{
 "cells": [
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   "source": [
    "<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)\n",
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  },
  {
   "cell_type": "markdown",
   "id": "79a63fb4",
   "metadata": {
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   },
   "source": [
    "# Resampling Methods"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3d916b4",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Introduction\n",
    "\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. \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.\n",
    "\n",
    "* Our simulations can be treated as *computer experiments*. This is particularly the case for Monte Carlo methods\n",
    "\n",
    "* The results can be analysed with the same statistical tools as we would use 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": "46cb3279",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Reminder on Statistics\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. \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": "0fe38e07",
   "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": "d9d6955b",
   "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 $p$.\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": "f41f7049",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\boldsymbol{y} = f(\\boldsymbol{x})+\\boldsymbol{\\varepsilon}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ee172f4",
   "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": "1aecc768",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\boldsymbol{\\tilde{y}} = \\boldsymbol{X}\\boldsymbol{\\beta}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12e9bdea",
   "metadata": {
    "editable": true
   },
   "source": [
    "We can calculate the expectation value of $\\boldsymbol{y}$ for a given element $i$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f9db9db",
   "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": "b10abe89",
   "metadata": {
    "editable": true
   },
   "source": [
    "while\n",
    "its variance is"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bec51521",
   "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": "4859640c",
   "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). \n",
    "\n",
    "With the OLS expressions for the parameters $\\boldsymbol{\\beta}$ we can evaluate the expectation value"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69978823",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\mathbb{E}(\\boldsymbol{\\beta}) = \\mathbb{E}[ (\\mathbf{X}^{\\top} \\mathbf{X})^{-1}\\mathbf{X}^{T} \\mathbf{Y}]=(\\mathbf{X}^{T} \\mathbf{X})^{-1}\\mathbf{X}^{T} \\mathbb{E}[ \\mathbf{Y}]=(\\mathbf{X}^{T} \\mathbf{X})^{-1} \\mathbf{X}^{T}\\mathbf{X}\\boldsymbol{\\beta}=\\boldsymbol{\\beta}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5caee9d9",
   "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 $\\boldsymbol{\\beta}$ is"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6791e5b4",
   "metadata": {
    "editable": true
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   "source": [
    "$$\n",
    "\\begin{eqnarray*}\n",
    "\\mbox{Var}(\\boldsymbol{\\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": "4f747992",
   "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",
    "$\\boldsymbol{\\sigma}^2 (\\boldsymbol{\\beta}_j ) = \\boldsymbol{\\sigma}^2 \\sqrt{\n",
    "[(\\mathbf{X}^{T} \\mathbf{X})^{-1}]_{jj} }$. 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": "d4679496",
   "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": "bd3534e1",
   "metadata": {
    "editable": true
   },
   "source": [
    "We see clearly that \n",
    "$\\mathbb{E} \\big[ \\boldsymbol{\\beta}^{\\mathrm{Ridge}} \\big] \\not= \\boldsymbol{\\beta}^{\\mathrm{OLS}}$ for any $\\lambda > 0$. We say then that the ridge estimator is biased.\n",
    "\n",
    "We can also compute the variance as"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "125b139e",
   "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": "98b59ea0",
   "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": "dcfd7a6c",
   "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": "30f43be3",
   "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."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3c1bf3c",
   "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 us 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  be 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.\n",
    "\n",
    "Two famous\n",
    "resampling methods are the **independent bootstrap** and **the jackknife**. \n",
    "\n",
    "The jackknife is a special case of the independent bootstrap. Still, the jackknife was made\n",
    "popular prior to the independent bootstrap. And as the popularity of\n",
    "the independent bootstrap soared, new variants, such as **the dependent bootstrap**.\n",
    "\n",
    "The Jackknife and independent bootstrap work for\n",
    "independent, identically distributed random variables.\n",
    "If these conditions are not\n",
    "satisfied, the methods will fail.  Yet, it should be said that if the data are\n",
    "independent, identically distributed, and we only want to estimate the\n",
    "variance of $\\overline{X}$ (which often is the case), then there is no\n",
    "need for bootstrapping. \n",
    "\n",
    "The Jackknife works by making many replicas of the estimator $\\widehat{\\beta}$. \n",
    "The jackknife is a resampling method where we systematically leave out one observation from the vector of observed values $\\boldsymbol{x} = (x_1,x_2,\\cdots,X_n)$. \n",
    "Let $\\boldsymbol{x}_i$ denote the vector"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3925f435",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\boldsymbol{x}_i = (x_1,x_2,\\cdots,x_{i-1},x_{i+1},\\cdots,x_n),\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc6328ee",
   "metadata": {
    "editable": true
   },
   "source": [
    "which equals the vector $\\boldsymbol{x}$ with the exception that observation\n",
    "number $i$ is left out. Using this notation, define\n",
    "$\\widehat{\\beta}_i$ to be the estimator\n",
    "$\\widehat{\\beta}$ computed using $\\vec{X}_i$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b751a941",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Runtime: 0.139224 sec\n",
      "Jackknife Statistics :\n",
      "original           bias      std. error\n",
      " 99.9792        99.9692        0.149921\n"
     ]
    }
   ],
   "source": [
    "from numpy import *\n",
    "from numpy.random import randint, randn\n",
    "from time import time\n",
    "\n",
    "def jackknife(data, stat):\n",
    "    n = len(data);t = zeros(n); inds = arange(n); t0 = time()\n",
    "    ## 'jackknifing' by leaving out an observation for each i                                                                                                                      \n",
    "    for i in range(n):\n",
    "        t[i] = stat(delete(data,i) )\n",
    "\n",
    "    # analysis                                                                                                                                                                     \n",
    "    print(\"Runtime: %g sec\" % (time()-t0)); print(\"Jackknife Statistics :\")\n",
    "    print(\"original           bias      std. error\")\n",
    "    print(\"%8g %14g %15g\" % (stat(data),(n-1)*mean(t)/n, (n*var(t))**.5))\n",
    "\n",
    "    return t\n",
    "\n",
    "\n",
    "# Returns mean of data samples                                                                                                                                                     \n",
    "def stat(data):\n",
    "    return mean(data)\n",
    "\n",
    "\n",
    "mu, sigma = 100, 15\n",
    "datapoints = 10000\n",
    "x = mu + sigma*random.randn(datapoints)\n",
    "# jackknife returns the data sample                                                                                                                                                \n",
    "t = jackknife(x, stat)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25ff562a",
   "metadata": {
    "editable": true
   },
   "source": [
    "### Bootstrap\n",
    "\n",
    "Bootstrapping is a nonparametric approach 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",
    "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.  \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 straight forward 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 (1) and (2), many\n",
    "estimates of $\\widehat{\\beta}$ could have been obtained. The\n",
    "idea is to use the relative frequency of $\\widehat{\\beta}^*$\n",
    "(think of a histogram) as an estimate of $p(\\boldsymbol{t})$.\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 $X_i$; 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.\n",
    "\n",
    "Instead of generating the histogram for the relative\n",
    "frequency of the observation $X_i$, just draw the values\n",
