptXOtVhHNGHbo8+Sn5l11e00o5G4r38mI7Qx0dtXU2RlQ8vbu3Jf+6AaTC+EuBlK5/q5WTLXjxC1z7GVG7B68EEapB4HIM/OgYQOPcl56FG8u3ZEb2NF3v6DFP7+B16/LyT0TNntzefdvLgwczbN7rtDYXohBNzY97dNDWUSQogqEdanC6UnD7PrnZn4fvI+/umptFm/hCdcGrMkruzvrgd3/cbLf34JgMHaln19h9D0q49o5u2pMroQohKkUBFCmB1rWxvavDoR7eUnSPhlBdnzF1DSrh11NT1GTSO5cQv2XeqCoeMthD/zOO0DfVVHFkJUklz6EUIIIUSNupHvb+lMK4QQQgiTJYWKEEIIIUyWFCpCCCGEMFlSqAghhBDCZEmhIoQQQgiTJYWKEEIIIUyWFCpCCCGEMFlSqAghhBDCZEmhIoQQQgiTJYWKEEIIIUyWFCpCCCGEMFlSqAghhBDCZEmhIoQQQgiTJYWKEEIIIUyWjeoAN0PTNKBsumghhBBCmIe/v7f//h6/FrMuVHJycgAICAhQnEQIIYQQNyonJwc3N7drrqPTrqecMVFGo5HU1FRcXFzQ6XRVuu/s7GwCAgJISUnB1dW1SvdtCuT8zJ+ln6Olnx9Y/jnK+Zm/6jpHTdPIycnBz88PK6tr90Ix6xYVKysr/P39q/UYrq6uFvsBBDk/S2Dp52jp5weWf45yfuavOs7xv1pS/iadaYUQQghhsqRQEUIIIYTJkkLlKvR6Pa+++ip6vV51lGoh52f+LP0cLf38wPLPUc7P/JnCOZp1Z1ohhBBCWDZpURFCCCGEyZJCRQghhBAmSwoVIYQQQpgsKVSEEEIIYbKkULkOt99+O4GBgdjb2+Pr68uIESNITU1VHatKnDx5kgcffJCQkBAcHBwIDQ3l1VdfpaioSHW0KvX222/ToUMHHB0dcXd3Vx3npn322WeEhIRgb29PdHQ0mzZtUh2pymzcuJEBAwbg5+eHTqfjt99+Ux2pSk2ZMoU2bdrg4uKCt7c3d9xxB0eOHFEdq0p9/vnnREVFlQ8SFhMTw4oVK1THqhZTpkxBp9MxceJE1VGqzGuvvYZOp6vwqFevnrI8Uqhch27duvHzzz9z5MgRFi1axPHjxxk0aJDqWFXi8OHDGI1GZs2aRXx8PNOnT+eLL77ghRdeUB2tShUVFTF48GAee+wx1VFu2k8//cTEiRN58cUX2bdvH7fccgt9+/YlOTlZdbQqkZeXR/PmzZk5c6bqKNViw4YNjB07lu3bt7NmzRpKSkro1asXeXl5qqNVGX9/f9599112797N7t276d69OwMHDiQ+Pl51tCq1a9cuZs+eTVRUlOooVa5p06acPXu2/BEXF6cujCZu2O+//67pdDqtqKhIdZRqMXXqVC0kJER1jGoxd+5czc3NTXWMm9K2bVttzJgxFZaFh4drzz//vKJE1QfQFi9erDpGtUpLS9MAbcOGDaqjVKs6depoX375peoYVSYnJ0dr2LChtmbNGq1Lly7ahAkTVEeqMq+++qrWvHlz1THKSYvKDcrIyGD+/Pl06NABW1tb1XGqRVZWFh4eHqpjiCsoKipiz5499OrVq8LyXr16sXXrVkWpxM3IysoCsNjfudLSUhYsWEBeXh4xMTGq41SZsWPH0r9/f3r06KE6SrVITEzEz8+PkJAQhg0bxokTJ5RlkULlOj333HM4OTnh6elJcnIyv//+u+pI1eL48eN88sknjBkzRnUUcQUXL16ktLQUHx+fCst9fHw4d+6colSisjRN46mnnqJTp040a9ZMdZwqFRcXh7OzM3q9njFjxrB48WIiIiJUx6oSCxYsYO/evUyZMkV1lGrRrl07vvvuO1atWsWcOXM4d+4cHTp0ID09XUmeWluoXKmz0L8fu3fvLl9/0qRJ7Nu3j9WrV2Ntbc3999+PZsKD+t7o+QGkpqbSp08fBg8ezEMPPaQo+fWrzDlaCp1OV+G5pmmXLROmb9y4cRw4cIAff/xRdZQq17hxY2JjY9m+fTuPPfYYI0eOJCEhQXWsm5aSksKECROYN28e9vb2quNUi759+3L33XcTGRlJjx49WLZsGQDffvutkjw2So5qAsaNG8ewYcOuuU5wcHD5z3Xr1qVu3bo0atSIJk2aEBAQwPbt2022KfNGzy81NZVu3boRExPD7Nmzqzld1bjRc7QEdevWxdra+rLWk7S0tMtaWYRpGz9+PEuWLGHjxo34+/urjlPl7OzsCAsLA6B169bs2rWLjz76iFmzZilOdnP27NlDWloa0dHR5ctKS0vZuHEjM2fOxGAwYG1trTBh1XNyciIyMpLExEQlx6+1hcrfhUdl/N2SYjAYqjJSlbqR8ztz5gzdunUjOjqauXPnYmVlHg1tN/NvaK7s7OyIjo5mzZo13HnnneXL16xZw8CBAxUmE9dL0zTGjx/P4sWLWb9+PSEhIaoj1QhN00z6/8zrdeutt152B8zo0aMJDw/nueees7giBcq+6w4dOsQtt9yi5Pi1tlC5Xjt37mTnzp106tSJOnXqcOLECV555RVCQ0NNtjXlRqSmptK1a1cCAwP54IMPuHDhQvlrKu+br2rJyclkZGSQnJxMaWkpsbGxAISFheHs7Kw23A166qmnGDFiBK1bty5vAUtOTraYfkW5ubkcO3as/HlSUhKxsbF4eHgQGBioMFnVGDt2LD/88AO///47Li4u5a1jbm5uODg4KE5XNV544QX69u1LQEAAOTk5LFiwgPXr17Ny5UrV0W6ai4vLZf2J/u6/aCn9jJ555hkGDBhAYGAgaWlpvPXWW2RnZzNy5Eg1gVTecmQODhw4oHXr1k3z8PDQ9Hq9FhwcrI0ZM0Y7ffq06mhVYu7cuRpwxYclGTly5BXP8a+//lIdrVI+/fRTLSgoSLOzs9NatWplUbe2/vXXX1f8txo5cqTqaFXiar9vc+fOVR2tyjzwwAPln08vLy/t1ltv1VavXq06VrWxtNuThw4dqvn6+mq2traan5+fdtddd2nx8fHK8ug0zYR7hAohhBCiVjOPzghCCCGEqJWkUBFCCCGEyZJCRQghhBAmSwoVIYQQQpgsKVSEEEIIYbKkUBFCCCGEyZJCRQghhBAmSwoVIYQQQpgsKVSEsEBdu3Zl4sSJqmNcUXp6Ot7e3pw8eRKA9evXo9PpuHTpUrUet7LH+eabb3B3d7+hbdq0acOvv/56Q9sIIa5MChUhxH86e/Ys9957L40bN8bKyuqqRdCiRYuIiIhAr9cTERHB4sWLL1tnypQpDBgwwOJmtv6nl19+meeffx6j0ag6ihBmTwoVIcR/MhgMeHl58eKLL9K8efMrrrNt2zaGDh3KiBEj2L9/PyNGjGDIkCHs2LGjfJ2CggK++uorHnrooZqKrkT//v3Jyspi1apVqqMIYfakUBHCwmVmZnL//fdTp04dHB0d6du3L4mJiRXWmTNnDgEBATg6OnLnnXcybdq0Cpc7goOD+eijj7j//vtxc3O74nFmzJhBz549mTx5MuHh4UyePJlbb72VGTNmlK+zYsUKbGxsrjnzeHp6Ovfccw/+/v44OjoSGRnJjz/+WGGdrl27Mn78eCZOnEidOnXw8fFh9uzZ5OXlMXr0aFxcXAgNDWXFihWX7X/Lli00b94ce3t72rVrR1xcXIXXv/nmGwIDA8vfi/T09AqvHz9+nIEDB+Lj44OzszNt2rRh7dq1FdaxtramX79+l+UWQtw4KVSEsHCjRo1i9+7dLFmyhG3btqFpGv369aO4uBgo++IeM2YMEyZMIDY2lp49e/L222/f8HG2bdtGr169Kizr3bs3W7duLX++ceNGWrdufc39FBYWEh0dzdKlSzl48CCPPPIII0aMqNAyA/Dtt99St25ddu7cyfjx43nssccYPHgwHTp0YO/evfTu3ZsRI0aQn59fYbtJkybxwQcfsGvXLry9vbn99tvL34sdO3bwwAMP8PjjjxMbG0u3bt146623Kmyfm5tLv379WLt2Lfv27aN3794MGDCA5OTkCuu1bduWTZs2Xd+bJ4S4OmXzNgshqs3f084fPXpUA7QtW7aUv3bx4kXNwcFB+/nnnzVNK5vSvX///hW2Hz58uObm5nbNff+bra2tNn/+/ArL5s+fr9nZ2ZU/HzhwoPbAAw9UWOevv/7SAC0zM/Oq59OvXz/t6aefrpChU6dO5c9LSko0JycnbcSIEeXLzp49qwHatm3bKhxnwYIF5eukp6drDg4O2k8//aRpmqbdc889Wp8+fSoce+jQoVd9L/4WERGhffLJJxWW/f7775qVlZVWWlp6zW2FENcmLSpCWLBDhw5hY2NDu3btypd5enrSuHFjDh06BMCRI0do27Zthe3+/fx66XS6Cs81TauwrKCgAHt7+2vuo7S0lLfffpuoqCg8PT1xdnZm9erVl7VYREVFlf9sbW2Np6cnkZGR5ct8fHwASEtLq7DdPy87eXh4VHgvDh06dNllqX8/z8vL49lnnyUiIgJ3d3ecnZ05fPjwZfkcHBwwGo0YDIZrnq8Q4tpsVAcQQlQfTdOuuvzvAuLfxcS1truWevXqce7cuQrL0tLSygsGgLp165KZmXnN/Xz44YdMnz6dGTNmEBkZiZOTExMnTqSoqKjCera2thWe63S6Csv+PqfrufPmn+/Ff5k0aRKrVq3igw8+ICwsDAcHBwYNGnRZvoyMDBwdHXFwcPjPfQohrk5aVISwYBEREZSUlFTo35Gens7Ro0dp0qQJAOHh4ezcubPCdrt3777hY8XExLBmzZoKy1avXk2HDh3Kn7ds2ZKEhIRr7mfTpk0MHDiQ++67j+bNm9OgQYPLOv/ejO3bt5f/nJmZydGjRwkPDwfK3q9/vv7v9f/ON2rUKO68804iIyOpV69e+Zgw/3Tw4EFatWpVZbmFqK2kUBHCgjVs2JCBAwfy8MMPs3nzZvbv3899991H/fr1GThwIADjx49n+fLlTJs2jcTERGbNmsWKFSsua2WJjY0lNjaW3NxcLly4QGxsbIWiY8KECaxevZr33nuPw4cP895777F27doKY6707t2b+Pj4a7aqhIWFsWbNGrZu3cqhQ4d49NFHL2upuRlvvPEG69at4+DBg4waNYq6detyxx13APDEE0+wcuVKpk6dytGjR5k5cyYrV668LN+vv/5KbGws+/fv5957771iq82mTZsu61wshLhxUqgIYeHmzp1LdHQ0t912GzExMWiaxvLly8svk3Ts2JEvvviCadOm0bx5c1auXMmTTz55WV+Sli1b0rJlS/bs2cMPP/xAy5Yt6devX/nrHTp0YMGCBcydO5eoqCi++eYbfvrppwr9YyIjI2ndujU///zzVfO+/PLLtGrVit69e9O1a1fq1atXXkhUhXfffZcJEyYQHR3N2bNnWbJkCXZ2dgC0b9+eL7/8kk8++YQWLVqwevVqXnrppQrbT58+nTp16tChQwcGDBhA7969L2s5OXPmDFu3bmX06NFVlluI2kqnVeZitBDCoj388MMcPny4Wm6vXb58Oc888wwHDx7Eysoy/1aaNGkSWVlZzJ49W3UUIcyedKYVQvDBBx/Qs2dPnJycWLFiBd9++y2fffZZtRyrX79+JCYmcubMGQICAqrlGKp5e3vzzDPPqI4hhEWQFhUhBEOGDGH9+vXk5OTQoEEDxo8fz5gxY1THEkIIKVSEEEIIYbos8wKxEEIIISyCFCpCCCGEMFlSqAghhBDCZEmhIoQQQgiTJYWKEEIIIUyWFCpCCCGEMFlSqAghhBDCZEmhIoQQQgiT9X+fZkvEqg05YAAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "
    "
+      ]
+     },
+     "metadata": {
+      "filenames": {
+       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week37_169_0.png"
+      }
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from sklearn.model_selection import KFold\n",
+    "from sklearn.linear_model import Ridge\n",
+    "from sklearn.model_selection import cross_val_score\n",
+    "from sklearn.preprocessing import PolynomialFeatures\n",
+    "\n",
+    "# A seed just to ensure that the random numbers are the same for every run.\n",
+    "# Useful for eventual debugging.\n",
+    "np.random.seed(3155)\n",
+    "\n",
+    "# Generate the data.\n",
+    "nsamples = 100\n",
+    "x = np.random.randn(nsamples)\n",
+    "y = 3*x**2 + np.random.randn(nsamples)\n",
+    "\n",
+    "## Cross-validation on Ridge regression using KFold only\n",
+    "\n",
+    "# Decide degree on polynomial to fit\n",
+    "poly = PolynomialFeatures(degree = 6)\n",
+    "\n",
+    "# Decide which values of lambda to use\n",
+    "nlambdas = 500\n",
+    "lambdas = np.logspace(-3, 5, nlambdas)\n",
+    "\n",
+    "# Initialize a KFold instance\n",
+    "k = 5\n",
+    "kfold = KFold(n_splits = k)\n",
+    "\n",
+    "# Perform the cross-validation to estimate MSE\n",
+    "scores_KFold = np.zeros((nlambdas, k))\n",
+    "\n",
+    "i = 0\n",
+    "for lmb in lambdas:\n",
+    "    ridge = Ridge(alpha = lmb)\n",
+    "    j = 0\n",
+    "    for train_inds, test_inds in kfold.split(x):\n",
+    "        xtrain = x[train_inds]\n",
+    "        ytrain = y[train_inds]\n",
+    "\n",
+    "        xtest = x[test_inds]\n",
+    "        ytest = y[test_inds]\n",
+    "\n",
+    "        Xtrain = poly.fit_transform(xtrain[:, np.newaxis])\n",
+    "        ridge.fit(Xtrain, ytrain[:, np.newaxis])\n",
+    "\n",
+    "        Xtest = poly.fit_transform(xtest[:, np.newaxis])\n",
+    "        ypred = ridge.predict(Xtest)\n",
+    "\n",
+    "        scores_KFold[i,j] = np.sum((ypred - ytest[:, np.newaxis])**2)/np.size(ypred)\n",
+    "\n",
+    "        j += 1\n",
+    "    i += 1\n",
+    "\n",
+    "\n",
+    "estimated_mse_KFold = np.mean(scores_KFold, axis = 1)\n",
+    "\n",
+    "## Cross-validation using cross_val_score from sklearn along with KFold\n",
+    "\n",
+    "# kfold is an instance initialized above as:\n",
+    "# kfold = KFold(n_splits = k)\n",
+    "\n",
+    "estimated_mse_sklearn = np.zeros(nlambdas)\n",
+    "i = 0\n",
+    "for lmb in lambdas:\n",
+    "    ridge = Ridge(alpha = lmb)\n",
+    "\n",
+    "    X = poly.fit_transform(x[:, np.newaxis])\n",
+    "    estimated_mse_folds = cross_val_score(ridge, X, y[:, np.newaxis], scoring='neg_mean_squared_error', cv=kfold)\n",
+    "\n",
+    "    # cross_val_score return an array containing the estimated negative mse for every fold.\n",
+    "    # we have to the the mean of every array in order to get an estimate of the mse of the model\n",
+    "    estimated_mse_sklearn[i] = np.mean(-estimated_mse_folds)\n",
+    "\n",
+    "    i += 1\n",
+    "\n",
+    "## Plot and compare the slightly different ways to perform cross-validation\n",
+    "\n",
+    "plt.figure()\n",
+    "\n",
+    "plt.plot(np.log10(lambdas), estimated_mse_sklearn, label = 'cross_val_score')\n",
+    "plt.plot(np.log10(lambdas), estimated_mse_KFold, 'r--', label = 'KFold')\n",
+    "\n",
+    "plt.xlabel('log10(lambda)')\n",
+    "plt.ylabel('mse')\n",
+    "\n",
+    "plt.legend()\n",
+    "\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "addf22bf",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## More examples on bootstrap and cross-validation and errors"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "f1af3e2c",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Degree of polynomial:   1\n",