    "$(X_1^*,X_2^*,\\cdots,X_n^*)$ with replacement from the vector\n",
    "$\\boldsymbol{X}$. \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 estimator $\\widehat \\sigma^2$ to the values\n",
    "$\\widehat \\beta^*$.\n",
    "\n",
    "Before we proceed however, we need to remind ourselves about a central\n",
    "theorem in statistics, namely the so-called **central limit theorem**.\n",
    "This theorem plays a central role in understanding why the Bootstrap\n",
    "(and other resampling methods) work so well on independent and\n",
    "identically distributed variables.\n",
    "\n",
    "Suppose we have a PDF $p(x)$ from which we generate  a series $N$\n",
    "of averages $\\langle x_i \\rangle$. Each mean value $\\langle x_i \\rangle$\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 $\\langle x_i \\rangle=x_i$ in the discussion\n",
    "which follows. \n",
    "\n",
    "If we compute the mean $z$ of $m$ such mean values $x_i$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa55ab5a",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "z=\\frac{x_1+x_2+\\dots+x_m}{m},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "697c0c94",
   "metadata": {
    "editable": true
   },
   "source": [
    "the question we pose is which is the PDF of the new variable $z$.\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": "bd26bbd1",
   "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": "68664e4f",
   "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.\n",
    "\n",
    "If we use the integral expression for the $\\delta$-function"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "742a107a",
   "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": "b6d624c1",
   "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": "46458586",
   "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": "ca119461",
   "metadata": {
    "editable": true
   },
   "source": [
    "with the integral over $x$ resulting in"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f75b40fc",
   "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": "a4b64e20",
   "metadata": {
    "editable": true
   },
   "source": [
    "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": "fc76951f",
   "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": "76979572",
   "metadata": {
    "editable": true
   },
   "source": [
    "resulting in"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3edff7d2",
   "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": "73a9341f",
   "metadata": {
    "editable": true
   },
   "source": [
    "and in the limit $m\\rightarrow \\infty$ we obtain"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88f1cc30",
   "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": "1aec913e",
   "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 $p(x)$. \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": "42b317e7",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\sigma_m=\n",
    "\\frac{\\sigma}{\\sqrt{m}}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5baf71d",
   "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"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e2b39e5",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\sigma_m\\approx \n",
    "\\frac{\\sigma}{\\sqrt{m-1}}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "472e7c2c",
   "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",
    "$\\tilde{p}(x)$.\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": 2,
   "id": "0ff7b796",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bootstrap Statistics :\n",
      "original           bias      std. error\n",
      " 99.8978  15.0232        99.8962        0.149063\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": "22680159",
   "metadata": {
    "editable": true
   },
   "source": [
    "We see that our new variance and from that the standard deviation, agrees with the central limit theorem.\n",
    "\n",
    "We plot then the histogram together with a best fit for the data set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "fe018bb3",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_51_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": "5bbd613c",
   "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 $\\mathcal{L}$ consisting of the data\n",
    "$\\mathbf{X}_\\mathcal{L}=\\{(y_j, \\boldsymbol{x}_j), j=0\\ldots n-1\\}$. \n",
    "\n",
    "Let us assume that the true data is generated from a noisy model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca3fde4a",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\boldsymbol{y}=f(\\boldsymbol{x}) + \\boldsymbol{\\epsilon}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e11f84b",
   "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": "026a65c8",
   "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": "e59918c7",
   "metadata": {
    "editable": true
   },
   "source": [
    "We can rewrite this as"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2fd3f73c",
   "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": "7daf46c9",
   "metadata": {
    "editable": true
   },
   "source": [
    "The first term represents 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 stochastic variable, idem for $\\boldsymbol{\\tilde{y}}$.\n",
    "We use a more compact notation in terms of the expectation value"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6094266b",
   "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": "643e0047",
   "metadata": {
    "editable": true
   },
   "source": [
    "and adding and subtracting $\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right]$ we get"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1319bde5",
   "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": "9c6d6da1",
   "metadata": {
    "editable": true
   },
   "source": [
    "which, using the abovementioned expectation values can be rewritten as"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "855756ef",
   "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": "34d24717",
   "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": "code",
   "execution_count": 4,
   "id": "d51b6100",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error: 0.013121574015585152\n",
      "Bias^2: 0.012073649446193166\n",
      "Var: 0.0010479245693919886\n",
      "0.013121574015585152 >= 0.012073649446193166 + 0.0010479245693919886 = 0.013121574015585155\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_65_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": "code",
   "execution_count": 5,
   "id": "bd636def",
   "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: 0.08426840630693411\n",
      "Bias^2: 0.0796891867672603\n",
      "Var: 0.004579219539673834\n",
      "0.08426840630693411 >= 0.0796891867672603 + 0.004579219539673834 = 0.08426840630693413\n",
      "Polynomial degree: 2\n",
      "Error: 0.10398646080125035\n",
      "Bias^2: 0.1007711427354898\n",
      "Var: 0.0032153180657605116\n",
      "0.10398646080125035 >= 0.1007711427354898 + 0.0032153180657605116 = 0.10398646080125032\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Polynomial degree: 3\n",
      "Error: 0.06547790180152355\n",
      "Bias^2: 0.06208238634231949\n",
      "Var: 0.0033955154592040936\n",
      "0.06547790180152355 >= 0.06208238634231949 + 0.0033955154592040936 = 0.06547790180152359\n",
      "Polynomial degree: 4\n",
      "Error: 0.06844519414009445\n",
      "Bias^2: 0.06453579006728324\n",
      "Var: 0.003909404072811226\n",
      "0.06844519414009445 >= 0.06453579006728324 + 0.003909404072811226 = 0.06844519414009446\n",
      "Polynomial degree: 5\n",
      "Error: 0.05227921801205686\n",
      "Bias^2: 0.0481872773043029\n",
      "Var: 0.004091940707753939\n",
      "0.05227921801205686 >= 0.0481872773043029 + 0.004091940707753939 = 0.052279218012056844\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Polynomial degree: 6\n",
      "Error: 0.037813671417389005\n",
      "Bias^2: 0.033657685071527665\n",
      "Var: 0.00415598634586135\n",
      "0.037813671417389005 >= 0.033657685071527665 + 0.00415598634586135 = 0.03781367141738902\n",
      "Polynomial degree: 7\n",
      "Error: 0.02760977349102253\n",
      "Bias^2: 0.022999498260366312\n",
      "Var: 0.004610275230656212\n",
      "0.02760977349102253 >= 0.022999498260366312 + 0.004610275230656212 = 0.027609773491022525\n",
      "Polynomial degree: 8\n",
      "Error: 0.017355848195593347\n",
      "Bias^2: 0.010331721306655127\n",
      "Var: 0.007024126888938232\n",
      "0.017355848195593347 >= 0.010331721306655127 + 0.007024126888938232 = 0.01735584819559336\n",
      "Polynomial degree: 9\n",
      "Error: 0.02660572763718093\n",
      "Bias^2: 0.010018312644137363\n",
      "Var: 0.016587414993043573\n",
      "0.02660572763718093 >= 0.010018312644137363 + 0.016587414993043573 = 0.026605727637180936\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Polynomial degree: 10\n",
      "Error: 0.021592704588025025\n",
      "Bias^2: 0.010516485576645508\n",
      "Var: 0.011076219011379514\n",
      "0.021592704588025025 >= 0.010516485576645508 + 0.011076219011379514 = 0.021592704588025022\n",