+      "Mean squared error on training data: 446033.51374050\n",
+      "Mean squared error on test data: 455173.80460179\n",
+      "Degree of polynomial:   2\n",
+      "Mean squared error on training data: 114550.54637219\n",
+      "Mean squared error on test data: 129963.83146596\n",
+      "Degree of polynomial:   3\n",
+      "Mean squared error on training data: 9054.61775176\n",
+      "Mean squared error on test data: 10572.87627342\n",
+      "Degree of polynomial:   4\n",
+      "Mean squared error on training data: 302.15313054\n",
+      "Mean squared error on test data: 433.26292364\n",
+      "Degree of polynomial:   5\n",
+      "Mean squared error on training data: 3.64316192\n",
+      "Mean squared error on test data: 7.23528337\n",
+      "Degree of polynomial:   6\n",
+      "Mean squared error on training data: 3.56589683\n",
+      "Mean squared error on test data: 10.50427787\n",
+      "Degree of polynomial:   7\n",
+      "Mean squared error on training data: 0.47313680\n",
+      "Mean squared error on test data: 1.53738247\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Degree of polynomial:   8\n",
+      "Mean squared error on training data: 0.04926746\n",
+      "Mean squared error on test data: 0.14629156\n",
+      "Degree of polynomial:   9\n",
+      "Mean squared error on training data: 0.02546675\n",
+      "Mean squared error on test data: 0.11202337\n",
+      "Degree of polynomial:  10\n",
+      "Mean squared error on training data: 0.02424794\n",
+      "Mean squared error on test data: 0.22467274\n",
+      "Degree of polynomial:  11\n",
+      "Mean squared error on training data: 0.01594452\n",
+      "Mean squared error on test data: 1.07641937\n",
+      "Degree of polynomial:  12\n",
+      "Mean squared error on training data: 0.00805074\n",
+      "Mean squared error on test data: 0.04295757\n",
+      "Degree of polynomial:  13\n",
+      "Mean squared error on training data: 0.00781918\n",
+      "Mean squared error on test data: 0.56965674\n",
+      "Degree of polynomial:  14\n",
+      "Mean squared error on training data: 0.00465099\n",
+      "Mean squared error on test data: 0.28443039\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Degree of polynomial:  15\n",
+      "Mean squared error on training data: 0.00420072\n",
+      "Mean squared error on test data: 568.47202442\n",
+      "Degree of polynomial:  16\n",
+      "Mean squared error on training data: 0.00325450\n",
+      "Mean squared error on test data: 48.97690235\n",
+      "Degree of polynomial:  17\n",
+      "Mean squared error on training data: 0.00242954\n",
+      "Mean squared error on test data: 2.52775466\n",
+      "Degree of polynomial:  18\n",
+      "Mean squared error on training data: 0.00219194\n",
+      "Mean squared error on test data: 429.23643365\n",
+      "Degree of polynomial:  19\n",
+      "Mean squared error on training data: 0.00154860\n",
+      "Mean squared error on test data: 238.16356503\n",
+      "Degree of polynomial:  20\n",
+      "Mean squared error on training data: 0.00140849\n",
+      "Mean squared error on test data: 1345.68592431\n",
+      "Degree of polynomial:  21\n",
+      "Mean squared error on training data: 0.00119699\n",
+      "Mean squared error on test data: 1836.21110005\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Degree of polynomial:  22\n",
+      "Mean squared error on training data: 0.00092904\n",
+      "Mean squared error on test data: 1182.64316482\n",
+      "Degree of polynomial:  23\n",
+      "Mean squared error on training data: 0.00089187\n",
+      "Mean squared error on test data: 3886.35846425\n",
+      "Degree of polynomial:  24\n",
+      "Mean squared error on training data: 0.00083346\n",
+      "Mean squared error on test data: 1346.92651068\n",
+      "Degree of polynomial:  25\n",
+      "Mean squared error on training data: 0.00079910\n",
+      "Mean squared error on test data: 7697.35412147\n",
+      "Degree of polynomial:  26\n",
+      "Mean squared error on training data: 0.00075597\n",
+      "Mean squared error on test data: 1078.81597834\n",
+      "Degree of polynomial:  27\n",
+      "Mean squared error on training data: 0.00068088\n",
+      "Mean squared error on test data: 3189.20355156\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Degree of polynomial:  28\n",
+      "Mean squared error on training data: 0.00063364\n",
+      "Mean squared error on test data: 692.24085321\n",
+      "Degree of polynomial:  29\n",
+      "Mean squared error on training data: 0.00063862\n",
+      "Mean squared error on test data: 3073.63180447\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7768/626635268.py:73: RuntimeWarning: divide by zero encountered in log10\n",
+      "  plt.plot(polynomial, np.log10(trainingerror), label='Training Error')\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7768/626635268.py:74: RuntimeWarning: divide by zero encountered in log10\n",
+      "  plt.plot(polynomial, np.log10(testerror), label='Test Error')\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "
    "
+      ]
+     },
+     "metadata": {
+      "filenames": {
+       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week37_171_6.png"
+      }
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Common imports\n",
+    "import os\n",
+    "import numpy as np\n",
+    "import pandas as pd\n",
+    "import matplotlib.pyplot as plt\n",
+    "from sklearn.linear_model import LinearRegression, Ridge, Lasso\n",
+    "from sklearn.model_selection import train_test_split\n",
+    "from sklearn.utils import resample\n",
+    "from sklearn.metrics import mean_squared_error\n",
+    "# Where to save the figures and data files\n",
+    "PROJECT_ROOT_DIR = \"Results\"\n",
+    "FIGURE_ID = \"Results/FigureFiles\"\n",
+    "DATA_ID = \"DataFiles/\"\n",
+    "\n",
+    "if not os.path.exists(PROJECT_ROOT_DIR):\n",
+    "    os.mkdir(PROJECT_ROOT_DIR)\n",
+    "\n",
+    "if not os.path.exists(FIGURE_ID):\n",
+    "    os.makedirs(FIGURE_ID)\n",
+    "\n",
+    "if not os.path.exists(DATA_ID):\n",
+    "    os.makedirs(DATA_ID)\n",
+    "\n",
+    "def image_path(fig_id):\n",
+    "    return os.path.join(FIGURE_ID, fig_id)\n",
+    "\n",
+    "def data_path(dat_id):\n",
+    "    return os.path.join(DATA_ID, dat_id)\n",
+    "\n",
+    "def save_fig(fig_id):\n",
+    "    plt.savefig(image_path(fig_id) + \".png\", format='png')\n",
+    "\n",
+    "infile = open(data_path(\"EoS.csv\"),'r')\n",
+    "\n",
+    "# Read the EoS data as  csv file and organize the data into two arrays with density and energies\n",
+    "EoS = pd.read_csv(infile, names=('Density', 'Energy'))\n",
+    "EoS['Energy'] = pd.to_numeric(EoS['Energy'], errors='coerce')\n",
+    "EoS = EoS.dropna()\n",
+    "Energies = EoS['Energy']\n",
+    "Density = EoS['Density']\n",
+    "#  The design matrix now as function of various polytrops\n",
+    "\n",
+    "Maxpolydegree = 30\n",
+    "X = np.zeros((len(Density),Maxpolydegree))\n",
+    "X[:,0] = 1.0\n",
+    "testerror = np.zeros(Maxpolydegree)\n",
+    "trainingerror = np.zeros(Maxpolydegree)\n",
+    "polynomial = np.zeros(Maxpolydegree)\n",
+    "\n",
+    "trials = 100\n",
+    "for polydegree in range(1, Maxpolydegree):\n",
+    "    polynomial[polydegree] = polydegree\n",
+    "    for degree in range(polydegree):\n",
+    "        X[:,degree] = Density**(degree/3.0)\n",
+    "\n",
+    "# loop over trials in order to estimate the expectation value of the MSE\n",
+    "    testerror[polydegree] = 0.0\n",
+    "    trainingerror[polydegree] = 0.0\n",
+    "    for samples in range(trials):\n",
+    "        x_train, x_test, y_train, y_test = train_test_split(X, Energies, test_size=0.2)\n",
+    "        model = LinearRegression(fit_intercept=False).fit(x_train, y_train)\n",
+    "        ypred = model.predict(x_train)\n",
+    "        ytilde = model.predict(x_test)\n",
+    "        testerror[polydegree] += mean_squared_error(y_test, ytilde)\n",
+    "        trainingerror[polydegree] += mean_squared_error(y_train, ypred) \n",
+    "\n",
+    "    testerror[polydegree] /= trials\n",
+    "    trainingerror[polydegree] /= trials\n",
+    "    print(\"Degree of polynomial: %3d\"% polynomial[polydegree])\n",
+    "    print(\"Mean squared error on training data: %.8f\" % trainingerror[polydegree])\n",
+    "    print(\"Mean squared error on test data: %.8f\" % testerror[polydegree])\n",
+    "\n",
+    "plt.plot(polynomial, np.log10(trainingerror), label='Training Error')\n",
+    "plt.plot(polynomial, np.log10(testerror), label='Test Error')\n",
+    "plt.xlabel('Polynomial degree')\n",
+    "plt.ylabel('log10[MSE]')\n",
+    "plt.legend()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c05b2a3a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Note that we kept the intercept column in the fitting here. This means that we need to set the **intercept** in the call to the **Scikit-Learn** function as **False**. Alternatively, we could have set up the design matrix $X$ without the first column of ones."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "be50bfa2",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## The same example but now with cross-validation\n",
+    "\n",
+    "In this example we keep the intercept column again but add cross-validation in order to estimate the best possible value of the means squared error."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "33fb2f51",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7768/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10\n",