      "Polynomial degree: 11\n",
      "Error: 0.07160048164233104\n",
      "Bias^2: 0.014436800088904942\n",
      "Var: 0.05716368155342608\n",
      "0.07160048164233104 >= 0.014436800088904942 + 0.05716368155342608 = 0.07160048164233102\n",
      "Polynomial degree: 12\n",
      "Error: 0.11547777218872497\n",
      "Bias^2: 0.01628578269596628\n",
      "Var: 0.09919198949275869\n",
      "0.11547777218872497 >= 0.01628578269596628 + 0.09919198949275869 = 0.11547777218872497\n",
      "Polynomial degree: 13\n",
      "Error: 0.22842468702219465\n",
      "Bias^2: 0.01975416527185249\n",
      "Var: 0.20867052175034223\n",
      "0.22842468702219465 >= 0.01975416527185249 + 0.20867052175034223 = 0.2284246870221947\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_66_4.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": "8cf88b3a",
   "metadata": {
    "editable": true
   },
   "source": [
    "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": "code",
   "execution_count": 6,
   "id": "86bfc49a",
   "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": {
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",
      "text/plain": [
       "<Figure size 1400x500 with 3 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_68_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": "code",
   "execution_count": 7,
   "id": "0c2a183a",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Degree of polynomial:   1\n",
      "Mean squared error on training data: 439230.69504801\n",
      "Mean squared error on test data: 481979.17861098\n",
      "Degree of polynomial:   2\n",
      "Mean squared error on training data: 115822.95008046\n",
      "Mean squared error on test data: 123711.53703498\n",
      "Degree of polynomial:   3\n",
      "Mean squared error on training data: 9011.85263220\n",
      "Mean squared error on test data: 10913.84780262\n",
      "Degree of polynomial:   4\n",
      "Mean squared error on training data: 303.47610036\n",
      "Mean squared error on test data: 426.30787294\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Degree of polynomial:   5\n",
      "Mean squared error on training data: 3.80354994\n",
      "Mean squared error on test data: 5.98822371\n",
      "Degree of polynomial:   6\n",
      "Mean squared error on training data: 3.66204648\n",
      "Mean squared error on test data: 8.14812206\n",
      "Degree of polynomial:   7\n",
      "Mean squared error on training data: 0.47075725\n",
      "Mean squared error on test data: 2.00607783\n",
      "Degree of polynomial:   8\n",
      "Mean squared error on training data: 0.04912436\n",
      "Mean squared error on test data: 0.21596432\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Degree of polynomial:   9\n",
      "Mean squared error on training data: 0.02522069\n",
      "Mean squared error on test data: 0.08576932\n",
      "Degree of polynomial:  10\n",
      "Mean squared error on training data: 0.02511518\n",
      "Mean squared error on test data: 1.20015436\n",
      "Degree of polynomial:  11\n",
      "Mean squared error on training data: 0.01640891\n",
      "Mean squared error on test data: 1.35533773\n",
      "Degree of polynomial:  12\n",
      "Mean squared error on training data: 0.00813803\n",
      "Mean squared error on test data: 0.17446471\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "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: 0.81333808\n",
      "Degree of polynomial:  15\n",
      "Mean squared error on training data: 0.00410478\n",
      "Mean squared error on test data: 92.09163947\n",
      "Degree of polynomial:  16\n",
      "Mean squared error on training data: 0.00315593\n",
      "Mean squared error on test data: 234.38827994\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Degree of polynomial:  17\n",
      "Mean squared error on training data: 0.00242999\n",
      "Mean squared error on test data: 1271.34367970\n",
      "Degree of polynomial:  18\n",
      "Mean squared error on training data: 0.00228740\n",
      "Mean squared error on test data: 108.21093775\n",
      "Degree of polynomial:  19\n",
      "Mean squared error on training data: 0.00156374\n",
      "Mean squared error on test data: 1385.79778008\n",
      "Degree of polynomial:  20\n",
      "Mean squared error on training data: 0.00137814\n",
      "Mean squared error on test data: 1944.86062977\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Degree of polynomial:  21\n",
      "Mean squared error on training data: 0.00118584\n",
      "Mean squared error on test data: 14716.58827236\n",
      "Degree of polynomial:  22\n",
      "Mean squared error on training data: 0.00092678\n",
      "Mean squared error on test data: 877.21517262\n",
      "Degree of polynomial:  23\n",
      "Mean squared error on training data: 0.00085892\n",
      "Mean squared error on test data: 5567.04664255\n",
      "Degree of polynomial:  24\n",
      "Mean squared error on training data: 0.00084707\n",
      "Mean squared error on test data: 1325.26124692\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Degree of polynomial:  25\n",
      "Mean squared error on training data: 0.00079125\n",
      "Mean squared error on test data: 129012.83870189\n",
      "Degree of polynomial:  26\n",
      "Mean squared error on training data: 0.00076908\n",
      "Mean squared error on test data: 18388.59354079\n",
      "Degree of polynomial:  27\n",
      "Mean squared error on training data: 0.00069123\n",
      "Mean squared error on test data: 2351.97979891\n",
      "Degree of polynomial:  28\n",
      "Mean squared error on training data: 0.00062592\n",
      "Mean squared error on test data: 3983.63037846\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Degree of polynomial:  29\n",
      "Mean squared error on training data: 0.00060704\n",
      "Mean squared error on test data: 3262.26814548\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58739/626635268.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_58739/626635268.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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u4qOPPiIgIKBa+/j7+xMWFlbh5WksFgsXpcUzw5Fmrlj3g2sDEhHP53DAHy+Yy31uA//Q8u+atoK4NDAcsOpLl4TndKVz/jVEgfHR/EPglJLC7VkvabyzGnKbBGfJkiVkZmbSo0cPfHx88PHxIT09nVdffRUfHx/sdu9tvhveIYZf7WaCY2z41ey2KSJSX9b9YI6/5RcKp9x0/Pelj6n+8oDeVEfPIN4QBcbH6j0G/EJgz19qoa8ht0lwhg0bxsqVK1m+fHnZq2fPnlx11VUsX74cm83m6hBdpnV0CAfCOrDHiMBSmANbZrs6JBHxVIYBf/zLXO49xnyEcqyOFwIWyFgAh7Y1aHhOV2EG8a4Nf/6gJtDzenP5jxfUilMDbpPghIaG0qlTpwqv4OBgmjZtSqdOnVwdnktZLBYGt4vhV3t3c8VaPaYSkXqy8Vez6NYnEPqOPfE2Yc2h5QBz+a9pDRdbfShtvYnp6PwZxKur7+1g84ftC/UHbA24TYIjVRvaNppfHCW9qdb9oCxfRJzPMCC9pPWm5/UQHFX5tqXFxivdPMFpyAH+KhMaA2nXmMulPdfkpNw6wZk5cyYTJ050dRiNQr/UpiyydOGI4Ycla7v5vFZExJm2zIaM+WZrQr87qt62w/lg9YE9KyFzTcPEVx8acoC/qvS703xMtun38lnNpUpuneBIuSA/H7qlxDLb0dlcocdUIuJspbU3adeYj6GqEtQEUkvGK3PXYmN7Mexabi67sgUHIDIJulxmLpeOHi1VUoLjQczHVCXdxZXgiIgzZSw0x7ax+pjTMlRHp9JB/6bW/2PzbQvgxfaw4G3nHTPz75IZxMOhaWvnHbe2BowDLLDmW8hc7epoGj0lOB7k1HbR/FZaaLxzKWTvcm1AIuI5Sse96Xo5RCRWb5+2Z5rFyAc3m/9Pqi8OB/xwPxzeCT89DLv+dM5xywb4q+cZxKurWVtof665PPtl18biBhrBfzFxlpZRwYREtWCZI9Vcsf4n1wYkIp5h15/m/08sVhhwT/X38w8xkxyo32Ljv78sT2ocxfDFLVCUX/fjltXfNPAIxlUZWHL9V06FA5tdG0sjpwTHwwxp24xf7HpMJSJOVFp70+lic6Timigd9G/V9PqZT8leBL89bS73vgmCm5mPln5/pu7H3uHCAf4qE9fdrG0y7DDnFVdH06gpwfEwR9fhGJtmQmGeawMSEfeWuRpWf2MuD7y35vunngYB4XB4F2yd69zYAJZ9ZM7VFBQFw8bDua+a6+e+Blvn1f64+dmwd6257OoC42OV/ndY/rFKEaqgBMfD9E5uwjaflmw3orAU58Omma4OSUTcWem4K+3Pg+h2Nd/fx9/cF5w/w3hhHqQ/Zy4Put+cE6vdWdDtKsCAL2+BgpzaHbtsBvFECIl2VsTOkdQPEvuCvRDmve6cYxoGbPwNFv7HTAwLc51zXBdSguNhAnxt9E+NYoa95JmxJt8Ukdrav7F8JOJB99f+OKWPqf7+CooL6x5XqYVvmy1D4YnQ87ry9SMmQHgCHNwCMx6r3bHLBvhrRPU3Rxt4n/m+eDLkHajbsTIWwuSz4MML4Pv7YPIImBAP/+4DX95mJj3bFzunrqkBKcHxQEPaRvNrWXfxH80eBiIiNTXrJXNW8DYjoHmX2h+n5UAIiYH8Q2YrgTMcOQizS8aDGfqI2VJUKiAczv+3ubz4XdjwS82P31gG+KtM6jCI7QJFubDgzdodI3MNfHol/Hc4bJsLPgHQ6lQIbW7+d9+72nwM9v198M4wmNAC3hwAX99hXtedy5ybsDqZj6sDEOcb2i6af37ZnsNGIKG5meZN2Fj/ChGRxungVljxmblc2lpQW1YbdLzA/EX811RoO6Lu8c15FfKzoFl76HLp8d+nDIbeN8PCt+Cr2+G2eSeeGPREDKNxTNFQFYvFrMX53yjzuva7w3xEVx1Z22HmBFj+iZnIWKzQ/WoY/BCEtzC3yd5lDnK4c5n52rEU8vbB7pXma+kH5nY2P3Oerrju5a9m7cHm+vTC9RGI07WICCQlJpL0A104x7YA1n6vBEdEambOK2aX65QhkNCr7sfrdLH5i3jN92btTF0mrszeBfMnmcvDxpsJ1Imc9oQ5Oej+DfD9/XDRO9U7ftZ2yNljDmroihnEq6v9ueYAhPvXmy0qJxuAMe+A2eq14G2wF5jr2p1jXsNmbStuG9bcfJV28zcMc2b1oxOencvMVrnSdaUueMscL8nF9IjKQw1p14xfyupwfnRtMCLiXrJ3wbIPzeVBDzjnmPE9ISLJfKRS19rAP56H4iMQ37v8F/CJ+AWZv2wtVrPAedWX1Tv+jqNmEPcNrFus9clqKx8XZ+7rldfIFOaZjxtf6Wb2LrMXQFJ/uOEXuPzj45ObE7FYIDzeTKqGjYdrv4QHt8Cdy+HiyeZcWS0Hgn+Y2YrTCCjB8VBD20Yz09EVO1Zz4s2DW10dkoi4i7mvmj10EvtBy/7OOabFUl5sXJdB//ZvhCXvm8unPWEetyrxPcsHJ/z2bji85+Tn2N4Ix7+pTOdLzILq3MzypLSUvRiWvAevpcGv/4SCLIjuCFf+D0Z/V/eWOYsFmiRDpwvh9Kdg9Lfw4FaIalO34zqJEhwP1SMpErt/JIsdJTeaWnFEpDpy9po9cwAG1bH25lilc1Ot/9ksEq6N358xB7lLHV795GvwgxDbGY4cgG/uOvm8WKWzdTfW+puj2XzLH03NedUc+NAwzB5rb/Qxf97SnmYXvAW3zII2p588Mawtq7X+jl1DSnA8lK/NysA2R3UX16jGIlId8/9tPv6JSzN71DhTTAeI7gCOovLBA2ti15/l3daHja/+fj5+5i93m5/5eGz5x5Vvay+CncvNZXdowQGzQDg4GrK2wS9PmD2ePr/WrM0JagojnoU7Fpt1MZXVK3kgJTgerEJ38S2zzZE5RUQqk3fAHPMEzHFv6uMv8U4Xme8rp9Z831+fLDnGxTXvth7T0exODvDDQ5U/ts/820zw/MOhaWrNY3QF30DoO9Zcnve62QLlG2zWT925HPrcWrEbvZdQguPBhrRtxmajORsdzc2/mDb+6uqQRKQxW/AWFOZATOeqi3frojTB2TKrevUwpTbPMsezsfqUJyo11e9OSDgFCg/DV2NPPEbY9kY2g3h19bweQuPM69NrDNy1HE59FALCXB2Zy7jRfz2pqejQADq3CC+bm0qPqUSkUvnZsKCk6/Wge+uvjqJJsvnox3DAqi+qt49hmEWyAGmjaj7hZymrDUZOAt8gM8Fa+Nbx2+xo5AP8VSYgDG6dA/euhbNfaHzTS7iAEhwPN7TtUd3F1/9sVtWLiBxtzyr47l5z4LyoNuVzR9WX0t5Uf1XzMdXa72H7IjMxGVzHbutNW5k9fsCsV9m7ruL37lRgfKygJhAc5eooGg0lOB5uSLtolhqtOUSI2WshY4GrQxKRxmD/Rkj/lznf0KR+sPJzc/3gB+u/ELXjBebYNNsXwYHNVW/rsJfX3vS5FUJj637+njeYBdTF+fDFzeV/+B09g7i7teDIcZTgeLiu8RGEBQXwq72buUKTb4p4r6zt5kBvbw02x0b5/WlzviGbnzmi7eWflLeu1KfQWHNQOCjvFVWZFVNg7xoIiDBraJzBYoHzXjcLiXcuLZ/TaudSwICIRAhp5pxzicsowfFwNquFwW2a8atddTgiXilnr9kz6t0R8HJH+Pkf5hxDFhu0GgbnvwH3bzBHtG13dsPFVfaYqooEp7gAfv8/c3ngPRAY4bzzh7eAs/5lLqc/Z3YNd6cB/uSkNBeVFxjaLppHl3ehCB9892+AfeshqrWrwxKR+nLkEKz51kweNqWbA+MBYIGkfubIsx1GurZeo/258O09ZrfsPX+bY+Qca/G7kJVhzm7d+ybnx9DlUljzjTkmzxe3QFicud4d62/kOEpwvMCg1s3IswQxz96eQbaVZiuOEhwRz1KUX5LUTIcNM8ypFkrFpZndszteUD5btKsFRkLr4WYB8V9TIeaYgfsKDsMfJS0sQx6qnzmhLBY4ZyJsm28+qtu72lyvFhyPoEdUXiAy2I/uiZHl3cU1bYOI5/n8Wph2A6z9zkxuojvAqY/Bncvgpt+h3+2NJ7kpVTomzl/Tjp8+Ye7rkLffHGyv29X1F0NwFJz7Svlnq0/NBxGURkkJjpcY2vaoOpxt88wRS0XEOQzD7HI881nXnH/P37D+J/OX88D74NZ5cNs8cy6pJimuiak62p5pjrh7cEt592ww64bmvW4un/oPsNXzw4Z2Z0O3q8zl2C6NewZxqTYlOF5iSNtodtCMNUaiOcDW+p9dHZKI5/hrGsx+GWZOKJ/HqCEt+8h8bzMChj124nqWxsgvGNqdZS4fPXXDrBfNEZWbd4P25zdMLGc+b05PcebzDXM+qXdKcLxEx7gwokP9+Vm9qUScqzAXfn6s/PPS9xv2/MWFsOIzcznt2oY9tzOUzjC+aro55s3BrbD4v+a60x5vuOkS/EPM1qKEXg1zPql3SnC8hMViYcjRj6k2/Gr+j1FE6mb2y3B4J/iFmp9X/A8Kchru/Ot+MGtVQmLNbt/uptWp5hg3OXvM6RNmPmvWECUPgpShro5O3JgSHC8ytG00K4wU9lsizcnmts52dUgi7u3gVpjzqrk88t/QpJX5b+tkg9c509IPzfduV9Z/rUp98PGDDiWPodKfhz8/NZeHPVF/82GJV1CC40UGtI7CZrXxc1E3c4UeU4nUzc//AHuBOSpv+/Ogx2hz/ZL3Gub8WTtg46/mcvd67GlU30oH/ds6BzDMMXLie7g0JHF/SnC8SGiAL71aNjlqdvEfj++aKSLVs/kPWP21OafSmc+ZrQ3drgSrrznk/64/6z+GPz8xOw0k9a/9DNuNQVJ/8xEbmNfz1PFVby9SDUpwvMzQds2Y4+hEocUPsraZswiLSM3Yi+GHB83lnjdATEdzOTjKbH0AWFLPxcYOR3nvqe7X1O+56pvVBl0vN5e7Xw3N2rg2HvEISnC8zNC20eTjzyx7Z3OFJt8Uqbklk80pBgIjYegjFb8rfUy14nOzh1V92TrHHD/GLxQ6nFd/52koQx6Gyz6Cs15wdSTiIZTgeJnU6BBaRASqu7hIbeUdgN+fMZeHPgpBTSp+33KgObhe4WFz2oT6sqykuLjzReZ4Mu7ON8Bs/fLxd3Uk4iGU4HgZi8XC0HbN+M3ezVyxYwkc3uPSmETcyu//B0cOQnRH6HHd8d9brZA2ylyur2Lj/Cz4+ytz2d0fT4nUEyU4Xmho22j2EskqS8mEm5qbSqR69qwqH4TuzGcr75bd7Sqz2HjHYti90vlxrJwKxfnQrD20UG8jkRNRguOF+rWKws/Hyg+F3cwVSnBETs4wzMJiw2F2CU8eVPm2Ic3M+Y2gfoqNS4uL067RWDEilVCC44UC/Wz0TWnKL46Sv/w2/g6Fea4NSqSxW/2NOdKuzR9Of+rk25cVG09x7r+vPavMbuhWX+hymfOOK+JhlOB4qaFtm7HGSGCvLRqKj8DmdFeHJNJ4FR2Bnx81l/vfCZEtT75P8mBzu4JsWPWF82IpHbm47Zlmt3QROSElOF5qSNtowFL+mEq9qUQqN+91OLQNQuNgwN3V26c+io2LC8wWIVBxschJKMHxUi2jgkmJCmZGaXfxdT+aA4eJSEVZO2DWS+by8Cdr1iW721Vg9YHtC50zqOba7+HIATPRSnXDiTVFGpASHC82pG00CxztybcGmTP57lrm6pBEGp9fHoeiPEjoUz5nUnWFxkDbs8xlZxQblxYXd7vSHP1XRCqlBMeLDW3XjEJ8mW10NVfoMZVIRdvmw8r/AZby+aZqqqzY+LO6FRtnbYcNpRNrXlX744h4CSU4Xqx3chOC/Gz8WNjFXLFJhcYiZRwO+OEBczntGojrVrvjpAyFiMSSwfm+rH08yz8BjPKRkkWkSkpwvJi/j43+qVEsdLQzV+xaDkX5Lo1JpNFY/pE5I7h/WN1mt3ZGsXGFiTWvrn0sIl5ECY6XG9o2mm1GNAetkWAvhJ2qwxEhPwt+fdJcHvygOXBfXXS/Giw2yFgAe/6u+f5bZsGhrWay1d4DJtYUaQBKcLzckLbNAAvzi1LNFRnzXRqPSKOQ/jzk7oWmraH3TXU/XmisOW4NwNJaFBuXTax5MfgF1T0eES+gBMfLxUUE0i42lMWONuaKbQtcG5CIq+1bDwveNJdHPAs+fs45bunEnH9+ag4cWF1HDsLfX5vLejwlUm1KcIQhbaNZ4mhrfshYYM65I+KtfnwYHMXQ+gxofZrzjttqKIQnVpwJvDpWTgV7gTl7eVya8+IR8XBKcIR+rZqyymhJAX7mIGL71rs6JBHXWPcTbJhhzvM0YoJzj221Qdq15nJNio2PLi7WxJoi1aYER+iWGEGxxYfljpKupxl6TCVeqLjQbL0B6HMrNG3l/HOUFhtvmweZa06+/e6VZu9GTawpUmNKcISwAF/aRB9Vh6NCY/FGC96EAxshOBoG3V8/5whrXrNi49KJNdudDcFN6ycmEQ+lBEcASEuKZHFpHY4KjcXb7PrT7DkFcNrjEBBWf+cqHdl4+SdVjztVlK+JNUXqQAmOAJCWGMFSR2vzw/71kLvftQGJNJSMhfDeuVB4GBL7Qtcr6/d8rU6F8ATIPwSrv658u7XfmduEtTALlEWkRpTgCGC24GQRwgajhblCdTjiDTalwwcjoSDLTG6u/Nwcebg+VbfYWBNritSJEhwBICUqmIggXxbZVYcjXmLdT/DxJVCUa84XdfW0+n00dbTuV4PFClvnwN51x39/aBts/N1c7qaJNUVqQwmOAGCxWEhLjGSJoQH/xAus+gI+u9IcX6bt2XDlFPALbrjzh8VBmxHm8omKjUsn1kweBE2SGy4uEQ+iBEfK9EiKLO9JtXMZFBe4NiCR+rDsI5h6vTmYX+dL4NL3wce/4eMoKzb+uGKxscMByz42l1VcLFJrSnCkTPfECLYYsRwkzPzLdudyV4ck4lwL3oavxoLhMOtgLngLbL6uiSX1NLOA+MhBWP1N+frN6ZC1DfzDof25rolNxAMowZEyXeMjsFmtLFQdjniiWS/BDyXj2/S5Dc591bXFu5UVG5cWF3e+GHwDGzwsEU/hU90Nv/66iu6MlRg+fDiBgfoH6i6C/X3MiTf3tOEM22KzDqe/q6MSqSPDgN+ehlkvmJ8HPQBDH2kc0x50vxrSn4Ots80pUoKjyltz0vR4SqQuqp3gjBw5skYHtlgsrF+/npSUlJrGJC6UlhjJkl2lLTglE282hl8EIrVhGOb0CwsmmZ+HPwn973JtTEcLj4fWp8O6H81WnIgk8/FwTCdo3s3V0Ym4tRo9otq9ezcOh6Nar6CgoPqKWepRj6RI/jKSKcQX8vbB/o2uDkmkdhx2+PqO8uTmrBcaV3JT6uiRjUsfVXW/Rn9YiNRRtROcUaNG1ehx09VXX01YmPPGlJgwYQK9evUiNDSU6OhoRo4cydq1a512fDGlJUZSiC9/lk28qToccUP2Ipg+BpZ9aI43M3IS9B7j6qhOLHU4hMbBkQOQuQpsftDlUldHJeL2qp3gTJ48mdDQ0GofeNKkSURFRdUqqBNJT09n7NixzJ8/nxkzZlBcXMzpp59Obm6u084hkNAkkKgQ//Lu4tuU4IibKcqHKdfAX9PMWbgvnmyOBtxY2Xwq1tu0OxuCmrguHhEPUe0anOowDIO9e/cSHR3tzMMC8OOPP1b4PHnyZKKjo1myZAmDBg1y+vm8lTngXwSL1xxVhyPiLgpz4dMrzK7WPgFw6YfQ5nRXR3Vy3a8pmezT0Ng3Ik5SoxqcoKAg9u7dW/Z5xIgR7Nq1q+xzZmYmzZs3d150VcjKygKgSZPK/9IpKCggOzu7wktOLi0pkiWlLTj71kHeAdcGJFId+Vnw4YVmcuMbDFf9zz2SG4CIBDjnZRj8oDlthIjUWY0SnPz8fAzDKPs8Z84cjhw5UmGbo7+vL4ZhcM899zBgwAA6depU6XYTJkwgPDy87JWQkFDvsXmCHkmRHCKUzWjiTXETRfnw/nlmzVhAOFz7lTnNgTvpeZ3Zfb2+J/sU8RJO/5dkaYDK/9tvv50VK1bw6aefVrndww8/TFZWVtkrIyOj3mPzBJ1bhONjtbCguLW5QnU40tit/wl2LYfASBj1LST0cnVEIuJibvenwh133MHXX3/N77//Tnx8fJXb+vv7ExYWVuElJxfga6Nji/DyiTczFro2IJGT2bHEfO8wEpp3cWkoItI41CjBsVgsFVpojv1cnwzD4Pbbb2f69On89ttvJCdrht36lJYYwWJHW/PDzqVQXOjagESqsmOp+d4izbVxiEijUaNeVIZh0KZNm7KkJicnh+7du2MteWZcn/U3Y8eO5ZNPPuGrr74iNDSU3bt3AxAeHq7pIOpBj6RIJs+JJcsSRnhxNuz6U83+0jg5HOb9CRCnBEdETDVKcCZPnlxfcZzUpEnmaKRDhgypsH7y5MmMHj264QPycGmJkYCFhfbWDLcuMYs3leBIY7R/AxRkg08gNGvn6mhEpJGoUYIzatSo+orjpBqid5aUi4sIJDYsgMW5bcwEZ9t86HeHq8MSOV5p/U3zruageSIiOGGgv/z8fKZMmUJubi7Dhw+ndevWzohLGoEeSZEs/ksTb0ojt1P1NyJyvBoVGd9///3cdVf5ZHWFhYX07duXMWPG8Mgjj9C9e3fmzZvn9CDFNbonRvCXkUwRvpC7Fw5scnVIIscrLTBW/Y2IHKVGCc4PP/zAsGHDyj5//PHHbN26lfXr13Pw4EEuueQSnn76aacHKa7RIymSAvxYRenEmxrwTxqZ4kLYvdJcVguOiBylRgnOtm3b6NChQ9nnn3/+mYsvvpikpCQsFgt33XUXy5Ytc3qQ4hod48Lx87EyXwP+SWOV+TfYCyAgApqkuDoaEWlEapTgWK3WCsW+8+fPp0+fPmWfIyIiOHjwoPOiE5fy87HSuUV4+bxUasGRxqa0/iauu+rDRKSCGiU47dq145tvvgFg1apVbNu2jaFDyyeG27p1KzExMc6NUFyqx9ETb+5do4k3pXHRAH8iUokaFxk/9NBDDBs2jGHDhnHWWWdVGFH4+++/p3fv3k4PUlwnLTGCA4Sx3Voy8eb2Ra4NSORoKjAWkUrUKMG56KKL+P777+nSpQt33303U6ZMqfB9UFAQt912m1MDFNcyB/yDuUWp5grV4UhjUZgLe1eby2rBEZFj1HgcnNNOO43TTjvthN89/vjjdQ5IGpfosADiIwNZnN2GS23pqsORxmPXCjAcENocwuJcHY2INDI1SnC2bdtWre0SExNrFYw0Tj2SIlnyZ0kdzo4lZtdcHz/XBiWyU4+nRKRyNUpwjq63Ke1NdfRs4oZhYLFYsNvtTgpPGoO0xEi+Wh7HYWsYocXZsHsFxPd0dVji7coKjLu7Ng4RaZRqlOBYLBbi4+MZPXo05557Lj4+mvfFG5ROvLnE0ZohlMxLpQRHXE0tOCJShRoVGW/fvp1bb72VKVOmcPbZZ/Phhx/i5+dH165dK7zEs7RrHkqgr435RSUD/mWo0FhcLO9A+dQhcWrBEZHj1SjBiY2N5cEHH2T16tVMnTqVgwcPcsopp9CnTx/+85//4HA46itOcSFfm5Uu8eEsLh0PZ1vJxJsirrKzZMT0yGQIauLaWESkUapRgnO0AQMG8N///pf169cTFBTELbfcwqFDh5wYmjQmPZIiWWmkUGzxgdxMOLjF1SGJN9MM4iJyErVOcObOncuNN95ImzZtyMnJ4d///jcRERFODE0ak7REc+LNddZW5gp1FxdX2lHSgtOih2vjEJFGq0YJzq5du3juuedo164dF1xwAWFhYcydO5eFCxdyyy23YLXWOl+SRq57YgQAsws04J80AiowFpGTqFE3qKSkJOLi4hg1ahTnnXcevr6+2O12VqxYUWG7Ll26ODVIcb2mIf4kRwWz5EAb4Du14IjrZO+Ew7vAYoXm+n+NiJxYjRKc4uJitm3bxlNPPcXTTz8NUGF2cUDj4Hiw7okR/LGvpNA4czUcOQSBEa4MSbxR6fg3zdqDX7BrYxGRRqtGCc7mzZvrKw5xAz2SIpm+NJzdPnHEFu80J95sPdzVYYm32akB/kTk5Gr8iEq8V+nEm/OLWjPSstOsw1GCIw1NM4iLSDVUuyp4xYoVNRrnZtWqVRQXF9cqKGmc2sSEEuLvw/zi0gH/VIcjDcwwysfAUQ8qEalCtROc7t27s3///mofuG/fvtWenFPcg81qoVtCRPmAf9sXg73ItUGJdzmwCfIPgc0fYjq6OhoRacSq/YjKMAwee+wxgoKCqrV9YWFhrYOSxistMYLXNsSRZw0lqPiwOfGm/pKWhlLaehPbGWy+ro1FRBq1aic4gwYNYu3atdU+cN++fQkMDKxVUNJ4pSVFYmDlT0tb+rLYnLZBCY40lB1LzHeNYCwiJ1HtBGfmzJn1GIa4i+4JZqHxrPxW9PVdbE682fc2F0clXkMFxiJSTRp6WGokPMiX1tEhmnhTGp69GHb9aS6rBUdETqLGCc6iRYu46qqrSE5OJjAwkKCgIJKTk7nqqqtYvHhxfcQojUxaYiR/Gq2wW3wgZzcc2urqkMQb7F0DxUfALxSatnZ1NCLSyNUowfnyyy/p378/Bw4c4K677uLdd9/lnXfe4a677uLgwYP079+fr776qr5ilUYiLSmCAvzY5FM6L5W6i0sDKJt/qhto3jsROYkaDfT3j3/8gyeffJKHHnrouO/GjRvHc889xyOPPML555/vtACl8emRZNbhzC5oRWvrGrMOp+tlLo5KPF5p/Y0eT4lINdToz6ANGzZw4YUXVvr9yJEj2bhxY52DksYtJSqEsICjBvxTC440hNIeVCowFpFqqFGC06pVK7788stKv//qq69ISUmpa0zSyFmtFtKSIllaWmic+bc58aZIfSnKN+8zUAuOiFRLjR5RPfnkk1x++eWkp6dz+umnExMTg8ViYffu3cyYMYOff/6Zzz77rL5ilUYkLTGSmWsj2OcbR1TRTnNU49anuTos8VS7V4KjGIKiIDzB1dGIiBuoUYJz0UUX8ccff/DKK6/w0ksvsXv3bgBiY2Pp27cv6enp9O3bt14ClcaltA5nsaMNI9hpzktV0wSnuAA2z4I138LGX6HlQDj/32Cx1EPE4tZ2HlV/o/tDRKqhRgkOmCMUK4mRrgkRWC3wR34rRvjONAuNqyM/GzbMgDXfwfoZUJBd/t3yj81RkXvdUC8xixsrKzDWqNkiUj01TnBEAEL8fWgTE8riPaUTby4xB2KzneCWOrwH1n5vJjWb08F+1DxlITHQ9izw8YcFb8JPj0LyIIjSOCdylJ0awVhEasapCc7q1as5++yz2bRpkzMPK41Uj6RIPtndgiO2UAKLDsOelRDX3fxy/0bz0dOa7yBjIXDUaMdNWkH7c6DdueZf5FYrOByQudpMgKaPgRtmaDJFMeVnwb515rIKjEWkmpya4BQWFrJ1q0a19RZpiZF8vGAbq21tSbMvhj8/g9UlSc3e1RU3jksrSWrOgag2x9dRWK0wchJM6mvOGJ3+PJz6aMP9MNJ47VxuvocnQnCUS0MREfdRowTnnnvuqfL7vXv31ikYcS+lhcYzj7QizbbYfMRUyupjFg23O9t8BBXe4uQHDG8B57wMU6+HWS9A6mmQeEo9RS9uo6zAuLtr4xARt1KjBOeVV16hW7duhIWFnfD7nJwcpwQl7iGpaRBNgv34Ia8H43ynY7X5mT2p2p0DrYdDYGTND9rpIlj3E6yYAl/cBLfMBv9Q5wcv7kMziItILdQowWndujV33303V1999Qm/X758OT16qJeDt7BYLKQlRvDL6ng+GvAr1w5sC74BdT/wWf+CrXPh4Bb48WE4//W6H1Pc185l5rt6UIlIDdRoJOMePXqwZMmSSr+3WCwYhlHp9+J50koeU83fVeyc5AYgIBwueBOwwLIPzboe8U45mZCVAVjMSTZFRKqpRi04L774IgUFBZV+37VrVxwOR52DEveRlmgmOEu3HnLugVsOgP