+      "  plt.plot(polynomial, np.log10(estimated_mse_sklearn), label='Test Error')\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "
    "
+      ]
+     },
+     "metadata": {
+      "filenames": {
+       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week37_174_1.png"
+      }
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Common imports\n",
+    "import os\n",
+    "import numpy as np\n",
+    "import pandas as pd\n",
+    "import matplotlib.pyplot as plt\n",
+    "from sklearn.linear_model import LinearRegression, Ridge, Lasso\n",
+    "from sklearn.metrics import mean_squared_error\n",
+    "from sklearn.model_selection import KFold\n",
+    "from sklearn.model_selection import cross_val_score\n",
+    "\n",
+    "\n",
+    "# Where to save the figures and data files\n",
+    "PROJECT_ROOT_DIR = \"Results\"\n",
+    "FIGURE_ID = \"Results/FigureFiles\"\n",
+    "DATA_ID = \"DataFiles/\"\n",
+    "\n",
+    "if not os.path.exists(PROJECT_ROOT_DIR):\n",
+    "    os.mkdir(PROJECT_ROOT_DIR)\n",
+    "\n",
+    "if not os.path.exists(FIGURE_ID):\n",
+    "    os.makedirs(FIGURE_ID)\n",
+    "\n",
+    "if not os.path.exists(DATA_ID):\n",
+    "    os.makedirs(DATA_ID)\n",
+    "\n",
+    "def image_path(fig_id):\n",
+    "    return os.path.join(FIGURE_ID, fig_id)\n",
+    "\n",
+    "def data_path(dat_id):\n",
+    "    return os.path.join(DATA_ID, dat_id)\n",
+    "\n",
+    "def save_fig(fig_id):\n",
+    "    plt.savefig(image_path(fig_id) + \".png\", format='png')\n",
+    "\n",
+    "infile = open(data_path(\"EoS.csv\"),'r')\n",
+    "\n",
+    "# Read the EoS data as  csv file and organize the data into two arrays with density and energies\n",
+    "EoS = pd.read_csv(infile, names=('Density', 'Energy'))\n",
+    "EoS['Energy'] = pd.to_numeric(EoS['Energy'], errors='coerce')\n",
+    "EoS = EoS.dropna()\n",
+    "Energies = EoS['Energy']\n",
+    "Density = EoS['Density']\n",
+    "#  The design matrix now as function of various polytrops\n",
+    "\n",
+    "Maxpolydegree = 30\n",
+    "X = np.zeros((len(Density),Maxpolydegree))\n",
+    "X[:,0] = 1.0\n",
+    "estimated_mse_sklearn = np.zeros(Maxpolydegree)\n",
+    "polynomial = np.zeros(Maxpolydegree)\n",
+    "k =5\n",
+    "kfold = KFold(n_splits = k)\n",
+    "\n",
+    "for polydegree in range(1, Maxpolydegree):\n",
+    "    polynomial[polydegree] = polydegree\n",
+    "    for degree in range(polydegree):\n",
+    "        X[:,degree] = Density**(degree/3.0)\n",
+    "        OLS = LinearRegression(fit_intercept=False)\n",
+    "# loop over trials in order to estimate the expectation value of the MSE\n",
+    "    estimated_mse_folds = cross_val_score(OLS, X, Energies, scoring='neg_mean_squared_error', cv=kfold)\n",
+    "#[:, np.newaxis]\n",
+    "    estimated_mse_sklearn[polydegree] = np.mean(-estimated_mse_folds)\n",
+    "\n",
+    "plt.plot(polynomial, np.log10(estimated_mse_sklearn), label='Test Error')\n",
+    "plt.xlabel('Polynomial degree')\n",
+    "plt.ylabel('log10[MSE]')\n",
+    "plt.legend()\n",
+    "plt.show()"
+   ]
+  }
+ ],
+ "metadata": {
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.10"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
\ No newline at end of file
diff --git a/doc/LectureNotes/_build/jupyter_execute/week37.py b/doc/LectureNotes/_build/jupyter_execute/week37.py
new file mode 100644
index 000000000..08c9e6b5e
--- /dev/null
+++ b/doc/LectureNotes/_build/jupyter_execute/week37.py
@@ -0,0 +1,1515 @@
+#!/usr/bin/env python
+# coding: utf-8
+
+# 
+# 
+
+# # Week 37: Statitsitcal interpretations and Resampling Methods
+# **Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University
+# 
+# Date: **Sep 11, 2023**
+# 
+# Copyright 1999-2023, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
+# 
+# 
+
+# ## Plans for week 37
+# 
+# **Material for the active learning sessions on Tuesday and Wednesday.**
+# 
+#   * Lecture from last week on calculations of expectation values
+# 
+#   * Exercise for week 37
+# 
+#   * Work on project 1
+# 
+#   * See also additional note on scaling (jupyter-notebook) sent separately. This will be discussed during the first hour of each session.
+# 
+#   * For more discussions of Ridge regression and calculation of averages, [Wessel van Wieringen's](https://arxiv.org/abs/1509.09169) article is highly recommended.
+# 
+#   
+# **Material for the lecture on Thursday September 7.**
+# 
+#   * Statistical interpretation of Ridge and Lasso regression
+# 
+#   * Resampling techniques, Bootstrap and cross validation and bias-variance tradeoff
+# 
+#   * Reads and Videos:
+# 
+#     * Hastie et al Chapter 7, here we recommend 7.1-7.5 and 7.10 (cross-validation) and 7.11 (bootstrap). 
+# 
+#     * [Video on cross validation](https://www.youtube.com/watch?v=fSytzGwwBVw)
+# 
+#     * [Video on bias-variance tradeoff](https://www.youtube.com/watch?v=EuBBz3bI-aA)
+
+# ## Material from last week and relevant for the weekly exercises
+
+# ## Linking the regression analysis with a statistical interpretation
+# 
+# We will now couple the discussions of ordinary least squares, Ridge
+# and Lasso regression with a statistical interpretation, that is we
+# move from a linear algebra analysis to a statistical analysis. In
+# particular, we will focus on what the regularization terms can result
+# in.  We will amongst other things show that the regularization
+# parameter can reduce considerably the variance of the parameters
+# $\beta$.
+# 
+# The
+# advantage of doing linear regression is that we actually end up with
+# analytical expressions for several statistical quantities.  
+# Standard least squares and Ridge regression  allow us to
+# derive quantities like the variance and other expectation values in a
+# rather straightforward way.
+# 
+# It is assumed that $\varepsilon_i
+# \sim \mathcal{N}(0, \sigma^2)$ and the $\varepsilon_{i}$ are
+# independent, i.e.:
+
+# $$
+# \begin{align*} 
+# \mbox{Cov}(\varepsilon_{i_1},
+# \varepsilon_{i_2}) & = \left\{ \begin{array}{lcc} \sigma^2 & \mbox{if}
+# & i_1 = i_2, \\ 0 & \mbox{if} & i_1 \not= i_2.  \end{array} \right.
+# \end{align*}
+# $$
+
+# The randomness of $\varepsilon_i$ implies that
+# $\mathbf{y}_i$ is also a random variable. In particular,
+# $\mathbf{y}_i$ is normally distributed, because $\varepsilon_i \sim
+# \mathcal{N}(0, \sigma^2)$ and $\mathbf{X}_{i,\ast} \, \boldsymbol{\beta}$ is a
+# non-random scalar. To specify the parameters of the distribution of
+# $\mathbf{y}_i$ we need to calculate its first two moments. 
+# 
+# Recall that $\boldsymbol{X}$ is a matrix of dimensionality $n\times p$. The
+# notation above $\mathbf{X}_{i,\ast}$ means that we are looking at the
+# row number $i$ and perform a sum over all values $p$.
+
+# ## Assumptions made
+# 
+# The assumption we have made here can be summarized as (and this is going to be useful when we discuss the bias-variance trade off)
+# that there exists a function $f(\boldsymbol{x})$ and  a normal distributed error $\boldsymbol{\varepsilon}\sim \mathcal{N}(0, \sigma^2)$
+# which describe our data
+
+# $$
+# \boldsymbol{y} = f(\boldsymbol{x})+\boldsymbol{\varepsilon}
+# $$
+
+# We approximate this function with our model from the solution of the linear regression equations, that is our
+# function $f$ is approximated by $\boldsymbol{\tilde{y}}$ where we want to minimize $(\boldsymbol{y}-\boldsymbol{\tilde{y}})^2$, our MSE, with
+
+# $$
+# \boldsymbol{\tilde{y}} = \boldsymbol{X}\boldsymbol{\beta}.
+# $$
+
+# ## Expectation value and variance
+# 
+# We can calculate the expectation value of $\boldsymbol{y}$ for a given element $i$
+
+# $$
+# \begin{align*} 
+# \mathbb{E}(y_i) & =
+# \mathbb{E}(\mathbf{X}_{i, \ast} \, \boldsymbol{\beta}) + \mathbb{E}(\varepsilon_i)
+# \, \, \, = \, \, \, \mathbf{X}_{i, \ast} \, \beta, 
+# \end{align*}
+# $$
+
+# while
+# its variance is
+
+# $$
+# \begin{align*} \mbox{Var}(y_i) & = \mathbb{E} \{ [y_i
+# - \mathbb{E}(y_i)]^2 \} \, \, \, = \, \, \, \mathbb{E} ( y_i^2 ) -
+# [\mathbb{E}(y_i)]^2  \\  & = \mathbb{E} [ ( \mathbf{X}_{i, \ast} \,
+# \beta + \varepsilon_i )^2] - ( \mathbf{X}_{i, \ast} \, \boldsymbol{\beta})^2 \\ &
+# = \mathbb{E} [ ( \mathbf{X}_{i, \ast} \, \boldsymbol{\beta})^2 + 2 \varepsilon_i
+# \mathbf{X}_{i, \ast} \, \boldsymbol{\beta} + \varepsilon_i^2 ] - ( \mathbf{X}_{i,
+# \ast} \, \beta)^2 \\  & = ( \mathbf{X}_{i, \ast} \, \boldsymbol{\beta})^2 + 2
+# \mathbb{E}(\varepsilon_i) \mathbf{X}_{i, \ast} \, \boldsymbol{\beta} +
+# \mathbb{E}(\varepsilon_i^2 ) - ( \mathbf{X}_{i, \ast} \, \boldsymbol{\beta})^2 
+# \\ & = \mathbb{E}(\varepsilon_i^2 ) \, \, \, = \, \, \,
+# \mbox{Var}(\varepsilon_i) \, \, \, = \, \, \, \sigma^2.  
+# \end{align*}
+# $$
+
+# Hence, $y_i \sim \mathcal{N}( \mathbf{X}_{i, \ast} \, \boldsymbol{\beta}, \sigma^2)$, that is $\boldsymbol{y}$ follows a normal distribution with 
+# mean value $\boldsymbol{X}\boldsymbol{\beta}$ and variance $\sigma^2$ (not be confused with the singular values of the SVD).
+
+# ## Expectation value and variance for $\boldsymbol{\beta}$
+# 
+# With the OLS expressions for the optimal parameters $\boldsymbol{\hat{\beta}}$ we can evaluate the expectation value
+
+# $$
+# \mathbb{E}(\boldsymbol{\hat{\beta}}) = \mathbb{E}[ (\mathbf{X}^{\top} \mathbf{X})^{-1}\mathbf{X}^{T} \mathbf{Y}]=(\mathbf{X}^{T} \mathbf{X})^{-1}\mathbf{X}^{T} \mathbb{E}[ \mathbf{Y}]=(\mathbf{X}^{T} \mathbf{X})^{-1} \mathbf{X}^{T}\mathbf{X}\boldsymbol{\beta}=\boldsymbol{\beta}.
+# $$
+
+# This means that the estimator of the regression parameters is unbiased.