53wpxX4Os7IL4nhMY69xzS+JU+nopqo0eVIlIjNWrBiY2NJSkpqb5iETfUNT4Cm9XC7ux8dh464tyDD30UYjrDkQPw1e2g1kHvs1MziItI7dQowRE5VqCfjQ7NzaLzJVsPOvfgPv5w0X/A5m+OfrzoHeceXxo/FRiLSC3VahycyMhILCeYD8ZisRAQEEBqaiqjR4/muuuuq3OA0vj1SIpk5Y4sPl+cQXZ+EQE+NgL9bAT62gjwLV82P1sJKPnsa6tGfh3dHob/E358CH7+ByQPhmZt6v+HEtczDLXgiEit1SrBGT9+PM888wxnnnkmvXv3xjAMFi1axI8//sjYsWPZvHkzt956K8XFxYwZM8bZMUsj0yMpkvfmbmHW+n3MWr+v2vv5WC1m0lOS8FyY1oJxp50geel9s9l1fNPv5aMc+/g58SeQRunQNsjbb46pFNPJ1dGIiJupVYIze/Zsnn76aW655ZYK69966y1+/vlnpk2bRpcuXXj11VeV4HiBMzrGMnZoK3YcPMKRIjtHihzkF9pLlu0cKbSTX1T+ubSUpthhcLigmMMFxQC88ut6zu0aR6tmIRVPYLXCyDfgjb6wazmkPwfDHmvYH1IaXmnrTUwn5/XQExGvYTFq0a87JCSE5cuXk5qaWmH9hg0b6NatGzk5OWzcuJEuXbqQm5vrtGDrKjs7m/DwcLKysiodrFDql2EYFNod5Bc6KiRAz/24hvR1e7m4RzwvXNL1xDuv+hL+NwosVrjuB0js06CxSwP7+R8w9zXoeb05wrWIeK3a/P6uVZFxkyZN+Oabb45b/80339CkSRMAcnNzCQ1Vt06pyGKx4O9jIzzIl9jwAJKjgukQF8bdw81HU18u28H2g3kn3rnjSOh6BRgOmH4T5Gc3XODS8HaUDPCnAmMRqYVaPaJ67LHHuPXWW/n999/p3bs3FouFhQsX8v333/Pmm+Z8RDNmzGDw4MFODVY8V7eECAakRjF7wz7e/mMTT55fSc3Fmc/BljlwaKtZeDzyjYYNVBqGw24+jgQVGItIrdSqBWfMmDGkp6cTHBzM9OnTmTp1KkFBQaSnp3PDDTcAcO+99zJlyhSnBiue7bahrQD4bFEGmYfzT7xRQDhc+BZggeUfw99fN1yA0nD2rYfCHPANgqi2ro5GRNxQrVpwAPr370///v2dGYt4ub4pTUlLjGDptkP8d/ZmHj6z/Yk3TOoHA8bB7JfhmzshvheENW/QWKWelRYYN+8Ktlr/b0pEvFitB/qz2+1MmzaNp59+mmeeeYYvvvgCu93uzNjEy1gsFsYONQvXP5q3lUN5hZVvPOQRiO0CRw7CV2M1yrGnKR3gTxNsikgt1SrB2bBhA+3bt+faa68te0R19dVX07FjRzZu3OjsGMWLnNoumvbNw8gttPP+3K2Vb+jjBxe9Az4BsPFXWPifhgtS6t+Okkl947q7Ng4RcVu1SnDuvPNOWrVqRUZGBkuXLmXZsmVs27aN5ORk7rzzTmfHKF7EbMUxa3Emz91MbskYOSfUrC0Mf9JcnvEYZK5pgAil3hUXwp6/zGUVGItILdUqwUlPT+f5558v6xIO0LRpU5599lnS09OdFpx4pzM7NSclKphDeUV8smBb1Rv3GgOthkFxPnxxsx5VeYI9f4G9EAIjITLZ1dGIiJuqVYLj7+/P4cOHj1ufk5ODn5+G0Je6sVkt3DLEbMV5e9Ym8ouqqO2yWuH8f4NfiNmteOOvDROk1J/SAuO47nCCOe9ERKqjVgnOOeecw0033cSCBQswDAPDMJg/fz633HIL5513nrNjFC80slsL4sID2Hu4gP8t2V71xmHNofs15vI8jYvj9jTAn4g4Qa0SnFdffZVWrVrRt29fAgICCAgIoF+/fqSmpjJx4kQnhyjeyM/Hys2DzVact9I3UmR3VL3DKTcDFrMFR7U47k0ziIuIE9QqwYmIiOCrr75i3bp1TJ06lf/973+sW7eOL774goiICCeHKN7qsl4JRIX4sf3gEb5evrPqjZskQ7uzzeUFk+o/OKkfBTmwtyRBVRdxEamDao+gdc8991T5/cyZM8uWX3rppVoHJFIqwNfGDQNSeO7HNbwxcwMXdG+B1VpFTUbfsbDmW/jzMzh1PAQ3bbhgxTl2/WnONRYaB6Gxro5GRNxYtROcZcuWVWs7i4oCxYmu7pPIpJkb2Lg3l59W7ebMzlWMWJzY1xz5dtefsORdGHR/wwXa0AwD8vabc3Id2gaHMsyeR31uA78gV0dXe3o8JSJOUu0E5/fff6/POEROKDTAl9H9WvLqbxv498wNjOgUW3kSbbFAn7HwxU2w8B3od5c5IKA7MgzI3VuSvByVxBzaZr6yMqDoBLOuF+XBsPENH6+z7DiqB5WISB1okhdp9K7rn8w7szfz145s0tftZUjb6Mo37ngBzBgPObth1XToennDBVoXO5bC0g8qJjDFlUw4WsZiPsaJSAT/UNjwizmic787ITCiIaJ2PrXgiIiT1HouKld54403SE5OJiAggB49ejBr1ixXhyT1LDLYjyt7JwLw7983VL2xjx/0HmMuz/u3ewz8Zxgw7QZYMtnsBbZ/fUlyY4GwePPRW5fLzEdu574K13wJdyyFf+yBe9fADT/Dlf+DZu2hIBsWvePqn6h28g7AwS3mslpwRKSO3KoFZ8qUKYwbN4433niD/v3789Zbb3HmmWfy999/k5iY6OrwpB6NGZTCB/O2smjLQRZuPkDv5CaVb9zzevjjX7B7BWydCy0b+az32+bDgU3gGwxnPme2yEQkQliL6j9is1ph4D0wfQzMfwP63Ap+wfUb99F2r4Tv7oWmqdB6OKQMrXkrUunjqSatzFGMRUTqwK1acF566SVuuOEGbrzxRtq3b8/EiRNJSEhg0qQTdwsuKCggOzu7wkvcU0xYABf3jAfg9ZO14gQ1KX80Nd8NBv5b/rH53nEkpF0DKYPNbu81rR/qeCFEtjSLj5d+4OwoK2cY8O3dkLHA/Fn+NxqeT4HJZ8PsibDn7+q1pOnxlIg4kdskOIWFhSxZsoTTTz+9wvrTTz+duXPnnnCfCRMmEB4eXvZKSEhoiFClntw6uBU2q4U/1u1l5fasqjfuc5v5vuY7s3WksSrMg1Vfmstdr6jbsWw+0H+cuTznVSguqNvxqmvNt7B9EfgGmdc9qi0Ydtg6G355HCb1hYmdzSRo7Q9QmHvi45QVGCvBEZG6c5sEZ9++fdjtdmJiYiqsj4mJYffu3Sfc5+GHHyYrK6vslZGR0RChSj1JaBLE+V3jgGrU4jRrC6mnAQYseKv+g6utNd9B4WHzkVSSEx6ldbvSHEPm8E7489O6H+9k7MXwyz/N5b5jYcQEuH0h3LkcznoBWp8OPgFm0fTid+HTy+G5lvDhBTD/Tdi/0dzXMNSCIyJO5TYJTqljuwgbhlFpt2F/f3/CwsIqvMS93VoyCeePq3azfs/xE75WUNqKs+wjyD9Ji4+r/PmJ+d71CrOOpq58/KHfHeby7IlmAlKfln9kFkUHNjF7b5VqkmwWe1/1P3hwi1kE3WuMmcjZC2Hjb/Djg/BaGryaBt+Og5w9YLFBbJf6jVlEvILbJDhRUVHYbLbjWmsyMzOPa9URz9U6JpQRHc0RbifN3Fj1xq1OhWbtoDAHln7YANHVUNYO2FgyvpQzu7P3GAVBTeHgZlj1hfOOe6zCPPh9grk8+AEIqOQPCN9AaHM6nP0C3LUCxi6C05+B5EFg9YUDG2HJe+a20e3de6BCEWk03CbB8fPzo0ePHsyYMaPC+hkzZtCvXz8XRSWuMHZoKgBf/bmTbftPMNhdKYvF7E0E5mOq+m7NqKkVUwADEvtBkxTnHdcvuPznnvUiOE4yUWltLZhkjjcUkWj2XKsOiwWatYF+t8Oob+CBTXDZR5B2LcR0gr6310+sIuJ13CbBAXM+rHfeeYd3332X1atXc/fdd7Nt2zZuueUWV4cmDahzfDiD2jTD7jB464+TtOJ0ucxszcjaZhbDNhaGUV4j062OxcUn0msM+IfB3tWw7gfnHz/vAMx+xVwe+g/z0VhtBIRB+3PhvNfg1jn1cy1ExCu5VYJz2WWXMXHiRJ588km6devGH3/8wffff09SUpKrQ5MGNrakFud/i7ezJ7uKEX99A8tbFxpTl/EdS2HfOvAJhA4jnX/8wAjodaO5/McLzh/wcNaLUJAFMZ2h8yXOPbaIiBO4VYIDcNttt7FlyxYKCgpYsmQJgwYNcnVI4gKnpDSlV8tICu0O3pl1km7gvW40az0yFsD2JQ0T4MmUjn3T/tzKa1fqqu9YM4HauRQ2OXEuuUPbYOHb5vJpTzinOFpExMn0fyZxW6W1OB8v2MbB3MLKNwyNhc4Xm8uNoRWnuAD+mmYu1+cjmeAo6DHaXJ71kvOO+/sEsydUy4GQOsx5xxURcSIlOOK2BrdpRqcWYeQV2pk8Z3PVG5cW3f79pdl7yZXW/gD5h8zxapIH1++5+t1htl5tmQXbFtT9eHtWldcODf+nWTQsItIIKcERt2WxWBg7xGzFeW/uFg7nF1W+cfOukDQAHMXlj1dcZXnp2DeXg9VWv+cKb1HeSjTrhbof75d/AoZZN9SiR92PJyJST5TgiFs7o2MsrZoFk51fzEfzt1W9cd+Sgf+WvFf5dAH1LScTNvxiLne7smHO2X8cWKyw/mfYtaL2x9kyB9b/ZA7GN2y808ITEakPSnDErVmtFm4racX57+xNFBTbK9+4zQiITDYfD5W2ojS0FZ+b8zS16AlRrRvmnE1bmRNxgtn7qTYMw5xXCsyBBJu2ck5sIiL1RAmOuL3zusURFx7AvpxCvvlzV+UbWm1HDfz3Zv0NgFcZwyhPrBqq9abUwHvN97+/gr3rar7/0RNqDn7QubGJiNQDJTji9nxtVq7p2xKAd2dvxqhqzJduV4F/OOzfABtmVL5dfdi9AjJXgc0fOl3YsOeO6QBtzwYMmDOxZvseO6FmaKyzoxMRcTolOOIRruidQICvlb93ZbNw84HKN/QPgbRrzOV5/26Y4EotL+l91PZMCIxs2HNDeSvOiinmWDbVVdmEmiIijZgSHPEIEUF+XNA9HoDJc7ZUvfEpN5tFt5vTYfdf9R8cQHEhrPzcXG7ox1Ol4ntAyhCzJ9mcV6u3T3Un1BQRaWSU4IjHuL5/SwB+/ns3GQeqmIQzIhHan2cuz59U/4GB+Tgsbz8ER0MrFw6ON/A+833pB3B4z8m3r82EmiIijYASHPEYrWNCGdg6CocBH8zbUvXGfcea7ys/h5y99R5bWXFxl0vB5lP/56tMywEQ3xvsBTDv9aq3PXpCzVMfq/2EmiIiLqAERzzKdSWtOJ8tyiC3oLjyDRN6m1217YWw+L/1G1TeAVj3k7nsqsdTpSwWGFTSirP4XTO2yhw9oWanixsmPhERJ1GCIx5lSJtokqOCOZxfzPSl26veuHTgv0XvQFEVM5LX1cqp4CgyR1OO6Vh/56mu1qebSUthTuWjOmtCTRFxc/q/lngUq9XCqL5JgFls7HBU0WW8/XkQ1gJy98JfU+svqNKZw7u6uPWmlMUCA+8xl+dPgoLDx2+jCTVFxM0pwRGPc3HPBEL9fdi0L5f09VXU19h8ofdN5vK8N8yB+JwtczXsWg5Wn/IZzRuDDudD09bmqM6LJ1f8ThNqiogHUIIjHifE34dLeyUA1egy3mOUOTpv5iqz27izlRYXtxkBwVHOP35tWW0w4G5zed7rFR/RaUJNEfEASnDEI43q2xKLBf5Yt5cNmSd4BFMqMNIc3RjMVhxnshebg+oBdL3Cucd2hi6XQngC5OyBZR+a6zShpoh4CCU44pESmwZxWvsYoBqtOKXzU63/CWa/7LwgNv1uJg+BTczC3sbG5gv97zKX57xqDkZYNqHmaE2oKSJuTQmOeKzr+ycDMH3pDrLyiirfsGkrGPyQufzLE+YjGmfU4xw99o2PX92PVx+6X20OPpi1DabfqAk1RcRjKMERj9UnpQntYkM5UmTns0UnmXtp6MNmd2iA2S/B9/fVbbbxI4dgzXfmcmN8PFXKN7B80MO/vzLf+46F0BjXxSQi4gRKcMRjWSyWslac9+duodh+koRlwN1w9ouAxRwb58tbzDqa2lg13RwtOLqDOf5NY9brBggIN5c1oaaIeAglOOLRzusWR5NgP3Zm5fPz39WYe6nXjXDh22aR7Yop8Pm1tRsEsHTm8G5XNv5u1v6hMOgBc/m0JzShpoh4BCU44tECfG1cdUoiAJPnbK7eTl0uhcs/Bps/rP0OPrkUCnKqf9J9G2D7QjNJ6nxpLaJ2gX63w4NbzG7zIiIeQAmOeLyr+yThY7WwaMtBVm7Pqt5Obc+Eq/4HvsHm+DgfjoQjB6u3b+kgeanD3KuWJTDS1RGIiDiNEhzxeDFhAZzdpTlQg1YcgJTBMOprCIgwexe9dw7kZFa9j8MBf35mLrt6Yk0RES+mBEe8wnUlxcbfrNhJ5uEa1NTE94Trvje7Uu/5C94dAYcyKt9+yx+Qvd0s2m1zZh2jFhGR2lKCI16hW0IEaYkRFNkNPp5/ki7jx4rpCNf/COGJcGCjmeTsW3/ibUuLiztdBL4BdQtaRERqTQmOeI3SVpyPF2yloNhes52btoLrfzAnqMzebiY5u1ZU3KbgMKz+2lxuLDOHi4h4KSU44jVGdIolNiyAfTmFfPPnrpofIDzebMmJ7QJ5+8yanG0Lyr//+ysoyjOToPiezgtcRERqTAmOeA1fm5Vr+iYBZrGxUZvpGIKjYNQ3kNAHCrLM3lUbfzO/Kxv75orGP/aNiIiHU4IjXuXK3on4+1hZtTObRVuq2e37WIERcM10aHWq2WLzyWXmTORbZwMW6HK5M0MWEZFaUIIjXiUy2I8L01oANewyfiy/YLjiM2h/HtgL4aeHzfUpQyC8Rd0DFRGROlGCI15ndD+z2PinVbvJOJBX+wP5+MPFk6HbVeXrNPaNiEijoARHvE7b2FD6pzbFYcCH87fW7WA2HzjvdRj6KHS5DDqc75wgRUSkTpTgiFe6rqQV57OF28gtqOWM4aWsVhj8gDlJp4+/E6ITEZG6UoIjXunUdtEkNQ0iO7+Y6Uu3uzocERFxMiU44pWsVguj+7UEYPLcLTgctegyLiIijZYSHPFaF/eIJ8Tfh017c/lj/V5XhyMiIk6kBEe8VmiAL5f0jAdg8pwtrg1GREScSgmOeLXR/VpisUD6ur1syMxxdTgiIuIkSnDEqyU1DWZYuxgA3ptbh4H/RESkUVGCI17v+v4tAfh88XY+XbitdnNUiYhIo6IER7xe31ZNObVdNIXFDh6evpLr3lvE7qx8V4clIiJ1oARHvJ7FYuE/1/bk0bPa4+djZebavZz+cjpfLtuh1hwRETelBEcEsFktjBmUwnd3DKBLfDjZ+cWMm7KcWz9ayr6cAleHJyIiNaQER+QorWNCmXZrP+4d3gYfq4UfV+3mjJf/4Me/drk6NBERqQElOCLH8LVZuWNYa766vT/tYkPZn1vILR8tZdxny8jKK3J1eCIiUg1KcEQq0TEunK9u78/Yoa2wWuDL5Ts5fWI6v6/NdHVoIiJyEkpwRKrg72Pj/jPaMe3WfqREBbMnu4DrJi/i4ekryKnrLOQiIlJvlOCIVEP3xEi+u3Mg1/dPBuDThRmMmPgH8zbud3FkIiJyIkpwRKop0M/G+HM78OmYPsRHBrL94BGu+M98nvh6FUcK7a4OT0REjmIxvGigj+zsbMLDw8nKyiIsLMzV4Ygbyyko5v++X80nC7YBkBwVzKNntScy2A+LBSyY4+tYAKvFgsVi7md+Z36usAyEB/kSHRrgqh9JRKTRqs3vbyU4InUwc20mD01bye5s54x8PLhNM67r35JBrZthtVqcckwREXenBOcklOBIfcjKK+LZH1czd+N+DAMMDBwO8zvDMDCgbL35bn6mwmeDQ0eKKP3XmNIsmOv6teTCtHiC/X1c8nOJiDQWSnBOQgmONGZb9+fy/tytfL44o6yHVmiAD5f3SuDavi1JaBLk4ghFRFxDCc5JKMERd5BTUMzUxRm8N3cLW/bnAWC1wPAOMVzXP5lTkptgsejxlYh4DyU4J6EER9yJw2Ewc10mk+dsYdb6fWXr2zcP47r+LTmvaxwBvjYXRigi0jCU4JyEEhxxV+v3HGby3C1MX7qd/CKzwKdpsB9XnpLI1X2SiAlT7ysR8VxKcE5CCY64u0N5hXy2KIMP5m5hZ5bZc8vHauGszs25fkAy3RIiXBugiEg9UIJzEkpwxFMU2x38/PceJs/ZzKItB8vWX94rgfHndiDITz2vRMRzKME5CSU44on+2pHFu7M388XyHRgGpEQFM/HybnSJj3B1aCIiTlGb39+aqkHEzXVqEc5Ll3Xj4xtPITYsgE37crnwjblMmrkRh8Nr/n4REalACY6Ih+jXKoofxw3kzE6xFDsMnvtxDVe9s4BdWUdcHZqISINTgiPiQSKC/HjjqjSeu6gzgb425m3az4iJs/hh5S5XhyYi0qDcIsHZsmULN9xwA8nJyQQGBtKqVSsef/xxCgsLXR2aSKNjsVi4rFci3905gM4twsk6UsStHy/lwakryC0ZIVlExNO5RYKzZs0aHA4Hb731FqtWreLll1/mzTff5JFHHnF1aCKNVkqzEKbd2o9bh7TCYoEpizM457XZrNh+yNWhiYjUO7ftRfWvf/2LSZMmsWnTpmrvo15U4q3mbtzHPVP+ZHd2Pj5WC/ee3pabBqVg04zlIuIGvKoXVVZWFk2aNKlym4KCArKzsyu8RLzRiQuQ56sAWUQ8llsmOBs3buS1117jlltuqXK7CRMmEB4eXvZKSEhooAhFGp9jC5DnbzqgAmQR8VguTXCeeOIJLBZLla/FixdX2Gfnzp2MGDGCSy65hBtvvLHK4z/88MNkZWWVvTIyMurzxxFp9I4uQO4SrwJkEfFcLq3B2bdvH/v27atym5YtWxIQYE4kuHPnToYOHcopp5zCe++9h9Vas/xMNTgi5QqLHbz8yzreTN+IYUBS0yD6JDclIsiX8CBfIgL9iAjyJSLQ/BwZZH4O9LVhsah2R0QajkdP1bBjxw6GDh1Kjx49+Oijj7DZbDU+hhIckeMdXYBcHX42a0kC5GsmQEF+RAT60iTEj7M6NaerJvwUESfz2ARn586dDB48mMTERD744IMKyU1sbGy1j6MER+TEsvKK+OGvXezLKeBQXhGHjhRxKK+IrCOFR30upMh+8v9dDGwdxR2ntqZ3ctWdAEREqstjE5z33nuP66677oTf1SR8JTgitWcYBnmF9rJkJ+uoROjQkULW7j7Mtyt2YS+Z/6p3chNuH5rKwNZReqQlInXisQmOsyjBEalfGQfymJS+kamLt1NodwDQNT6c209tzbB20Vg17o6I1IISnJNQgiPSMHZn5fP2H5v4ZOFW8ovMRKddbChjh6ZyVufmGmBQRGpECc5JKMERaVj7cgr47+zNfDhvKzkl3dBTooK5bWgq53eLw9fmlkNxiUgDU4JzEtW9QHa7naKiogaMTNyVr69vrXr0eZusvCLem7uFd+dsJuuI+W8rPjKQWwa34uIe8QT46hqKSOWU4JzEyS6QYRjs3r2bQ4cONXxw4rYiIiKIjY1VIW015BQU89H8rbwzaxP7cgoBiAnzZ8zAFK48JZEgPx8XRygijZESnJM42QXatWsXhw4dIjo6mqCgIP3CkioZhkFeXh6ZmZlERETQvHlzV4fkNo4U2pmyaBtvpm8qG3+nSbAf/VOjSG4aRFLTYFpGBZMcFUxkkK/+LYp4OSU4J1HVBbLb7axbt47o6GiaNm3qogjFHe3fv5/MzEzatGmjx1U1VFBsZ/rSHbwxcwMZB0488WdogA/JUcEkNQ1W8iPipWqT4Kg9uERpzU1QUJCLIxF3U3rPFBUVKcGpIX8fG1f0TuSSHvH8sX4v6/fksGV/Llv25bFlfy67svI5nF/Miu1ZrNieddz+xyY/neMj6JPShNAAXxf8NCLSmCjBOYb+GpSa0j1Tdz42K6e2i+HUdjEV1ucX2dm6P68k6clly/48tpYs76wk+bFZLXRLiGBAahQDWkfRLSFCvbVEvJASHBFptAJ8bbSNDaVtbOhx3+UX2dl2IK8k8cllY2YuCzbvZ8v+PJZsPciSrQd55df1BPvZ6JPSlAGtoxjYOopWzUKUlIp4ASU4cpwhQ4bQrVs3Jk6cWK3tt2zZQnJyMsuWLaNbt271GptIqQBfG21iQmkTUzH5yTiQx5wN+5i9YR9zNuzjYF4Rv67J5Nc1mQDEhgXQPzWKAa2b0j81iujQAFeELyL1TEXGJfLz89m8eTPJyckEBLjH//BO9lfoqFGjeO+992p83AMHDuDr60to6PF/NZ+I3W5n7969REVF4eNTfzlzaSJ1IvPmzaNPnz71du6quOO94y0cDoO/d2Uze8M+Zq/fx8ItBygsdlTYpm1MKP1Tzdad3slNCPbX330ijY2KjL3Mrl27ypanTJnC+PHjWbt2bdm6wMDACtsXFRXh63vy4ssmTWo2C7TNZqvRrO519csvv9CxY8cK6yrr+VbZz1zda+Gs/cQ1rFYLnVqE06lFOLcMbkV+kZ3FWw6aCc+Gvazamc3aPYdZu+cw787ZjK/NQvfESAakRtE/NYqu8eH4qH5HxC3pX24lzJmTi13yqm6jWmxsbNkrPDwci8VS9jk/P5+IiAg+//xzhgwZQkBAAB999BH79+/niiuuID4+nqCgIDp37synn35a4bhDhgxh3LhxZZ9btmzJ//3f/3H99dcTGhpKYmIib7/9dtn3W7ZswWKxsHz5cgBmzpyJxWLh119/pWfPngQFBdGvX78KyRfA008/TXR0NKGhodx444089NBD1XrE1bRp0wo/e2xsbFnS8cQTT9CtWzfeffddUlJS8Pf3xzAMLBYLb775Jueffz7BwcE8/fTTAEyaNIlWrVrh5+dH27Zt+fDDDyucq7L9xD0F+NoY0DqKh85sx7d3DGTJP4bz+pXduaJ3AvGRgRTZDRZuPsBLM9Zx0aS5dH9yBje+v5j3525hQ2ZOtf9tiojrqQWnEkeK7HQY/5NLzv33k2c4bUTXBx98kBdffJHJkyfj7+9Pfn4+PXr04MEHHyQsLIzvvvuOa665hpSUFE455ZRKj/Piiy/y1FNP8cgjjzB16lRuvfVWBg0aRLt27Srd59FHH+XFF1+kWbNm3HLLLVx//fXMmTMHgI8//phnnnmGN954g/79+/PZZ5/x4osvVvoIqiY2bNjA559/zrRp0yp023788ceZMGECL7/8MjabjS+++IK77rqLiRMnctppp/Htt99y3XXXER8fz9ChQyvdTzxHk2A/zukSxzld4jAMg20H8spqd+Zs2E/WkSJ+Wb2HX1bvAY6p32kVRXSYHkmKNFZKcDzcuHHjuPDCCyusu++++8qW77jjDn788Uf+97//VZngnHXWWdx2222AmTS9/PLLzJw5s8oE55lnnmHw4MEAPPTQQ5x99tnk5+cTEBDAa6+9xg033MB1110HwPjx4/n555/Jyck56c/Ur18/rNaKjY9ZWVllyUdhYSEffvghzZo1q7DNlVdeyfXXX1/h8+jRo8t+rnvuuYf58+fzwgsvVEhwjt1PPJPFYiGpqTmmzlWnJGF3GPy9M5tZG/YyZ8M+Fm05yO7sfKYt3c60pduB8vqdAa2b0ju5KSGq3xFpNPSvsRKBvjb+fvIMl53bWXr27Fnhs91u59lnn2XKlCns2LGDgoICCgoKCA4OrvI4Xbp0KVsufRSWmZlZ7X1KpzHIzMwkMTGRtWvXliUWpXr37s1vv/120p9pypQptG/fvsK6o1tWkpKSjktu4PhrsXr1am666aYK6/r3788rr7xS5X7iHWxWC53jw+kcH85tQ1Ir1O/M2bCPv3ZmVajf8bFaaBkVTHigL6EBPoQF+BIWaL6HHrUcdoLvNdmoiPMpwamExWLxiIn/jk1cXnzxRV5++WUmTpxI586dCQ4OZty4cRQWFlZ5nGMLay0WCw6Ho5Ktj9+ntMfX0fsc2wusuvUNCQkJpKamVvp9ZcnaidafKIZj150s+RPvUFq/M6B1FAAHcwuZt2k/s9abCc+2A3lsyDx5C+SJ+NmshAX6kNQ0mAvTWnBu1zjCNBqzSJ24/29wqZFZs2Zx/vnnc/XVVwNmwrF+/frjWkTqW9u2bVm4cCHXXHNN2brFixc3aAzt27dn9uzZXHvttWXr5s6d2+DXQtxTZLAfZ3VuzlmdzdbJjAN5ZBzMI/tIMYfzi8jOLyb7SBHZ+UVHrTOXzfciDhcUYxhQaHewL6eQfTmFLNl6kKe+/ZuzOjfnsp4J9E5uooEJRWpBCY6XSU1NZdq0acydO5fIyEheeukldu/e3eC/1O+44w7GjBlDz5496devH1OmTGHFihWkpKScdN/9+/eze/fuCusiIiJqPAbN/fffz6WXXkpaWhrDhg3jm2++Yfr06fzyyy81Oo4IQEKTIBKa1GwuO4fDILewmOz8YrLyipizYR9TFmewITOH6Ut3MH3pDpKjgrm0ZwIX9WihQQlFakAJjpd57LHH2Lx5M2eccQZBQUHcdNNNjBw5kqys4ycyrE9XXXUVmzZt4r777iM/P59LL72U0aNHs3DhwpPue9pppx237tNPP+Xyyy+vUQwjR47klVde4V//+hd33nknycnJTJ48mSFDhtToOCK1ZbVaCC2p0WkREUiHuDBuHJjM0m0HmbIog29X7GLzvlye+3ENL/y8lqFto7msVwJD2zbT+DwiJ6GRjEtoNFrXGz58OLGxsceNRdPY6d6R+pJTUMx3K3YyZVEGS7cdKlvfLNSfi9LiuaxXAslRqhETz6eRjMVt5OXl8eabb3LGGWdgs9n49NNP+eWXX5gxY4arQxNpNEL8fbisVyKX9Upk/Z7DfL44g+lLd7D3cAFvpm/kzfSN9E5uwmU9Ezirc3MC/dQbS6SUWnBK6K/whnXkyBHOPfdcli5dSkFBAW3btuUf//jHcWP2uAPdO9KQCosd/LZmD1MWZZC+bi+Okv+Dh/r7MLxDDK2iQ4iPDCQ+MoiEJoE0C/FXkbK4PbXgiNsIDAxUMa9ILfj5WBnRqTkjOjVnV9YRpi3ZzpTFGWQcOML0ZTuO2z7A12omO5GBZiF0SeJjJkBBhAeqO7p4JiU4IiJuqnl4ILef2prbhqQyf9N+Fmw+wPaDR8g4mMf2A3nsys4nv8jBhsycSsfoCQvwKUt8EpsGkRIVTEqzEFKaBdM02E+tP+K2lOCIiLg5q9VCv9Qo+qVGVVhfWOxg5yEz4ck4UPqeR8bBI2w/kMf+3EKy84tZtTObVTuzjztuWIBPWbLTqlkIrZqZyU9S0yD8fVTvI42bEhwREQ/l52OlZVQwLSvpaZVbUGy2+BzIY/vBPLbsz2PTvlw27c1hx6EjZOcXszzjEMszDlXYz2qB+MggUpoFkxIVQqto8z01OoRmof4N8JOJnJwSHBERLxXs70Pb2FDaxoYe911+kZ0t+3PZtNdMeDaWvG/am8vhgmK2Hchj24E8Zq7dW2G/lk2D6JPStOwVG67Ce3ENJTgiInKcAF8b7WLDaBdbsceKYRjszSkoSXxKk58cNu3LJeOA2Qq0ZX8eny3KACA5Kpg+KU3KEp6YMCU80jCU4IiISLVZLBaiQwOIDg2gT0rTCt9l5xexeMsB5m86wPxN+/lrRxab9+WyeV8uny40E56UqGBOSWlKn5Qm9E1pSrQSHqknSnBERMQpwgJ8ObVdDKe2iwHMhGfRZjPZmb/pAH/tzDJrfPbl8unCbQCkNAsua905JbkJ0aEat0ecQwmOGzvZ/wRGjRrFe++9V6tjt2zZknHjxjFu3LiTbrd169bj1k+YMIGHHnqoVucWEc8QFuDLsPYxDGtvJjxZR45KeDbvZ9XO7LJHXZ8sMBMeH6uFiCA/mgT7mu9BfkQGm58jg/xoEuxHZOm6ID8ig30J8fdRUiTHUYLjxnbt2lW2PGXKFMaPH8/atWvL1gUGBjZIHE8++SRjxoypsC409PiiRTCf39vtdnx8Kt56hYWF+Pn51fjctd1PRBpeeKAvp3WI4bQOJQlPXhELt5S28Ozn713ZFDsM9uUUsC+noNrH9bWZSVFkkC9+PlZsVis+Vgs2iwWbtfzlY7VgPebdVrKdj81cDvH3JTzQl4ggXyICfQkPKv3sR0SgL0F+NiVTbkIJTmUMA4ryXHNu3yCoxj+g2NjYsuXw8HAsFkuFdd988w1PPPEEq1atIi4ujlGjRvHoo4+WJRdPPPEE7777Lnv27KFp06ZcfPHFvPrqqwwZMoStW7dy9913c/fddwNmYlKZ0NDQCuc92syZMxk6dCg//vgjjz76KCtWrOCnn37in//8J506dcLPz48PPviAjh07kp6eTnp6Ovfffz9//vknTZo0YdSoUTz99NNlMQ8ZMuSE+4mI+wkP8mV4hxiGlyQ8+UV2DuUVcSC3kIN5Ja/cQg7kFnEwr/CY9eZ2R4rsFNkN9h4uYO/h6idFteVrsxAeWDHpCS9JhCIC/Qjys+HnY8Xfx1ryXvFz6bL/Cb7z97Fhsyp5chYlOJUpyoP/i3PNuR/ZCX51myH4p59+4uqrr+bVV19l4MCBbNy4kZtuugmAxx9/nKlTp/Lyyy/z2Wef0bFjR3bv3s2ff/4JwPTp0+natSs33XTTcS0ztfXAAw/wwgsvkJKSQkREBADvv/8+t956K3PmzMEwDHbs2MFZZ53F6NGj+eCDD1izZg1jxowhICCAJ554ouxYx+4nIp4hwNdGbLitRl3LjxTay5KfrCNFFNod2O0GdsPA7ih/FTsMHCXvdsPAbneY64zy74rsBjkFxRzKKyLrSGHJexGHjhRxKK+QIru5zb6cQvblFAK5Tr8Gof4+xIQH0Dw8gNiwkvfwQJqHBxBT8jkiyFetSNWgBMdDPfPMMzz00EOMGjUKgJSUFJ566ikeeOABHn/8cbZt20ZsbCynnXYavr6+JCYm0rt3bwCaNGmCzWarsmXmaA8++CD/+Mc/Kqz79ttvGTJkSNnnJ598kuHDh1fYJjU1leeff77s86OPPkpCQgKvv/46FouFdu3asXPnTh588EHGjx+P1Wo94X4i4r0C/WwE+gUSF1G/j+QNw+BISQtT1pGiSpKgIvKL7BQU2yksdlBQ8iose7dTaHdQUOSo8G53lP+hdrigmMNVTK0B4O9jLUl8zCSoNAEq/RwTFkBUiB8+Nmu9XpPGTglOZXyDzJYUV527jpYsWcKiRYt45plnytbZ7Xby8/PJy8vjkksuYeLEiaSkpDBixAjOOusszj333ONqY6rj/vvvZ/To0RXWtWjRosLnnj17HrffsetWr15N3759K/xl0r9/f3Jycti+fTuJiYmVHktEpD5ZLBaC/HwI8vNxejJVbC9PeA7kFbI7K998ZeezK+sIu7Py2VWybn9uIQXFjrLxhiqPF5oG+xMT5k9MWAAxYf5EhwYcs+xP0xB/j30spgSnMhZLnR8TuZLD4eCf//wnF1544XHfBQQEkJCQwNq1a5kxYwa//PILt912G//6179IT0/H17dmswtHRUWRmppa5TbBwcdfy2PXGYZxXLNr6SOoo9ef6FgiIu7Kx2bFx2YlyA8ig/1o1Syk0m0Liu1kZhewK6s8+dmdbSY/O7PyyczOJ/NwAfajirVPNM9YKasFmoWaSVB0qD+RQX4E+NrMGiFfsy6orGaodL3PCb4/arlJsHkMV1OC46HS0tJYu3ZtlYlHYGAg5513Hueddx5jx46lXbt2rFy5krS0NPz8/LDb7Q0YMXTo0IFp06ZVSHTmzp1LaGjocS1CIiLeyN/HZs7+3qTyln6Hw2B/biGZh/PJzC5gT3Y+e7IL2HPYTID2lKzbl1OAw6Dks/MKtCdf14uhbaOddrzaUoLjocaPH88555xDQkICl1xyCVarlRUrVrBy5Uqefvpp3nvvPex2O6eccgpBQUF8+OGHBAYGkpSUBJjj2/zxxx9cfvnl+Pv7ExUVVem5Dh8+zO7duyusCwoKIiwsrJI9Tuy2225j4sSJ3HHHHdx+++2sXbuWxx9/nHvuuaes/kZERKpmtVpoFupPs1B/OlbRV8buMNifU1CW8Ow5nM+hvKKS2iE7BUWO8uViR8lne1ltUUHR0bVG5dv7N5LaHyU4HuqMM87g22+/5cknn+T555/H19eXdu3aceONNwIQERHBs88+yz333IPdbqdz58588803NG1qDr3+5JNPcvPNN9OqVSsKCgqq7K00fvx4xo8fX2HdzTffzJtvvlmjmFu0aMH333/P/fffT9euXWnSpAk33HDDcQXMIiJSdzarheiwAKLDAuhMuKvDcTqL4UX9bLOzswkPDycrK+u41oX8/Hw2b95McnIyAQGaG0WqT/eOiEj9qur3d2UaRzuSiIiIiBMpwRERERGPowRHREREPI4SHBEREfE4SnCO4UU11+IkumdERBofJTglSkfvzctz0Qzi4rZK75majgAtIiL1R+PglLDZbERERJCZmQmYA9VptlapimEY5OXlkZmZSUREBDab64cmFxERkxKco5TOnF2a5IhUR0RERLVmXRcRkYajBOcoFouF5s2bEx0dTVFRkavDETfg6+urlhsRkUZICc4J2Gw2/dISERFxYyoyFhEREY+jBEdEREQ8jhIcERER8TheVYNTOiBbdna2iyMRERGR6ir9vV2TgVW9KsE5fPgwAAkJCS6ORERERGrq8OHDhIeHV2tbi+FF48w7HA527txJaGhohUH8srOzSUhIICMjg7CwMBdG6L50DetG16/udA3rRtev7nQN66aq62cYBocPHyYuLg6rtXrVNV7VgmO1WomPj6/0+7CwMN2UdaRrWDe6fnWna1g3un51p2tYN5Vdv+q23JRSkbGIiIh4HCU4IiIi4nGU4AD+/v48/vjj+Pv7uzoUt6VrWDe6fnWna1g3un51p2tYN86+fl5VZCwiIiLeQS04IiIi4nGU4IiIiIjHUYIjIiIiHkcJjoiIiHgcJTjAG2+8QXJyMgEBAfTo0YNZs2a5OiS38MQTT2CxWCq8YmNjXR1Wo/bHH39w7rnnEhcXh8Vi4csvv6zwvWEYPPHEE8TFxREYGMiQIUNYtWqVa4JthE52/UaPHn3cPdmnTx/XBNsITZgwgV69ehEaGkp0dDQjR45k7dq1FbbRPVi16lxD3YdVmzRpEl26dCkb0K9v37788MMPZd876x70+gRnypQpjBs3jkcffZRly5YxcOBAzjzzTLZt2+bq0NxCx44d2bVrV9lr5cqVrg6pUcvNzaVr1668/vrrJ/z++eef56WXXuL1119n0aJFxMbGMnz48LJ51Lzdya4fwIgRIyrck99//30DRti4paenM3bsWObPn8+MGTMoLi7m9NNPJzc3t2wb3YNVq841BN2HVYmPj+fZZ59l8eLFLF68mFNPPZXzzz+/LIlx2j1oeLnevXsbt9xyS4V17dq1Mx566CEXReQ+Hn/8caNr166uDsNtAcYXX3xR9tnhcBixsbHGs88+W7YuPz/fCA8PN958800XRNi4HXv9DMMwRo0aZZx//vkuiccdZWZmGoCRnp5uGIbuwdo49hoahu7D2oiMjDTeeecdp96DXt2CU1hYyJIlSzj99NMrrD/99NOZO3eui6JyL+vXrycuLo7k5GQuv/xyNm3a5OqQ3NbmzZvZvXt3hfvR39+fwYMH636sgZkzZxIdHU2bNm0YM2YMmZmZrg6p0crKygKgSZMmgO7B2jj2GpbSfVg9drudzz77jNzcXPr27evUe9CrE5x9+/Zht9uJiYmpsD4mJobdu3e7KCr3ccopp/DBBx/w008/8Z///Ifdu3fTr18/9u/f7+rQ3FLpPaf7sfbOPPNMPv74Y3777TdefPFFFi1axKmnnkpBQYGrQ2t0DMPgnnvuYcCAAXTq1AnQPVhTJ7qGoPuwOlauXElISAj+/v7ccsstfPHFF3To0MGp96BXzSZeGYvFUuGzYRjHrZPjnXnmmWXLnTt3pm/fvrRq1Yr333+fe+65x4WRuTfdj7V32WWXlS136tSJnj17kpSUxHfffceFF17owsgan9tvv50VK1Ywe/bs477TPVg9lV1D3Ycn17ZtW5YvX86hQ4eYNm0ao0aNIj09vex7Z9yDXt2CExUVhc1mOy4rzMzMPC57lJMLDg6mc+fOrF+/3tWhuKXSHmi6H52nefPmJCUl6Z48xh133MHXX3/N77//Tnx8fNl63YPVV9