+# 
+# We can also calculate the variance
+# 
+# The variance of the optimal value $\boldsymbol{\hat{\beta}}$ is
+
+# $$
+# \begin{eqnarray*}
+# \mbox{Var}(\boldsymbol{\hat{\beta}}) & = & \mathbb{E} \{ [\boldsymbol{\beta} - \mathbb{E}(\boldsymbol{\beta})] [\boldsymbol{\beta} - \mathbb{E}(\boldsymbol{\beta})]^{T} \}
+# \\
+# & = & \mathbb{E} \{ [(\mathbf{X}^{T} \mathbf{X})^{-1} \, \mathbf{X}^{T} \mathbf{Y} - \boldsymbol{\beta}] \, [(\mathbf{X}^{T} \mathbf{X})^{-1} \, \mathbf{X}^{T} \mathbf{Y} - \boldsymbol{\beta}]^{T} \}
+# \\
+# % & = & \mathbb{E} \{ [(\mathbf{X}^{T} \mathbf{X})^{-1} \, \mathbf{X}^{T} \mathbf{Y}] \, [(\mathbf{X}^{T} \mathbf{X})^{-1} \, \mathbf{X}^{T} \mathbf{Y}]^{T} \} - \boldsymbol{\beta} \, \boldsymbol{\beta}^{T}
+# % \\
+# % & = & \mathbb{E} \{ (\mathbf{X}^{T} \mathbf{X})^{-1} \, \mathbf{X}^{T} \mathbf{Y} \, \mathbf{Y}^{T} \, \mathbf{X} \, (\mathbf{X}^{T} \mathbf{X})^{-1}  \} - \boldsymbol{\beta} \, \boldsymbol{\beta}^{T}
+# % \\
+# & = & (\mathbf{X}^{T} \mathbf{X})^{-1} \, \mathbf{X}^{T} \, \mathbb{E} \{ \mathbf{Y} \, \mathbf{Y}^{T} \} \, \mathbf{X} \, (\mathbf{X}^{T} \mathbf{X})^{-1} - \boldsymbol{\beta} \, \boldsymbol{\beta}^{T}
+# \\
+# & = & (\mathbf{X}^{T} \mathbf{X})^{-1} \, \mathbf{X}^{T} \, \{ \mathbf{X} \, \boldsymbol{\beta} \, \boldsymbol{\beta}^{T} \,  \mathbf{X}^{T} + \sigma^2 \} \, \mathbf{X} \, (\mathbf{X}^{T} \mathbf{X})^{-1} - \boldsymbol{\beta} \, \boldsymbol{\beta}^{T}
+# % \\
+# % & = & (\mathbf{X}^T \mathbf{X})^{-1} \, \mathbf{X}^T \, \mathbf{X} \, \boldsymbol{\beta} \, \boldsymbol{\beta}^T \,  \mathbf{X}^T \, \mathbf{X} \, (\mathbf{X}^T % \mathbf{X})^{-1}
+# % \\
+# % & & + \, \, \sigma^2 \, (\mathbf{X}^T \mathbf{X})^{-1} \, \mathbf{X}^T  \, \mathbf{X} \, (\mathbf{X}^T \mathbf{X})^{-1} - \boldsymbol{\beta} \boldsymbol{\beta}^T
+# \\
+# & = & \boldsymbol{\beta} \, \boldsymbol{\beta}^{T}  + \sigma^2 \, (\mathbf{X}^{T} \mathbf{X})^{-1} - \boldsymbol{\beta} \, \boldsymbol{\beta}^{T}
+# \, \, \, = \, \, \, \sigma^2 \, (\mathbf{X}^{T} \mathbf{X})^{-1},
+# \end{eqnarray*}
+# $$
+
+# where we have used  that $\mathbb{E} (\mathbf{Y} \mathbf{Y}^{T}) =
+# \mathbf{X} \, \boldsymbol{\beta} \, \boldsymbol{\beta}^{T} \, \mathbf{X}^{T} +
+# \sigma^2 \, \mathbf{I}_{nn}$. From $\mbox{Var}(\boldsymbol{\beta}) = \sigma^2
+# \, (\mathbf{X}^{T} \mathbf{X})^{-1}$, one obtains an estimate of the
+# variance of the estimate of the $j$-th regression coefficient:
+# $\boldsymbol{\sigma}^2 (\boldsymbol{\beta}_j ) = \boldsymbol{\sigma}^2 [(\mathbf{X}^{T} \mathbf{X})^{-1}]_{jj} $. This may be used to
+# construct a confidence interval for the estimates.
+# 
+# In a similar way, we can obtain analytical expressions for say the
+# expectation values of the parameters $\boldsymbol{\beta}$ and their variance
+# when we employ Ridge regression, allowing us again to define a confidence interval. 
+# 
+# It is rather straightforward to show that
+
+# $$
+# \mathbb{E} \big[ \boldsymbol{\beta}^{\mathrm{Ridge}} \big]=(\mathbf{X}^{T} \mathbf{X} + \lambda \mathbf{I}_{pp})^{-1} (\mathbf{X}^{\top} \mathbf{X})\boldsymbol{\beta}^{\mathrm{OLS}}.
+# $$
+
+# We see clearly that 
+# $\mathbb{E} \big[ \boldsymbol{\beta}^{\mathrm{Ridge}} \big] \not= \boldsymbol{\beta}^{\mathrm{OLS}}$ for any $\lambda > 0$.
+# 
+# We can also compute the variance as
+
+# $$
+# \mbox{Var}[\boldsymbol{\beta}^{\mathrm{Ridge}}]=\sigma^2[  \mathbf{X}^{T} \mathbf{X} + \lambda \mathbf{I} ]^{-1}  \mathbf{X}^{T} \mathbf{X} \{ [  \mathbf{X}^{\top} \mathbf{X} + \lambda \mathbf{I} ]^{-1}\}^{T},
+# $$
+
+# and it is easy to see that if the parameter $\lambda$ goes to infinity then the variance of Ridge parameters $\boldsymbol{\beta}$ goes to zero. 
+# 
+# With this, we can compute the difference
+
+# $$
+# \mbox{Var}[\boldsymbol{\beta}^{\mathrm{OLS}}]-\mbox{Var}(\boldsymbol{\beta}^{\mathrm{Ridge}})=\sigma^2 [  \mathbf{X}^{T} \mathbf{X} + \lambda \mathbf{I} ]^{-1}[ 2\lambda\mathbf{I} + \lambda^2 (\mathbf{X}^{T} \mathbf{X})^{-1} ] \{ [  \mathbf{X}^{T} \mathbf{X} + \lambda \mathbf{I} ]^{-1}\}^{T}.
+# $$
+
+# The difference is non-negative definite since each component of the
+# matrix product is non-negative definite. 
+# This means the variance we obtain with the standard OLS will always for $\lambda > 0$ be larger than the variance of $\boldsymbol{\beta}$ obtained with the Ridge estimator. This has interesting consequences when we discuss the so-called bias-variance trade-off below. 
+# 
+# For more discussions of Ridge regression and calculation of averages, [Wessel van Wieringen's](https://arxiv.org/abs/1509.09169) article is highly recommended.
+
+# ## Material for lecture Thursday September 14
+
+# ## Deriving OLS from a probability distribution
+# 
+# Our basic assumption when we derived the OLS equations was to assume
+# that our output is determined by a given continuous function
+# $f(\boldsymbol{x})$ and a random noise $\boldsymbol{\epsilon}$ given by the normal
+# distribution with zero mean value and an undetermined variance
+# $\sigma^2$.
+# 
+# We found above that the outputs $\boldsymbol{y}$ have a mean value given by
+# $\boldsymbol{X}\hat{\boldsymbol{\beta}}$ and variance $\sigma^2$. Since the entries to
+# the design matrix are not stochastic variables, we can assume that the
+# probability distribution of our targets is also a normal distribution
+# but now with mean value $\boldsymbol{X}\hat{\boldsymbol{\beta}}$. This means that a
+# single output $y_i$ is given by the Gaussian distribution
+
+# $$
+# y_i\sim \mathcal{N}(\boldsymbol{X}_{i,*}\boldsymbol{\beta}, \sigma^2)=\frac{1}{\sqrt{2\pi\sigma^2}}\exp{\left[-\frac{(y_i-\boldsymbol{X}_{i,*}\boldsymbol{\beta})^2}{2\sigma^2}\right]}.
+# $$
+
+# ## Independent and Identically Distrubuted (iid)
+# 
+# We assume now that the various $y_i$ values are stochastically distributed according to the above Gaussian distribution. 
+# We define this distribution as
+
+# $$
+# p(y_i, \boldsymbol{X}\vert\boldsymbol{\beta})=\frac{1}{\sqrt{2\pi\sigma^2}}\exp{\left[-\frac{(y_i-\boldsymbol{X}_{i,*}\boldsymbol{\beta})^2}{2\sigma^2}\right]},
+# $$
+
+# which reads as finding the likelihood of an event $y_i$ with the input variables $\boldsymbol{X}$ given the parameters (to be determined) $\boldsymbol{\beta}$.
+# 
+# Since these events are assumed to be independent and identicall distributed we can build the probability distribution function (PDF) for all possible event $\boldsymbol{y}$ as the product of the single events, that is we have
+
+# $$
+# p(\boldsymbol{y},\boldsymbol{X}\vert\boldsymbol{\beta})=\prod_{i=0}^{n-1}\frac{1}{\sqrt{2\pi\sigma^2}}\exp{\left[-\frac{(y_i-\boldsymbol{X}_{i,*}\boldsymbol{\beta})^2}{2\sigma^2}\right]}=\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta}).
+# $$
+
+# We will write this in a more compact form reserving $\boldsymbol{D}$ for the domain of events, including the ouputs (targets) and the inputs. That is
+# in case we have a simple one-dimensional input and output case
+
+# $$
+# \boldsymbol{D}=[(x_0,y_0), (x_1,y_1),\dots, (x_{n-1},y_{n-1})].
+# $$
+
+# In the more general case the various inputs should be replaced by the possible features represented by the input data set $\boldsymbol{X}$. 
+# We can now rewrite the above probability as
+
+# $$
+# p(\boldsymbol{D}\vert\boldsymbol{\beta})=\prod_{i=0}^{n-1}\frac{1}{\sqrt{2\pi\sigma^2}}\exp{\left[-\frac{(y_i-\boldsymbol{X}_{i,*}\boldsymbol{\beta})^2}{2\sigma^2}\right]}.
+# $$
+
+# It is a conditional probability (see below) and reads as the likelihood of a domain of events $\boldsymbol{D}$ given a set of parameters $\boldsymbol{\beta}$.
+
+# ## Maximum Likelihood Estimation (MLE)
+# 
+# In statistics, maximum likelihood estimation (MLE) is a method of
+# estimating the parameters of an assumed probability distribution,
+# given some observed data. This is achieved by maximizing a likelihood
+# function so that, under the assumed statistical model, the observed
+# data is the most probable. 
+# 
+# We will assume here that our events are given by the above Gaussian
+# distribution and we will determine the optimal parameters $\beta$ by
+# maximizing the above PDF. However, computing the derivatives of a
+# product function is cumbersome and can easily lead to overflow and/or
+# underflowproblems, with potentials for loss of numerical precision.
+# 
+# In practice, it is more convenient to maximize the logarithm of the
+# PDF because it is a monotonically increasing function of the argument.
+# Alternatively, and this will be our option, we will minimize the
+# negative of the logarithm since this is a monotonically decreasing
+# function.
+# 
+# Note also that maximization/minimization of the logarithm of the PDF
+# is equivalent to the maximization/minimization of the function itself.
+
+# ## A new Cost Function
+# 
+# We could now define a new cost function to minimize, namely the negative logarithm of the above PDF
+
+# $$
+# C(\boldsymbol{\beta}=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})},
+# $$
+
+# which becomes
+
+# $$
+# C(\boldsymbol{\beta}=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}.
+# $$
+
+# Taking the derivative of the *new* cost function with respect to the parameters $\beta$ we recognize our familiar OLS equation, namely
+
+# $$
+# \boldsymbol{X}^T\left(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right) =0,
+# $$
+
+# which leads to the well-known OLS equation for the optimal paramters $\beta$
+
+# $$
+# \hat{\boldsymbol{\beta}}^{\mathrm{OLS}}=\left(\boldsymbol{X}^T\boldsymbol{X}\right)^{-1}\boldsymbol{X}^T\boldsymbol{y}!
+# $$
+
+# Before we make a similar analysis for Ridge and Lasso regression, we need a short reminder on statistics.
+
+# ## More basic Statistics and Bayes' theorem
+# 
+# A central theorem in statistics is Bayes' theorem. This theorem plays a similar role as the good old Pythagoras' theorem in geometry.
+# Bayes' theorem is extremely simple to derive. But to do so we need some basic axioms from statistics.
+# 
+# Assume we have two domains of events $X=[x_0,x_1,\dots,x_{n-1}]$ and $Y=[y_0,y_1,\dots,y_{n-1}]$.
+# 
+# We define also the likelihood for $X$ and $Y$ as $p(X)$ and $p(Y)$ respectively.
+# The likelihood of a specific event $x_i$ (or $y_i$) is then written as $p(X=x_i)$ or just $p(x_i)=p_i$. 
+# 
+# **Union of events is given by.**
+
+# $$
+# p(X \cup Y)= p(X)+p(Y)-p(X \cap Y).
+# $$
+
+# **The product rule (aka joint probability) is given by.**
+
+# $$
+# p(X \cup Y)= p(X,Y)= p(X\vert Y)p(Y)=p(Y\vert X)p(X),
+# $$
+
+# where we read $p(X\vert Y)$ as the likelihood of obtaining $X$ given $Y$.
+# 
+# If we have independent events then $p(X,Y)=p(X)p(Y)$.
+
+# ## Marginal Probability
+# 
+# The marginal probability is defined in terms of only one of the set of variables $X,Y$. For a discrete probability we have
+
+# $$
+# p(X)=\sum_{i=0}^{n-1}p(X,Y=y_i)=\sum_{i=0}^{n-1}p(X\vert Y=y_i)p(Y=y_i)=\sum_{i=0}^{n-1}p(X\vert y_i)p(y_i).
+# $$
+
+# ## Conditional  Probability
+# 
+# The conditional  probability, if $p(Y) > 0$, is
+
+# $$
+# p(X\vert Y)= \frac{p(X,Y)}{p(Y)}=\frac{p(X,Y)}{\sum_{i=0}^{n-1}p(Y\vert X=x_i)p(x_i)}.
+# $$
+
+# ## Bayes' Theorem
+# 
+# If we combine the conditional probability with the marginal probability and the standard product rule, we have
+
+# $$
+# p(X\vert Y)= \frac{p(X,Y)}{p(Y)},
+# $$
+
+# which we can rewrite as
+
+# $$
+# p(X\vert Y)= \frac{p(X,Y)}{\sum_{i=0}^{n-1}p(Y\vert X=x_i)p(x_i)}=\frac{p(Y\vert X)p(X)}{\sum_{i=0}^{n-1}p(Y\vert X=x_i)p(x_i)},
+# $$
+
+# which is Bayes' theorem. It allows us to evaluate the uncertainty in in $X$ after we have observed $Y$. We can easily interchange $X$ with $Y$.
+
+# ## Interpretations of Bayes' Theorem
+# 
+# The quantity $p(Y\vert X)$ on the right-hand side of the theorem is
+# evaluated for the observed data $Y$ and can be viewed as a function of
+# the parameter space represented by $X$. This function is not
+# necesseraly normalized and is normally called the likelihood function.
+# 
+# The function $p(X)$ on the right hand side is called the prior while the function on the left hand side is the called the posterior probability. The denominator on the right hand side serves as a normalization factor for the posterior distribution.
+# 
+# Let us try to illustrate Bayes' theorem through an example.
+
+# ## Example of Usage of Bayes' theorem
+# 
+# Let us suppose that you are undergoing a series of mammography scans in
+# order to rule out possible breast cancer cases.  We define the
+# sensitivity for a positive event by the variable $X$. It takes binary
+# values with $X=1$ representing a positive event and $X=0$ being a
+# negative event. We reserve $Y$ as a classification parameter for
+# either a negative or a positive breast cancer confirmation. (Short note on wordings: positive here means having breast cancer, although none of us would consider this being a  positive thing).
+# 
+# We let $Y=1$ represent the the case of having breast cancer and $Y=0$ as not.
+# 
+# Let us assume that if you have breast cancer, the test will be positive with a probability of $0.8$, that is we have
+
+# $$
+# p(X=1\vert Y=1) =0.8.
+# $$
+
+# This obviously sounds  scary since many would conclude that if the test is positive, there is a likelihood of $80\%$ for having cancer.
+# It is however not correct, as the following Bayesian analysis shows.
+
+# ## Doing it correctly
+# 
+# If we look at various national surveys on breast cancer, the general likelihood of developing breast cancer is a very small number.
+# Let us assume that the prior probability in the population as a whole is
+
+# $$
+# p(Y=1) =0.004.
+# $$
+
+# We need also to account for the fact that the test may produce a false positive result (false alarm). Let us here assume that we have
+
+# $$
+# p(X=1\vert Y=0) =0.1.
+# $$
+
+# Using Bayes' theorem we can then find the posterior probability that the person has breast cancer in case of a positive test, that is we can compute
+
+# $$
+# p(Y=1\vert X=1)=\frac{p(X=1\vert Y=1)p(Y=1)}{p(X=1\vert Y=1)p(Y=1)+p(X=1\vert Y=0)p(Y=0)}=\frac{0.8\times 0.004}{0.8\times 0.004+0.1\times 0.996}=0.031.
+# $$
+
+# That is, in case of a positive test, there is only a $3\%$ chance of having breast cancer!
+
+# ## Bayes' Theorem and Ridge and Lasso Regression
+# 
+# Using Bayes' theorem we can gain a better intuition about Ridge and Lasso regression. 
+# 
+# For ordinary least squares we postulated that the maximum likelihood for the doamin of events $\boldsymbol{D}$ (one-dimensional case)
+
+# $$
+# \boldsymbol{D}=[(x_0,y_0), (x_1,y_1),\dots, (x_{n-1},y_{n-1})],
+# $$
+
+# is given by
+
+# $$
+# p(\boldsymbol{D}\vert\boldsymbol{\beta})=\prod_{i=0}^{n-1}\frac{1}{\sqrt{2\pi\sigma^2}}\exp{\left[-\frac{(y_i-\boldsymbol{X}_{i,*}\boldsymbol{\beta})^2}{2\sigma^2}\right]}.
+# $$
+
+# In Bayes' theorem this function plays the role of the so-called likelihood. We could now ask the question what is the posterior probability of a parameter set $\boldsymbol{\beta}$ given a domain of events $\boldsymbol{D}$?  That is, how can we define the posterior probability
+
+# $$
+# p(\boldsymbol{\beta}\vert\boldsymbol{D}).
+# $$
+
+# Bayes' theorem comes to our rescue here since (omitting the normalization constant)
+
+# $$
+# p(\boldsymbol{\beta}\vert\boldsymbol{D})\propto p(\boldsymbol{D}\vert\boldsymbol{\beta})p(\boldsymbol{\beta}).
+# $$
+
+# We have a model for $p(\boldsymbol{D}\vert\boldsymbol{\beta})$ but need one for the **prior** $p(\boldsymbol{\beta}$!
+
+# ## Ridge and Bayes
+# 
+# With the posterior probability defined by a likelihood which we have
+# already modeled and an unknown prior, we are now ready to make
+# additional models for the prior.
+# 
+# We can, based on our discussions of the variance of $\boldsymbol{\beta}$ and the mean value, assume that the prior for the values $\boldsymbol{\beta}$ is given by a Gaussian with mean value zero and variance $\tau^2$, that is
+
+# $$
+# p(\boldsymbol{\beta})=\prod_{j=0}^{p-1}\exp{\left(-\frac{\beta_j^2}{2\tau^2}\right)}.
+# $$
+
+# Our posterior probability becomes then (omitting the normalization factor which is just a constant)
+
+# $$
+# p(\boldsymbol{\beta\vert\boldsymbol{D})}=\prod_{i=0}^{n-1}\frac{1}{\sqrt{2\pi\sigma^2}}\exp{\left[-\frac{(y_i-\boldsymbol{X}_{i,*}\boldsymbol{\beta})^2}{2\sigma^2}\right]}\prod_{j=0}^{p-1}\exp{\left(-\frac{\beta_j^2}{2\tau^2}\right)}.
+# $$
+
+# We can now optimize this quantity with respect to $\boldsymbol{\beta}$. As we
+# did for OLS, this is most conveniently done by taking the negative
+# logarithm of the posterior probability. Doing so and leaving out the
+# constants terms that do not depend on $\beta$, we have
+
+# $$
+# C(\boldsymbol{\beta})=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}+\frac{1}{2\tau^2}\vert\vert\boldsymbol{\beta}\vert\vert_2^2,
+# $$
+
+# and replacing $1/2\tau^2$ with $\lambda$ we have
+
+# $$
+# C(\boldsymbol{\beta})=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}+\lambda\vert\vert\boldsymbol{\beta}\vert\vert_2^2,
+# $$
+
+# which is our Ridge cost function!  Nice, isn't it?
+
+# ## Lasso and Bayes
+# 
+# To derive the Lasso cost function, we simply replace the Gaussian prior with an exponential distribution ([Laplace in this case](https://en.wikipedia.org/wiki/Laplace_distribution)) with zero mean value,  that is
+
+# $$
+# p(\boldsymbol{\beta})=\prod_{j=0}^{p-1}\exp{\left(-\frac{\vert\beta_j\vert}{\tau}\right)}.
+# $$
+
+# Our posterior probability becomes then (omitting the normalization factor which is just a constant)
+
+# $$
+# p(\boldsymbol{\beta}\vert\boldsymbol{D})=\prod_{i=0}^{n-1}\frac{1}{\sqrt{2\pi\sigma^2}}\exp{\left[-\frac{(y_i-\boldsymbol{X}_{i,*}\boldsymbol{\beta})^2}{2\sigma^2}\right]}\prod_{j=0}^{p-1}\exp{\left(-\frac{\vert\beta_j\vert}{\tau}\right)}.
+# $$
+
+# Taking the negative
+# logarithm of the posterior probability and leaving out the
+# constants terms that do not depend on $\beta$, we have
+
+# $$
+# C(\boldsymbol{\beta}=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}+\frac{1}{\tau}\vert\vert\boldsymbol{\beta}\vert\vert_1,
+# $$
+
+# and replacing $1/\tau$ with $\lambda$ we have
+
+# $$
+# C(\boldsymbol{\beta}=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}+\lambda\vert\vert\boldsymbol{\beta}\vert\vert_1,
+# $$
+
+# which is our Lasso cost function!
+
+# ## Why resampling methods
+# 
+# Before we proceed, we need to rethink what we have been doing. In our
+# eager to fit the data, we have omitted several important elements in
+# our regression analysis. In what follows we will
+# 1. look at statistical properties, including a discussion of mean values, variance and the so-called bias-variance tradeoff
+# 
+# 2. introduce resampling techniques like cross-validation, bootstrapping and jackknife and more
+# 
+# and discuss how to select a given model (one of the difficult parts in machine learning).
+
+# ## Resampling methods
+# Resampling methods are an indispensable tool in modern
+# statistics. They involve repeatedly drawing samples from a training
+# set and refitting a model of interest on each sample in order to
+# obtain additional information about the fitted model. For example, in
+# order to estimate the variability of a linear regression fit, we can
+# repeatedly draw different samples from the training data, fit a linear
+# regression to each new sample, and then examine the extent to which
+# the resulting fits differ. Such an approach may allow us to obtain
+# information that would not be available from fitting the model only
+# once using the original training sample.
+# 
+# Two resampling methods are often used in Machine Learning analyses,
+# 1. The **bootstrap method**
+# 
+# 2. and **Cross-Validation**
+# 
+# In addition there are several other methods such as the Jackknife and the Blocking methods. We will discuss in particular
+# cross-validation and the bootstrap method.
+
+# ## Resampling approaches can be computationally expensive
+# 
+# Resampling approaches can be computationally expensive, because they
+# involve fitting the same statistical method multiple times using
+# different subsets of the training data. However, due to recent
+# advances in computing power, the computational requirements of
+# resampling methods generally are not prohibitive. In this chapter, we
+# discuss two of the most commonly used resampling methods,
+# cross-validation and the bootstrap. Both methods are important tools
+# in the practical application of many statistical learning
+# procedures. For example, cross-validation can be used to estimate the
+# test error associated with a given statistical learning method in
+# order to evaluate its performance, or to select the appropriate level
+# of flexibility. The process of evaluating a model’s performance is
+# known as model assessment, whereas the process of selecting the proper
+# level of flexibility for a model is known as model selection. The
+# bootstrap is widely used.
+
+# ## Why resampling methods ?
+# **Statistical analysis.**
+# 
+# * Our simulations can be treated as *computer experiments*. This is particularly the case for Monte Carlo methods which are widely used in statistical analyses.
+# 
+# * The results can be analysed with the same statistical tools as we would use when analysing experimental data.
+# 
+# * As in all experiments, we are looking for expectation values and an estimate of how accurate they are, i.e., possible sources for errors.
+
+# ## Statistical analysis
+# 
+# * As in other experiments, many numerical  experiments have two classes of errors:
+# 
+#   * Statistical errors
+# 
+#   * Systematical errors
+# 
+# * Statistical errors can be estimated using standard tools from statistics
+# 
+# * Systematical errors are method specific and must be treated differently from case to case.
+
+# ## Resampling methods
+# 
+# With all these analytical equations for both the OLS and Ridge
+# regression, we will now outline how to assess a given model. This will
+# lead to a discussion of the so-called bias-variance tradeoff (see
+# below) and so-called resampling methods.
+# 
+# One of the quantities we have discussed as a way to measure errors is
+# the mean-squared error (MSE), mainly used for fitting of continuous
+# functions. Another choice is the absolute error.