k1PBHdh8fz8/MjNTWVnj17MmHCBLp27corr7zi1HvQqxMcPz8/evTowYwZMyqsnzFjBv369XNRVO6roKCA1atX07x5c1eH4paSk5OJjY2tcD8WFhaSnp6u+7GW9u/fT0ZGhu7JEoZhcPvttzN9+nR+++03kpOTK3yve/DkTnYNT0T34ckZhkFBQYFz70EnFUC7rc8++8zw9fU1/vvf/xp///23MW7cOCM4ONjYsmWLq0Nr9O69915j5syZxqZNm4z58+cb55xzjhEaGqprV4XDhw8by5YtM5YtW2YAxksvvWQsW7bM2Lp1q2EYhvHss88a4eHhxvTp042VK1caV1xxhdG8eXMjOzvbxZE3DlVdv8OHDxv33nuvMXfuXGPz5s3G77//bvTt29do0aKFrl+JW2+91QgPDzdmzpxp7Nq1q+yVl5dXto3uwaqd7BrqPjy5hx9+2Pjjjz+MzZs3GytWrDAeeeQRw2q1Gj///LNhGM67B70+wTEMw/j3v/9tJCUlGX5+fkZaWlqF7n5Sucsuu8xo3ry54evra8TFxRkXXnihsWrVKleH1aj9/vvvBnDca9SoUYZhmN10H3/8cSM2Ntbw9/c3Bg0aZKxcudK1QTciVV2/vLw84/TTTzeaNWtm+Pr6GomJicaoUaOMbdu2uTrsRuNE1w4wJk+eXLaN7sGqnewa6j48ueuvv77sd26zZs2MYcOGlSU3huG8e9BiGIZRyxYlERERkUbJq2twRERExDMpwRERERGPowRHREREPI4SHBEREfE4SnBERETE4yjBEREREY+jBEdEREQ8jhIcERER8ThKcESkzMyZM7FYLBw6dMjVoZzUe++9R0RERI32admyJRMnTqzRPqNHj2bkyJE12kdEXE8JjogHGT16NBaLBYvFgq+vLykpKdx3333k5ua6OjSnu+yyy1i3bp2rwxCRRsrH1QGIiHONGDGCyZMnU1RUxKxZs7jxxhvJzc1l0qRJrg7NqQIDAwkMDHR1GE5ht9uxWCxYrfqbU8RZ9K9JxMP4+/sTGxtLQkICV155JVdddRVffvklAAUFBdx5551ER0cTEBDAgAEDWLRo0QmPk5ubS1hYGFOnTq2w/ptvviE4OJjDhw+zZcsWLBYL06dPZ+jQoQQFBdG1a1fmzZtXYZ9p06bRsWNH/P39admyJS+++GKF71u2bMnTTz/NtddeS0hICElJSXz11Vfs3buX888/n5CQEDp37szixYvL9jn2EdXGjRs5//zziYmJISQkhF69evHLL7/U6NrZ7XbuueceIiIiaNq0KQ888ADHTtdnGAbPP/88KSkpBAYG0rVr1+Ou0ddff03r1q0JDAxk6NChvP/++xUe/ZXG/u2339KhQwf8/f3ZunUrhYWFPPDAA7Ro0YLg4GBOOeUUZs6cWeHYc+fOZdCgQQQGBpKQkMCdd97pkS10InWlBEfEwwUGBlJUVATAAw88wLRp03j//fdZunQpqampnHHGGRw4cOC4/YKDg7n88suZPHlyhfWTJ0/m4osvJjQ0tGzdo48+yn333cfy5ctp06YNV1xxBcXFxQAsWbKESy+9lMsvv5yVK1fyxBNP8Nhjj/Hee+9VOO7LL79M//79WbZsGWeffTbXXHMN1157LVdffXVZrNdee+1xCUepnJwczjrrLH755ReWLVvGGWecwbnnnsu2bduqfa1efPFF3n33Xf773/8ye/ZsDhw4wBdffFFhm3/84x9MnjyZSZMmsWrVKu6++26uvvpq0tPTAdiyZQsXX3wxI0eOZPny5dx88808+uijx50rLy+PCRMm8M4777Bq1Sqio6O57rrrmDNnDp999hkrVqzgkksuYcSIEaxfvx6AlStXcsYZZ3DhhReyYsUKpkyZwuzZs7n99tur/TOKeA0nzX4uIo3AqFGjjPPPP7/s84IFC4ymTZsal156qZGTk2P4+voaH3/8cdn3hYWFRlxcnPH8888bhmEYv//+uwEYBw8eLNvfZrMZO3bsMAzDMPbu3Wv4+voaM2fONAzDMDZv3mwAxjvvvFN2zFWrVhmAsXr1asMwDOPKK680hg8fXiHO+++/3+jQoUPZ56SkJOPqq68u+7xr1y4DMB577LGydfPmzTMAY9euXYZhGMbkyZON8PDwKq9Hhw4djNdee63CeV5++eVKt2/evLnx7LPPln0uKioy4uPjy65pTk6OERAQYMydO7fCfjfccINxxRVXGIZhGA8++KDRqVOnCt8/+uijFa7r5MmTDcBYvnx52TYbNmwwLBZL2bUuNWzYMOPhhx82DMMwrrnmGuOmm26q8P2sWbMMq9VqHDlypIorIeJ91IIj4mG+/fZbQkJCCAgIoG/fvgwaNIjXXnuNjRs3UlRURP/+/cu29fX1pXfv3qxevfqEx+rduzcdO3bkgw8+AODDDz8kMTGRQYMGVdiuS5cuZcvNmzcHIDMzE4DVq1dXOCdA//79Wb9+PXa7/YTHiImJAaBz587HrSs97rFyc3N54IEH6NChAxEREYSEhLBmzZpqt+BkZWWxa9cu+vbtW7bOx8eHnj17ln3++++/yc/PZ/jw4YSEhJS9PvjgAzZu3AjA2rVr6dWrV4Vj9+7d+7jz+fn5VfiZly5dimEYtGnTpsKx09PTy469ZMkS3nvvvQrfn3HGGTgcDjZv3lytn1PEW6jIWMTDDB06lEmTJuHr60tcXBy+vr4A7Nq1CwCLxVJhe8Mwjlt3tBtvvJHXX3+dhx56iMmTJ3Pdddcdt33pOY4+vsPhqPT4xgkeM53oGFUd91j3338/P/30Ey+88AKpqakEBgZy8cUXU1hYWOnPVlOl5/7uu+9o0aJFhe/8/f2B6v+8gYGBFbZzOBzYbDaWLFmCzWarsG1ISEjZNjfffDN33nnnccdLTEysxU8k4rmU4Ih4mODgYFJTU49bn5qaip+fH7Nnz+bKK68EoKioiMWLFzNu3LhKj3f11VfzwAMP8Oqrr7Jq1SpGjRpVo3g6dOjA7NmzK6ybO3cubdq0Oe4XeV3MmjWL0aNHc8EFFwBmTc6WLVuqvX94eDjNmzdn/vz5ZS1UxcXFLFmyhLS0NICyguBt27YxePDgEx6nXbt2fP/99xXWHV0cXZnu3btjt9vJzMxk4MCBJ9wmLS2NVatWnfC/r4hUpARHxEsEBwdz6623cv/999OkSRMSExN5/vnnycvL44Ybbqh0v8jISC688ELuv/9+Tj/9dOLj42t03nvvvZdevXrx1FNPcdlllzFv3jxef/113njjjbr+SBWkpqYyffp0zj33XCwWC4899lilrT2Vueuuu3j22Wdp3bo17du356WXXqow6GFoaCj33Xcfd999Nw6HgwEDBpCdnc3cuXMJCQlh1KhR3Hzzzbz00ks8+OCD3HDDDSxfvrysoLqqlrI2bdpw1VVXce211/Liiy/SvXt39u3bx2+//Ubnzp0566yzePDBB+nTpw9jx45lzJgxBAcHs3r1ambMmMFrr71Wm8sm4rFUgyPiRZ599lkuuugirrnmGtLS0tiwYQM//fQTkZGRVe53ww03UFhYyPXXX1/jc6alpfH555/z2Wef0alTJ8aPH8+TTz7J6NGja/lTnNjLL79MZGQk/fr149xzz+WMM84oa3mprnvvvZdrr72W0aNH07dvX0JDQ8tahEo99dRTjB8/ngkTJtC+fXvOOOMMvvnmG5KTkwFITk5m6tSpTJ8+nS5dujBp0qSyXlSlj7EqM3nyZK699lruvfde2rZty3nnnceCBQtISEgAzDql9PR01q9fz8CBA+nevTuPPfZYWd2TiJSzGCd6OCwicpSPP/6Yu+66i507d+Ln5+fqcNzOM888w5tvvklGRoarQxHxGnpEJSKVysvLY/PmzUyYMIGbb75ZyU01vfHGG/Tq1YumTZsyZ84c/vWvf2msGpEGpkdUIlKp559/nm7duhETE8PDDz/s6nDcxvr16zn//PPp0KEDTz31FPfeey9PPPGEq8MS8Sp6RCUiIiIeRy04IiIi4nGU4IiIiIjHUYIjIiIiHkcJjoiIiHgcJTgiIiLicZTgiIiIiMdRgiMiIiIeRwmOiIiIeJz/B0YMUMrYhsNdAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_69_9.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": "2c6c9e89",
   "metadata": {
    "editable": true
   },
   "source": [
    "## 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). \n",
    "\n",
    "* Define a range of interest for the penalty parameter.\n",
    "\n",
    "* Divide the data set into training and test set comprising samples $\\{1, \\ldots, n\\} \\setminus i$ and $\\{ i \\}$, respectively.\n",
    "\n",
    "* Fit the linear regression model by means of ridge estimation  for each $\\lambda$ in the grid using the training set, and the corresponding estimate of the error variance $\\boldsymbol{\\sigma}_{-i}^2(\\lambda)$, as"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71738b2a",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\begin{align*}\n",
    "\\boldsymbol{\\beta}_{-i}(\\lambda) & =  ( \\boldsymbol{X}_{-i, \\ast}^{T}\n",
    "\\boldsymbol{X}_{-i, \\ast} + \\lambda \\boldsymbol{I}_{pp})^{-1}\n",
    "\\boldsymbol{X}_{-i, \\ast}^{T} \\boldsymbol{y}_{-i}\n",
    "\\end{align*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14db46b6",
   "metadata": {
    "editable": true
   },
   "source": [
    "* Evaluate the prediction performance of these models on the test set by $\\log\\{L[y_i, \\boldsymbol{X}_{i, \\ast}; \\boldsymbol{\\beta}_{-i}(\\lambda), \\boldsymbol{\\sigma}_{-i}^2(\\lambda)]\\}$. Or, by the prediction error $|y_i - \\boldsymbol{X}_{i, \\ast} \\boldsymbol{\\beta}_{-i}(\\lambda)|$, the relative error, the error squared or the R2 score function.\n",
    "\n",
    "* Repeat the first three steps  such that each sample plays the role of the test set once.\n",
    "\n",
    "* Average the prediction performances of the test sets at each grid point of the penalty bias/parameter. It is an estimate of the prediction performance of the model corresponding to this value of the penalty parameter on novel data. It is defined as"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "95e5c8e4",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\begin{align*}\n",
    "\\frac{1}{n} \\sum_{i = 1}^n \\log\\{L[y_i, \\mathbf{X}_{i, \\ast}; \\boldsymbol{\\beta}_{-i}(\\lambda), \\boldsymbol{\\sigma}_{-i}^2(\\lambda)]\\}.\n",
    "\\end{align*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e60f51d",
   "metadata": {
    "editable": true
   },
   "source": [
    "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\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": 8,
   "id": "2cef0eb7",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
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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==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_75_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": "f501c9cf",
   "metadata": {
    "editable": true
   },
   "source": [
    "More examples of the application of cross-validation follow here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "30e1e320",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58739/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10\n",
      "  plt.plot(polynomial, np.log10(estimated_mse_sklearn), label='Test Error')\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_77_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()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "383e5c2a",
   "metadata": {
    "editable": true
   },
   "source": [
    "Note that we have kept the intercept in the first column of design matrix $\\boldsymbol{X}$. When we call the corresponding **Scikit-Learn** function we need thus to set the intercept to **False**. Libraries like **Scikit-Learn** normally scale the design matrix and do not fit intercept. See the discussions below."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f9cd409",
   "metadata": {
    "editable": true
   },
   "source": [
    "## More on Rescaling data\n",
    "\n",
    "We end this chapter by adding some words on scaling and how to deal with the intercept for regression cases.\n",
    "\n",
    "When you are comparing your own code with for example **Scikit-Learn**'s\n",
    "library, there are some technicalities to keep in mind.  The examples\n",
    "here demonstrate some of these aspects with potential pitfalls.\n",
    "\n",
    "The discussion here focuses on the role of the intercept, how we can\n",
    "set up the design matrix, what scaling we should use and other topics\n",
    "which tend  confuse us.\n",
    "\n",
    "The intercept can be interpreted as the expected value of our\n",
    "target/output variables when all other predictors are set to zero.\n",
    "Thus, if we cannot assume that the expected outputs/targets are zero\n",
    "when all predictors are zero (the columns in the design matrix), it\n",
    "may be a bad idea to implement a model which penalizes the intercept.\n",
    "Furthermore, in for example Ridge and Lasso regression, the default solutions\n",
    "from the library **Scikit-Learn** (when not shrinking $\\beta_0$) for the unknown parameters\n",