+# 
+# In the discussions below we will focus on the MSE and in particular since we will split the data into test and training data,
+# we discuss the
+# 1. prediction error or simply the **test error** $\mathrm{Err_{Test}}$, where we have a fixed training set and the test error is the MSE arising from the data reserved for testing. We discuss also the 
+# 
+# 2. training error $\mathrm{Err_{Train}}$, which is the average loss over the training data.
+# 
+# As our model becomes more and more complex, more of the training data tends to  used. The training may thence adapt to more complicated structures in the data. This may lead to a decrease in the bias (see below for code example) and a slight increase of the variance for the test error.
+# For a certain level of complexity the test error will reach minimum, before starting to increase again. The
+# training error reaches a saturation.
+
+# ## Resampling methods: Bootstrap
+# Bootstrapping is a [non-parametric approach](https://en.wikipedia.org/wiki/Nonparametric_statistics) to statistical inference
+# that substitutes computation for more traditional distributional
+# assumptions and asymptotic results. Bootstrapping offers a number of
+# advantages: 
+# 1. The bootstrap is quite general, although there are some cases in which it fails.  
+# 
+# 2. Because it does not require distributional assumptions (such as normally distributed errors), the bootstrap can provide more accurate inferences when the data are not well behaved or when the sample size is small.  
+# 
+# 3. It is possible to apply the bootstrap to statistics with sampling distributions that are difficult to derive, even asymptotically. 
+# 
+# 4. It is relatively simple to apply the bootstrap to complex data-collection plans (such as stratified and clustered samples).
+# 
+# The textbook by [Davison on the Bootstrap Methods and their Applications](https://www.cambridge.org/core/books/bootstrap-methods-and-their-application/ED2FD043579F27952363566DC09CBD6A) provides many more insights and proofs. In this course we will take a more practical approach and use the results and theorems provided in the literature. For those interested in reading more about the bootstrap methods, we recommend the above text and the one by [Efron and Tibshirani](https://www.routledge.com/An-Introduction-to-the-Bootstrap/Efron-Tibshirani/p/book/9780412042317).
+# 
+# Before we proceed however, we need to remind ourselves about a central theorem in statistics, namely the so-called **central limit theorem**.
+
+# ## The Central Limit Theorem
+# 
+# Suppose we have a PDF $p(x)$ from which we generate  a series $N$
+# of averages $\mathbb{E}[x_i]$. Each mean value $\mathbb{E}[x_i]$
+# is viewed as the average of a specific measurement, e.g., throwing 
+# dice 100 times and then taking the average value, or producing a certain
+# amount of random numbers. 
+# For notational ease, we set $\mathbb{E}[x_i]=x_i$ in the discussion
+# which follows. We do the same for $\mathbb{E}[z]=z$.
+# 
+# If we compute the mean $z$ of $m$ such mean values $x_i$
+
+# $$
+# z=\frac{x_1+x_2+\dots+x_m}{m},
+# $$
+
+# the question we pose is which is the PDF of the new variable $z$.
+
+# ## Finding the Limit
+# 
+# The probability of obtaining an average value $z$ is the product of the 
+# probabilities of obtaining arbitrary individual mean values $x_i$,
+# but with the constraint that the average is $z$. We can express this through
+# the following expression
+
+# $$
+# \tilde{p}(z)=\int dx_1p(x_1)\int dx_2p(x_2)\dots\int dx_mp(x_m)
+#     \delta(z-\frac{x_1+x_2+\dots+x_m}{m}),
+# $$
+
+# where the $\delta$-function enbodies the constraint that the mean is $z$.
+# All measurements that lead to each individual $x_i$ are expected to
+# be independent, which in turn means that we can express $\tilde{p}$ as the 
+# product of individual $p(x_i)$.  The independence assumption is important in the derivation of the central limit theorem.
+
+# ## Rewriting the $\delta$-function
+# 
+# If we use the integral expression for the $\delta$-function
+
+# $$
+# \delta(z-\frac{x_1+x_2+\dots+x_m}{m})=\frac{1}{2\pi}\int_{-\infty}^{\infty}
+#    dq\exp{\left(iq(z-\frac{x_1+x_2+\dots+x_m}{m})\right)},
+# $$
+
+# and inserting $e^{i\mu q-i\mu q}$ where $\mu$ is the mean value
+# we arrive at
+
+# $$
+# \tilde{p}(z)=\frac{1}{2\pi}\int_{-\infty}^{\infty}
+#    dq\exp{\left(iq(z-\mu)\right)}\left[\int_{-\infty}^{\infty}
+#    dxp(x)\exp{\left(iq(\mu-x)/m\right)}\right]^m,
+# $$
+
+# with the integral over $x$ resulting in
+
+# $$
+# \int_{-\infty}^{\infty}dxp(x)\exp{\left(iq(\mu-x)/m\right)}=
+#   \int_{-\infty}^{\infty}dxp(x)
+#    \left[1+\frac{iq(\mu-x)}{m}-\frac{q^2(\mu-x)^2}{2m^2}+\dots\right].
+# $$
+
+# ## Identifying Terms
+# 
+# The second term on the rhs disappears since this is just the mean and 
+# employing the definition of $\sigma^2$ we have
+
+# $$
+# \int_{-\infty}^{\infty}dxp(x)e^{\left(iq(\mu-x)/m\right)}=
+#   1-\frac{q^2\sigma^2}{2m^2}+\dots,
+# $$
+
+# resulting in
+
+# $$
+# \left[\int_{-\infty}^{\infty}dxp(x)\exp{\left(iq(\mu-x)/m\right)}\right]^m\approx
+#   \left[1-\frac{q^2\sigma^2}{2m^2}+\dots \right]^m,
+# $$
+
+# and in the limit $m\rightarrow \infty$ we obtain
+
+# $$
+# \tilde{p}(z)=\frac{1}{\sqrt{2\pi}(\sigma/\sqrt{m})}
+#     \exp{\left(-\frac{(z-\mu)^2}{2(\sigma/\sqrt{m})^2}\right)},
+# $$
+
+# which is the normal distribution with variance
+# $\sigma^2_m=\sigma^2/m$, where $\sigma$ is the variance of the PDF $p(x)$
+# and $\mu$ is also the mean of the PDF $p(x)$.
+
+# ## Wrapping it up
+# 
+# Thus, the central limit theorem states that the PDF $\tilde{p}(z)$ of
+# the average of $m$ random values corresponding to a PDF $p(x)$ 
+# is a normal distribution whose mean is the 
+# mean value of the PDF $p(x)$ and whose variance is the variance
+# of the PDF $p(x)$ divided by $m$, the number of values used to compute $z$.
+# 
+# The central limit theorem leads to the well-known expression for the
+# standard deviation, given by
+
+# $$
+# \sigma_m=
+# \frac{\sigma}{\sqrt{m}}.
+# $$
+
+# The latter is true only if the average value is known exactly. This is obtained in the limit
+# $m\rightarrow \infty$  only. Because the mean and the variance are measured quantities we obtain 
+# the familiar expression in statistics (the so-called Bessel correction)
+
+# $$
+# \sigma_m\approx 
+# \frac{\sigma}{\sqrt{m-1}}.
+# $$
+
+# In many cases however the above estimate for the standard deviation,
+# in particular if correlations are strong, may be too simplistic. Keep
+# in mind that we have assumed that the variables $x$ are independent
+# and identically distributed. This is obviously not always the
+# case. For example, the random numbers (or better pseudorandom numbers)
+# we generate in various calculations do always exhibit some
+# correlations.
+# 
+# The theorem is satisfied by a large class of PDFs. Note however that for a
+# finite $m$, it is not always possible to find a closed form /analytic expression for
+# $\tilde{p}(x)$.
+
+# ## Confidence Intervals
+# 
+# Confidence intervals are used in statistics and represent a type of estimate
+# computed from the observed data. This gives a range of values for an
+# unknown parameter such as the parameters $\boldsymbol{\beta}$ from linear regression.
+# 
+# With the OLS expressions for the parameters $\boldsymbol{\beta}$ we found 
+# $\mathbb{E}(\boldsymbol{\beta}) = \boldsymbol{\beta}$, which means that the estimator of the regression parameters is unbiased.
+# 
+# We found also that the variance of the estimate of the $j$-th regression coefficient is
+# $\boldsymbol{\sigma}^2 (\boldsymbol{\beta}_j ) = \boldsymbol{\sigma}^2 [(\mathbf{X}^{T} \mathbf{X})^{-1}]_{jj} $.
+# 
+# This quantity will be used to
+# construct a confidence interval for the estimates.
+
+# ## Standard Approach based on the Normal Distribution
+# 
+# We will assume that the parameters $\beta$ follow a normal
+# distribution.  We can then define the confidence interval.  Here we will be using as
+# shorthands $\mu_{\beta}$ for the above mean value and $\sigma_{\beta}$
+# for the standard deviation. We have then a confidence interval
+
+# $$
+# \left(\mu_{\beta}\pm \frac{z\sigma_{\beta}}{\sqrt{n}}\right),
+# $$
+
+# where $z$ defines the level of certainty (or confidence). For a normal
+# distribution typical parameters are $z=2.576$ which corresponds to a
+# confidence of $99\%$ while $z=1.96$ corresponds to a confidence of
+# $95\%$.  A confidence level of $95\%$ is commonly used and it is
+# normally referred to as a *two-sigmas* confidence level, that is we
+# approximate $z\approx 2$.
+# 
+# For more discussions of confidence intervals (and in particular linked with a discussion of the bootstrap method), see chapter 5 of the textbook by [Davison on the Bootstrap Methods and their Applications](https://www.cambridge.org/core/books/bootstrap-methods-and-their-application/ED2FD043579F27952363566DC09CBD6A)
+# 
+# In this text you will also find an in-depth discussion of the
+# Bootstrap method, why it works and various theorems related to it.
+
+# ## Resampling methods: Bootstrap background
+# 
+# Since $\widehat{\beta} = \widehat{\beta}(\boldsymbol{X})$ is a function of random variables,
+# $\widehat{\beta}$ itself must be a random variable. Thus it has
+# a pdf, call this function $p(\boldsymbol{t})$. The aim of the bootstrap is to
+# estimate $p(\boldsymbol{t})$ by the relative frequency of
+# $\widehat{\beta}$. You can think of this as using a histogram
+# in the place of $p(\boldsymbol{t})$. If the relative frequency closely
+# resembles $p(\vec{t})$, then using numerics, it is straight forward to
+# estimate all the interesting parameters of $p(\boldsymbol{t})$ using point
+# estimators.
+
+# ## Resampling methods: More Bootstrap background
+# 
+# In the case that $\widehat{\beta}$ has
+# more than one component, and the components are independent, we use the
+# same estimator on each component separately.  If the probability
+# density function of $X_i$, $p(x)$, had been known, then it would have
+# been straightforward to do this by: 
+# 1. Drawing lots of numbers from $p(x)$, suppose we call one such set of numbers $(X_1^*, X_2^*, \cdots, X_n^*)$. 
+# 
+# 2. Then using these numbers, we could compute a replica of $\widehat{\beta}$ called $\widehat{\beta}^*$. 
+# 
+# By repeated use of the above two points, many
+# estimates of $\widehat{\beta}$ can  be obtained. The
+# idea is to use the relative frequency of $\widehat{\beta}^*$
+# (think of a histogram) as an estimate of $p(\boldsymbol{t})$.
+
+# ## Resampling methods: Bootstrap approach
+# 
+# But
+# unless there is enough information available about the process that
+# generated $X_1,X_2,\cdots,X_n$, $p(x)$ is in general
+# unknown. Therefore, [Efron in 1979](https://projecteuclid.org/euclid.aos/1176344552)  asked the
+# question: What if we replace $p(x)$ by the relative frequency
+# of the observation $X_i$?
+# 
+# If we draw observations in accordance with
+# the relative frequency of the observations, will we obtain the same
+# result in some asymptotic sense? The answer is yes.
+
+# ## Resampling methods: Bootstrap steps
+# 
+# The independent bootstrap works like this: 
+# 
+# 1. Draw with replacement $n$ numbers for the observed variables $\boldsymbol{x} = (x_1,x_2,\cdots,x_n)$. 
+# 
+# 2. Define a vector $\boldsymbol{x}^*$ containing the values which were drawn from $\boldsymbol{x}$. 
+# 
+# 3. Using the vector $\boldsymbol{x}^*$ compute $\widehat{\beta}^*$ by evaluating $\widehat \beta$ under the observations $\boldsymbol{x}^*$. 
+# 
+# 4. Repeat this process $k$ times. 
+# 
+# When you are done, you can draw a histogram of the relative frequency
+# of $\widehat \beta^*$. This is your estimate of the probability
+# distribution $p(t)$. Using this probability distribution you can
+# estimate any statistics thereof. In principle you never draw the
+# histogram of the relative frequency of $\widehat{\beta}^*$. Instead
+# you use the estimators corresponding to the statistic of interest. For
+# example, if you are interested in estimating the variance of $\widehat
+# \beta$, apply the etsimator $\widehat \sigma^2$ to the values
+# $\widehat \beta^*$.
+
+# ## Code example for the Bootstrap method
+# 
+# The following code starts with a Gaussian distribution with mean value
+# $\mu =100$ and variance $\sigma=15$. We use this to generate the data
+# used in the bootstrap analysis. The bootstrap analysis returns a data
+# set after a given number of bootstrap operations (as many as we have
+# data points). This data set consists of estimated mean values for each
+# bootstrap operation. The histogram generated by the bootstrap method
+# shows that the distribution for these mean values is also a Gaussian,
+# centered around the mean value $\mu=100$ but with standard deviation
+# $\sigma/\sqrt{n}$, where $n$ is the number of bootstrap samples (in
+# this case the same as the number of original data points). The value
+# of the standard deviation is what we expect from the central limit
+# theorem.
+
+# In[1]:
+
+
+get_ipython().run_line_magic('matplotlib', 'inline')
+
+import numpy as np
+from time import time
+from scipy.stats import norm
+import matplotlib.pyplot as plt
+
+# Returns mean of bootstrap samples 
+# Bootstrap algorithm
+def bootstrap(data, datapoints):
+    t = np.zeros(datapoints)
+    n = len(data)
+    # non-parametric bootstrap         
+    for i in range(datapoints):
+        t[i] = np.mean(data[np.random.randint(0,n,n)])
+    # analysis    
+    print("Bootstrap Statistics :")
+    print("original           bias      std. error")
+    print("%8g %8g %14g %15g" % (np.mean(data), np.std(data),np.mean(t),np.std(t)))
+    return t
+
+# We set the mean value to 100 and the standard deviation to 15
+mu, sigma = 100, 15
+datapoints = 10000
+# We generate random numbers according to the normal distribution
+x = mu + sigma*np.random.randn(datapoints)
+# bootstrap returns the data sample                                    
+t = bootstrap(x, datapoints)
+
+
+# We see that our new variance and from that the standard deviation, agrees with the central limit theorem.
+
+# ## Plotting the Histogram
+
+# In[2]:
+
+
+# the histogram of the bootstrapped data (normalized data if density = True)
+n, binsboot, patches = plt.hist(t, 50, density=True, facecolor='red', alpha=0.75)
+# add a 'best fit' line  
+y = norm.pdf(binsboot, np.mean(t), np.std(t))
+lt = plt.plot(binsboot, y, 'b', linewidth=1)
+plt.xlabel('x')
+plt.ylabel('Probability')
+plt.grid(True)
+plt.show()
+
+
+# ## The bias-variance tradeoff
+# 
+# We will discuss the bias-variance tradeoff in the context of
+# continuous predictions such as regression. However, many of the
+# intuitions and ideas discussed here also carry over to classification
+# tasks. Consider a dataset $\mathcal{D}$ consisting of the data
+# $\mathbf{X}_\mathcal{D}=\{(y_j, \boldsymbol{x}_j), j=0\ldots n-1\}$. 
+# 
+# Let us assume that the true data is generated from a noisy model
+
+# $$
+# \boldsymbol{y}=f(\boldsymbol{x}) + \boldsymbol{\epsilon}
+# $$
+
+# where $\epsilon$ is normally distributed with mean zero and standard deviation $\sigma^2$.
+# 
+# In our derivation of the ordinary least squares method we defined then
+# an approximation to the function $f$ in terms of the parameters
+# $\boldsymbol{\beta}$ and the design matrix $\boldsymbol{X}$ which embody our model,
+# that is $\boldsymbol{\tilde{y}}=\boldsymbol{X}\boldsymbol{\beta}$. 
+# 
+# Thereafter we found the parameters $\boldsymbol{\beta}$ by optimizing the means squared error via the so-called cost function
+
+# $$
+# C(\boldsymbol{X},\boldsymbol{\beta}) =\frac{1}{n}\sum_{i=0}^{n-1}(y_i-\tilde{y}_i)^2=\mathbb{E}\left[(\boldsymbol{y}-\boldsymbol{\tilde{y}})^2\right].
+# $$
+
+# We can rewrite this as
+
+# $$
+# \mathbb{E}\left[(\boldsymbol{y}-\boldsymbol{\tilde{y}})^2\right]=\frac{1}{n}\sum_i(f_i-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right])^2+\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right])^2+\sigma^2.
+# $$
+
+# The three terms represent the square of the bias of the learning
+# method, which can be thought of as the error caused by the simplifying
+# assumptions built into the method. The second term represents the
+# variance of the chosen model and finally the last terms is variance of
+# the error $\boldsymbol{\epsilon}$.
+# 
+# To derive this equation, we need to recall that the variance of $\boldsymbol{y}$ and $\boldsymbol{\epsilon}$ are both equal to $\sigma^2$. The mean value of $\boldsymbol{\epsilon}$ is by definition equal to zero. Furthermore, the function $f$ is not a stochastics variable, idem for $\boldsymbol{\tilde{y}}$.
+# We use a more compact notation in terms of the expectation value
+
+# $$
+# \mathbb{E}\left[(\boldsymbol{y}-\boldsymbol{\tilde{y}})^2\right]=\mathbb{E}\left[(\boldsymbol{f}+\boldsymbol{\epsilon}-\boldsymbol{\tilde{y}})^2\right],
+# $$
+
+# and adding and subtracting $\mathbb{E}\left[\boldsymbol{\tilde{y}}\right]$ we get
+
+# $$
+# \mathbb{E}\left[(\boldsymbol{y}-\boldsymbol{\tilde{y}})^2\right]=\mathbb{E}\left[(\boldsymbol{f}+\boldsymbol{\epsilon}-\boldsymbol{\tilde{y}}+\mathbb{E}\left[\boldsymbol{\tilde{y}}\right]-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right])^2\right],
+# $$
+
+# which, using the abovementioned expectation values can be rewritten as
+
+# $$
+# \mathbb{E}\left[(\boldsymbol{y}-\boldsymbol{\tilde{y}})^2\right]=\mathbb{E}\left[(\boldsymbol{y}-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right])^2\right]+\mathrm{Var}\left[\boldsymbol{\tilde{y}}\right]+\sigma^2,
+# $$
+
+# that is the rewriting in terms of the so-called bias, the variance of the model $\boldsymbol{\tilde{y}}$ and the variance of $\boldsymbol{\epsilon}$.
+
+# ## A way to Read the Bias-Variance Tradeoff
+# 
+# 
+# 
+# 
+# 
    Figure 1: 
    
+# 
+
+# ## Example code for Bias-Variance tradeoff
+
+# In[3]:
+
+
+import matplotlib.pyplot as plt
+import numpy as np
+from sklearn.linear_model import LinearRegression, Ridge, Lasso
+from sklearn.preprocessing import PolynomialFeatures
+from sklearn.model_selection import train_test_split
+from sklearn.pipeline import make_pipeline
+from sklearn.utils import resample
+
+np.random.seed(2018)
+
+n = 500
+n_boostraps = 100
+degree = 18  # A quite high value, just to show.
+noise = 0.1
+
+# Make data set.
+x = np.linspace(-1, 3, n).reshape(-1, 1)
+y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2) + np.random.normal(0, 0.1, x.shape)
+
+# Hold out some test data that is never used in training.
+x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2)
+
+# Combine x transformation and model into one operation.
+# Not neccesary, but convenient.
+model = make_pipeline(PolynomialFeatures(degree=degree), LinearRegression(fit_intercept=False))
+
+# The following (m x n_bootstraps) matrix holds the column vectors y_pred
+# for each bootstrap iteration.
+y_pred = np.empty((y_test.shape[0], n_boostraps))
+for i in range(n_boostraps):
+    x_, y_ = resample(x_train, y_train)
+
+    # Evaluate the new model on the same test data each time.
+    y_pred[:, i] = model.fit(x_, y_).predict(x_test).ravel()
+
+# Note: Expectations and variances taken w.r.t. different training
+# data sets, hence the axis=1. Subsequent means are taken across the test data
+# set in order to obtain a total value, but before this we have error/bias/variance
+# calculated per data point in the test set.
+# Note 2: The use of keepdims=True is important in the calculation of bias as this 
+# maintains the column vector form. Dropping this yields very unexpected results.
+error = np.mean( np.mean((y_test - y_pred)**2, axis=1, keepdims=True) )
+bias = np.mean( (y_test - np.mean(y_pred, axis=1, keepdims=True))**2 )
+variance = np.mean( np.var(y_pred, axis=1, keepdims=True) )
+print('Error:', error)
+print('Bias^2:', bias)
+print('Var:', variance)
+print('{} >= {} + {} = {}'.format(error, bias, variance, bias+variance))
+
+plt.plot(x[::5, :], y[::5, :], label='f(x)')
+plt.scatter(x_test, y_test, label='Data points')
+plt.scatter(x_test, np.mean(y_pred, axis=1), label='Pred')
+plt.legend()
+plt.show()
+
+
+# ## Understanding what happens
+
+# In[4]:
+
+
+import matplotlib.pyplot as plt
+import numpy as np
+from sklearn.linear_model import LinearRegression, Ridge, Lasso
+from sklearn.preprocessing import PolynomialFeatures
+from sklearn.model_selection import train_test_split
+from sklearn.pipeline import make_pipeline
+from sklearn.utils import resample
+
+np.random.seed(2018)
+
+n = 40
+n_boostraps = 100
+maxdegree = 14
+
+
+# Make data set.
+x = np.linspace(-3, 3, n).reshape(-1, 1)
+y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)+ np.random.normal(0, 0.1, x.shape)
+error = np.zeros(maxdegree)
+bias = np.zeros(maxdegree)
+variance = np.zeros(maxdegree)
+polydegree = np.zeros(maxdegree)
+x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2)
+
+for degree in range(maxdegree):
+    model = make_pipeline(PolynomialFeatures(degree=degree), LinearRegression(fit_intercept=False))
+    y_pred = np.empty((y_test.shape[0], n_boostraps))
+    for i in range(n_boostraps):
+        x_, y_ = resample(x_train, y_train)
+        y_pred[:, i] = model.fit(x_, y_).predict(x_test).ravel()
+
+    polydegree[degree] = degree
+    error[degree] = np.mean( np.mean((y_test - y_pred)**2, axis=1, keepdims=True) )
+    bias[degree] = np.mean( (y_test - np.mean(y_pred, axis=1, keepdims=True))**2 )
+    variance[degree] = np.mean( np.var(y_pred, axis=1, keepdims=True) )
+    print('Polynomial degree:', degree)
+    print('Error:', error[degree])
+    print('Bias^2:', bias[degree])
+    print('Var:', variance[degree])
+    print('{} >= {} + {} = {}'.format(error[degree], bias[degree], variance[degree], bias[degree]+variance[degree]))
+
+plt.plot(polydegree, error, label='Error')
+plt.plot(polydegree, bias, label='bias')
+plt.plot(polydegree, variance, label='Variance')
+plt.legend()
+plt.show()
+
+
+# ## Summing up
+# 
+# The bias-variance tradeoff summarizes the fundamental tension in
+# machine learning, particularly supervised learning, between the
+# complexity of a model and the amount of training data needed to train
+# it.  Since data is often limited, in practice it is often useful to
+# use a less-complex model with higher bias, that is  a model whose asymptotic
+# performance is worse than another model because it is easier to
+# train and less sensitive to sampling noise arising from having a
+# finite-sized training dataset (smaller variance). 
+# 
+# The above equations tell us that in
+# order to minimize the expected test error, we need to select a
+# statistical learning method that simultaneously achieves low variance
+# and low bias. Note that variance is inherently a nonnegative quantity,
+# and squared bias is also nonnegative. Hence, we see that the expected
+# test MSE can never lie below $Var(\epsilon)$, the irreducible error.
+# 
+# What do we mean by the variance and bias of a statistical learning
+# method? The variance refers to the amount by which our model would change if we
+# estimated it using a different training data set. Since the training
+# data are used to fit the statistical learning method, different
+# training data sets  will result in a different estimate. But ideally the
+# estimate for our model should not vary too much between training
+# sets. However, if a method has high variance  then small changes in
+# the training data can result in large changes in the model. In general, more
+# flexible statistical methods have higher variance.
+# 
+# You may also find this recent [article](https://www.pnas.org/content/116/32/15849) of interest.
+
+# ## Another Example from Scikit-Learn's Repository
+
+# In[5]:
+
+
+"""
+============================
+Underfitting vs. Overfitting
+============================
+
+This example demonstrates the problems of underfitting and overfitting and
+how we can use linear regression with polynomial features to approximate
+nonlinear functions. The plot shows the function that we want to approximate,
+which is a part of the cosine function. In addition, the samples from the
+real function and the approximations of different models are displayed. The
+models have polynomial features of different degrees. We can see that a
+linear function (polynomial with degree 1) is not sufficient to fit the
+training samples. This is called **underfitting**. A polynomial of degree 4
+approximates the true function almost perfectly. However, for higher degrees
+the model will **overfit** the training data, i.e. it learns the noise of the
+training data.
+We evaluate quantitatively **overfitting** / **underfitting** by using
+cross-validation. We calculate the mean squared error (MSE) on the validation
+set, the higher, the less likely the model generalizes correctly from the
+training data.
+"""
+
+print(__doc__)
+
+import numpy as np
+import matplotlib.pyplot as plt
+from sklearn.pipeline import Pipeline
+from sklearn.preprocessing import PolynomialFeatures
+from sklearn.linear_model import LinearRegression
+from sklearn.model_selection import cross_val_score
+
+
+def true_fun(X):
+    return np.cos(1.5 * np.pi * X)
+
+np.random.seed(0)
+
+n_samples = 30
+degrees = [1, 4, 15]
+
+X = np.sort(np.random.rand(n_samples))
+y = true_fun(X) + np.random.randn(n_samples) * 0.1
+
+plt.figure(figsize=(14, 5))
+for i in range(len(degrees)):
+    ax = plt.subplot(1, len(degrees), i + 1)
+    plt.setp(ax, xticks=(), yticks=())
+
+    polynomial_features = PolynomialFeatures(degree=degrees[i],
+                                             include_bias=False)
+    linear_regression = LinearRegression()
+    pipeline = Pipeline([("polynomial_features", polynomial_features),
+                         ("linear_regression", linear_regression)])
+    pipeline.fit(X[:, np.newaxis], y)
+
+    # Evaluate the models using crossvalidation
+    scores = cross_val_score(pipeline, X[:, np.newaxis], y,
+                             scoring="neg_mean_squared_error", cv=10)
+
+    X_test = np.linspace(0, 1, 100)
+    plt.plot(X_test, pipeline.predict(X_test[:, np.newaxis]), label="Model")
+    plt.plot(X_test, true_fun(X_test), label="True function")
+    plt.scatter(X, y, edgecolor='b', s=20, label="Samples")
+    plt.xlabel("x")
+    plt.ylabel("y")
+    plt.xlim((0, 1))
+    plt.ylim((-2, 2))
+    plt.legend(loc="best")
+    plt.title("Degree {}\nMSE = {:.2e}(+/- {:.2e})".format(
+        degrees[i], -scores.mean(), scores.std()))
+plt.show()
+
+
+# ## Various steps in cross-validation
+# 
+# When the repetitive splitting of the data set is done randomly,
+# samples may accidently end up in a fast majority of the splits in
+# either training or test set. Such samples may have an unbalanced
+# influence on either model building or prediction evaluation. To avoid
+# this $k$-fold cross-validation structures the data splitting. The
+# samples are divided into $k$ more or less equally sized exhaustive and
+# mutually exclusive subsets. In turn (at each split) one of these
+# subsets plays the role of the test set while the union of the
+# remaining subsets constitutes the training set. Such a splitting
+# warrants a balanced representation of each sample in both training and
+# test set over the splits. Still the division into the $k$ subsets
+# involves a degree of randomness. This may be fully excluded when
+# choosing $k=n$. This particular case is referred to as leave-one-out
+# cross-validation (LOOCV).
+
+# ## Cross-validation in brief
+# 
+# For the various values of $k$
+# 
+# 1. shuffle the dataset randomly.
+# 
+# 2. Split the dataset into $k$ groups.
+# 
+# 3. For each unique group:
+# 
+# a. Decide which group to use as set for test data
+# 
+# b. Take the remaining groups as a training data set
+# 
+# c. Fit a model on the training set and evaluate it on the test set
+# 
+# d. Retain the evaluation score and discard the model
+# 
+# 5. Summarize the model using the sample of model evaluation scores
+
+# ## Code Example for Cross-validation and $k$-fold Cross-validation
+# 
+# The code here uses Ridge regression with cross-validation (CV)  resampling and $k$-fold CV in order to fit a specific polynomial.
+
+# In[6]:
+
+
+import numpy as np
+import matplotlib.pyplot as plt
+from sklearn.model_selection import KFold
+from sklearn.linear_model import Ridge
+from sklearn.model_selection import cross_val_score
+from sklearn.preprocessing import PolynomialFeatures
+
+# A seed just to ensure that the random numbers are the same for every run.
+# Useful for eventual debugging.
+np.random.seed(3155)
+
+# Generate the data.
+nsamples = 100
+x = np.random.randn(nsamples)
+y = 3*x**2 + np.random.randn(nsamples)
+
+## Cross-validation on Ridge regression using KFold only
+
+# Decide degree on polynomial to fit
+poly = PolynomialFeatures(degree = 6)
+
+# Decide which values of lambda to use
+nlambdas = 500
+lambdas = np.logspace(-3, 5, nlambdas)
+
+# Initialize a KFold instance
+k = 5
+kfold = KFold(n_splits = k)
+
+# Perform the cross-validation to estimate MSE
+scores_KFold = np.zeros((nlambdas, k))
+
+i = 0
+for lmb in lambdas:
+    ridge = Ridge(alpha = lmb)
+    j = 0
+    for train_inds, test_inds in kfold.split(x):
+        xtrain = x[train_inds]
+        ytrain = y[train_inds]
+
+        xtest = x[test_inds]
+        ytest = y[test_inds]
+
+        Xtrain = poly.fit_transform(xtrain[:, np.newaxis])
+        ridge.fit(Xtrain, ytrain[:, np.newaxis])
+
+        Xtest = poly.fit_transform(xtest[:, np.newaxis])
+        ypred = ridge.predict(Xtest)
+
+        scores_KFold[i,j] = np.sum((ypred - ytest[:, np.newaxis])**2)/np.size(ypred)
+
+        j += 1
+    i += 1
+
+
+estimated_mse_KFold = np.mean(scores_KFold, axis = 1)
+
+## Cross-validation using cross_val_score from sklearn along with KFold
+
+# kfold is an instance initialized above as:
+# kfold = KFold(n_splits = k)
+
+estimated_mse_sklearn = np.zeros(nlambdas)
+i = 0
+for lmb in lambdas:
+    ridge = Ridge(alpha = lmb)
+
+    X = poly.fit_transform(x[:, np.newaxis])
+    estimated_mse_folds = cross_val_score(ridge, X, y[:, np.newaxis], scoring='neg_mean_squared_error', cv=kfold)
+
+    # cross_val_score return an array containing the estimated negative mse for every fold.
+    # we have to the the mean of every array in order to get an estimate of the mse of the model
+    estimated_mse_sklearn[i] = np.mean(-estimated_mse_folds)
+
+    i += 1
+
+## Plot and compare the slightly different ways to perform cross-validation
+
+plt.figure()
+
+plt.plot(np.log10(lambdas), estimated_mse_sklearn, label = 'cross_val_score')
+plt.plot(np.log10(lambdas), estimated_mse_KFold, 'r--', label = 'KFold')
+
+plt.xlabel('log10(lambda)')
+plt.ylabel('mse')
+
+plt.legend()
+
+plt.show()
+
+
+# ## More examples on bootstrap and cross-validation and errors
+
+# In[7]:
+
+
+# Common imports
+import os
+import numpy as np
+import pandas as pd
+import matplotlib.pyplot as plt
+from sklearn.linear_model import LinearRegression, Ridge, Lasso
+from sklearn.model_selection import train_test_split
+from sklearn.utils import resample
+from sklearn.metrics import mean_squared_error
+# Where to save the figures and data files
+PROJECT_ROOT_DIR = "Results"
+FIGURE_ID = "Results/FigureFiles"
+DATA_ID = "DataFiles/"
+
+if not os.path.exists(PROJECT_ROOT_DIR):
+    os.mkdir(PROJECT_ROOT_DIR)
+
+if not os.path.exists(FIGURE_ID):
+    os.makedirs(FIGURE_ID)
+
+if not os.path.exists(DATA_ID):
+    os.makedirs(DATA_ID)
+
+def image_path(fig_id):
+    return os.path.join(FIGURE_ID, fig_id)
+
+def data_path(dat_id):
+    return os.path.join(DATA_ID, dat_id)
+
+def save_fig(fig_id):
+    plt.savefig(image_path(fig_id) + ".png", format='png')
+
+infile = open(data_path("EoS.csv"),'r')
+
+# Read the EoS data as  csv file and organize the data into two arrays with density and energies
+EoS = pd.read_csv(infile, names=('Density', 'Energy'))
+EoS['Energy'] = pd.to_numeric(EoS['Energy'], errors='coerce')
+EoS = EoS.dropna()
+Energies = EoS['Energy']
+Density = EoS['Density']
+#  The design matrix now as function of various polytrops
+
+Maxpolydegree = 30
+X = np.zeros((len(Density),Maxpolydegree))
+X[:,0] = 1.0
+testerror = np.zeros(Maxpolydegree)
+trainingerror = np.zeros(Maxpolydegree)
+polynomial = np.zeros(Maxpolydegree)
+
+trials = 100
+for polydegree in range(1, Maxpolydegree):
+    polynomial[polydegree] = polydegree
+    for degree in range(polydegree):
+        X[:,degree] = Density**(degree/3.0)
+
+# loop over trials in order to estimate the expectation value of the MSE
+    testerror[polydegree] = 0.0
+    trainingerror[polydegree] = 0.0
+    for samples in range(trials):
+        x_train, x_test, y_train, y_test = train_test_split(X, Energies, test_size=0.2)
+        model = LinearRegression(fit_intercept=False).fit(x_train, y_train)
+        ypred = model.predict(x_train)
+        ytilde = model.predict(x_test)
+        testerror[polydegree] += mean_squared_error(y_test, ytilde)
+        trainingerror[polydegree] += mean_squared_error(y_train, ypred) 
+
+    testerror[polydegree] /= trials
+    trainingerror[polydegree] /= trials
+    print("Degree of polynomial: %3d"% polynomial[polydegree])
+    print("Mean squared error on training data: %.8f" % trainingerror[polydegree])
+    print("Mean squared error on test data: %.8f" % testerror[polydegree])
+
+plt.plot(polynomial, np.log10(trainingerror), label='Training Error')
+plt.plot(polynomial, np.log10(testerror), label='Test Error')
+plt.xlabel('Polynomial degree')
+plt.ylabel('log10[MSE]')
+plt.legend()
+plt.show()
+
+
+# Note that we kept the intercept column in the fitting here. This means that we need to set the **intercept** in the call to the **Scikit-Learn** function as **False**. Alternatively, we could have set up the design matrix $X$ without the first column of ones.
+
+# ## The same example but now with cross-validation
+# 
+# In this example we keep the intercept column again but add cross-validation in order to estimate the best possible value of the means squared error.
+
+# In[8]:
+
+
+# Common imports
+import os
+import numpy as np
+import pandas as pd
+import matplotlib.pyplot as plt
+from sklearn.linear_model import LinearRegression, Ridge, Lasso
+from sklearn.metrics import mean_squared_error
+from sklearn.model_selection import KFold
+from sklearn.model_selection import cross_val_score
+
+
+# Where to save the figures and data files
+PROJECT_ROOT_DIR = "Results"
+FIGURE_ID = "Results/FigureFiles"
+DATA_ID = "DataFiles/"
+
+if not os.path.exists(PROJECT_ROOT_DIR):
+    os.mkdir(PROJECT_ROOT_DIR)
+
+if not os.path.exists(FIGURE_ID):
+    os.makedirs(FIGURE_ID)
+
+if not os.path.exists(DATA_ID):
+    os.makedirs(DATA_ID)
+
+def image_path(fig_id):
+    return os.path.join(FIGURE_ID, fig_id)
+
+def data_path(dat_id):
+    return os.path.join(DATA_ID, dat_id)
+
+def save_fig(fig_id):
+    plt.savefig(image_path(fig_id) + ".png", format='png')
+
+infile = open(data_path("EoS.csv"),'r')
+
+# Read the EoS data as  csv file and organize the data into two arrays with density and energies
+EoS = pd.read_csv(infile, names=('Density', 'Energy'))
+EoS['Energy'] = pd.to_numeric(EoS['Energy'], errors='coerce')
+EoS = EoS.dropna()
+Energies = EoS['Energy']
+Density = EoS['Density']
+#  The design matrix now as function of various polytrops
+
+Maxpolydegree = 30
+X = np.zeros((len(Density),Maxpolydegree))
+X[:,0] = 1.0
+estimated_mse_sklearn = np.zeros(Maxpolydegree)
+polynomial = np.zeros(Maxpolydegree)
+k =5
+kfold = KFold(n_splits = k)
+
+for polydegree in range(1, Maxpolydegree):
+    polynomial[polydegree] = polydegree
+    for degree in range(polydegree):
+        X[:,degree] = Density**(degree/3.0)
+        OLS = LinearRegression(fit_intercept=False)
+# loop over trials in order to estimate the expectation value of the MSE
+    estimated_mse_folds = cross_val_score(OLS, X, Energies, scoring='neg_mean_squared_error', cv=kfold)
+#[:, np.newaxis]
+    estimated_mse_sklearn[polydegree] = np.mean(-estimated_mse_folds)
+
+plt.plot(polynomial, np.log10(estimated_mse_sklearn), label='Test Error')
+plt.xlabel('Polynomial degree')
+plt.ylabel('log10[MSE]')
+plt.legend()
+plt.show()
+
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