    "$\\boldsymbol{\\beta}$, are derived under the assumption that both $\\boldsymbol{y}$ and\n",
    "$\\boldsymbol{X}$ are zero centered, that is we subtract the mean values.\n",
    "\n",
    "If our predictors represent different scales, then it is important to\n",
    "standardize the design matrix $\\boldsymbol{X}$ by subtracting the mean of each\n",
    "column from the corresponding column and dividing the column with its\n",
    "standard deviation. Most machine learning libraries do this as a default. This means that if you compare your code with the results from a given library,\n",
    "the results may differ. \n",
    "\n",
    "The\n",
    "[Standardscaler](https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.StandardScaler.html)\n",
    "function in **Scikit-Learn** does this for us.  For the data sets we\n",
    "have been studying in our various examples, the data are in many cases\n",
    "already scaled and there is no need to scale them. You as a user of different machine learning algorithms, should always perform  a\n",
    "survey of your data, with a critical assessment of them in case you need to scale the data.\n",
    "\n",
    "If you need to scale the data, not doing so will give an *unfair*\n",
    "penalization of the parameters since their magnitude depends on the\n",
    "scale of their corresponding predictor.\n",
    "\n",
    "Suppose as an example that you \n",
    "you have an input variable given by the heights of different persons.\n",
    "Human height might be measured in inches or meters or\n",
    "kilometers. If measured in kilometers, a standard linear regression\n",
    "model with this predictor would probably give a much bigger\n",
    "coefficient term, than if measured in millimeters.\n",
    "This can clearly lead to problems in evaluating the cost/loss functions.\n",
    "\n",
    "Keep in mind that when you transform your data set before training a model, the same transformation needs to be done\n",
    "on your eventual new data set  before making a prediction. If we translate this into a Python code, it would could be implemented as follows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "eab81633",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\n#Model training, we compute the mean value of y and X\\ny_train_mean = np.mean(y_train)\\nX_train_mean = np.mean(X_train,axis=0)\\nX_train = X_train - X_train_mean\\ny_train = y_train - y_train_mean\\n\\n# The we fit our model with the training data\\ntrained_model = some_model.fit(X_train,y_train)\\n\\n\\n#Model prediction, we need also to transform our data set used for the prediction.\\nX_test = X_test - X_train_mean #Use mean from training data\\ny_pred = trained_model(X_test)\\ny_pred = y_pred + y_train_mean\\n'"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "#Model training, we compute the mean value of y and X\n",
    "y_train_mean = np.mean(y_train)\n",
    "X_train_mean = np.mean(X_train,axis=0)\n",
    "X_train = X_train - X_train_mean\n",
    "y_train = y_train - y_train_mean\n",
    "\n",
    "# The we fit our model with the training data\n",
    "trained_model = some_model.fit(X_train,y_train)\n",
    "\n",
    "\n",
    "#Model prediction, we need also to transform our data set used for the prediction.\n",
    "X_test = X_test - X_train_mean #Use mean from training data\n",
    "y_pred = trained_model(X_test)\n",
    "y_pred = y_pred + y_train_mean\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ca51a54",
   "metadata": {
    "editable": true
   },
   "source": [
    "Let us try to understand what this may imply mathematically when we\n",
    "subtract the mean values, also known as *zero centering*. For\n",
    "simplicity, we will focus on  ordinary regression, as done in the above example.\n",
    "\n",
    "The cost/loss function  for regression is"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa3a4110",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "C(\\beta_0, \\beta_1, ... , \\beta_{p-1}) = \\frac{1}{n}\\sum_{i=0}^{n} \\left(y_i - \\beta_0 - \\sum_{j=1}^{p-1} X_{ij}\\beta_j\\right)^2,.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f499302",
   "metadata": {
    "editable": true
   },
   "source": [
    "Recall also that we use the squared value. This expression can lead to an\n",
    "increased penalty for higher differences between predicted and\n",
    "output/target values.\n",
    "\n",
    "What we have done is to single out the $\\beta_0$ term in the\n",
    "definition of the mean squared error (MSE).  The design matrix $X$\n",
    "does in this case not contain any intercept column.  When we take the\n",
    "derivative with respect to $\\beta_0$, we want the derivative to obey"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1f7ba52",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\frac{\\partial C}{\\partial \\beta_j} = 0,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ff75b7f",
   "metadata": {
    "editable": true
   },
   "source": [
    "for all $j$. For $\\beta_0$ we have"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eac37d3c",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\frac{\\partial C}{\\partial \\beta_0} = -\\frac{2}{n}\\sum_{i=0}^{n-1} \\left(y_i - \\beta_0 - \\sum_{j=1}^{p-1} X_{ij} \\beta_j\\right).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e653464",
   "metadata": {
    "editable": true
   },
   "source": [
    "Multiplying away the constant $2/n$, we obtain"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8afa60a1",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\sum_{i=0}^{n-1} \\beta_0 = \\sum_{i=0}^{n-1}y_i - \\sum_{i=0}^{n-1} \\sum_{j=1}^{p-1} X_{ij} \\beta_j.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "055b7975",
   "metadata": {
    "editable": true
   },
   "source": [
    "Let us specialize first to the case where we have only two parameters $\\beta_0$ and $\\beta_1$.\n",
    "Our result for $\\beta_0$ simplifies then to"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2bf6e5d",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "n\\beta_0 = \\sum_{i=0}^{n-1}y_i - \\sum_{i=0}^{n-1} X_{i1} \\beta_1.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e15afbd5",
   "metadata": {
    "editable": true
   },
   "source": [
    "We obtain then"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2f9a064",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\beta_0 = \\frac{1}{n}\\sum_{i=0}^{n-1}y_i - \\beta_1\\frac{1}{n}\\sum_{i=0}^{n-1} X_{i1}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e8035d8",
   "metadata": {
    "editable": true
   },
   "source": [
    "If we define"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0bbcef44",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\mu_{\\boldsymbol{x}_1}=\\frac{1}{n}\\sum_{i=0}^{n-1} X_{i1},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "919462c2",
   "metadata": {
    "editable": true
   },
   "source": [
    "and the mean value of the outputs as"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a0899ec",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\mu_y=\\frac{1}{n}\\sum_{i=0}^{n-1}y_i,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b255ec5",
   "metadata": {
    "editable": true
   },
   "source": [
    "we have"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7716aca1",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\beta_0 = \\mu_y - \\beta_1\\mu_{\\boldsymbol{x}_1}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24863f48",
   "metadata": {
    "editable": true
   },
   "source": [
    "In the general case with more parameters than $\\beta_0$ and $\\beta_1$, we have"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c10f940",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\beta_0 = \\frac{1}{n}\\sum_{i=0}^{n-1}y_i - \\frac{1}{n}\\sum_{i=0}^{n-1}\\sum_{j=1}^{p-1} X_{ij}\\beta_j.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7afefe95",
   "metadata": {
    "editable": true
   },
   "source": [
    "We can rewrite the latter equation as"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2e7bc1a",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\beta_0 = \\frac{1}{n}\\sum_{i=0}^{n-1}y_i - \\sum_{j=1}^{p-1} \\mu_{\\boldsymbol{x}_j}\\beta_j,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ded7d78",
   "metadata": {
    "editable": true
   },
   "source": [
    "where we have defined"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bcac7366",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\mu_{\\boldsymbol{x}_j}=\\frac{1}{n}\\sum_{i=0}^{n-1} X_{ij},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bafe8156",
   "metadata": {
    "editable": true
   },
   "source": [
    "the mean value for all elements of the column vector $\\boldsymbol{x}_j$.\n",
    "\n",
    "Replacing $y_i$ with $y_i - y_i - \\overline{\\boldsymbol{y}}$ and centering also our design matrix results in a cost function (in vector-matrix disguise)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c91d280",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "C(\\boldsymbol{\\beta}) = (\\boldsymbol{\\tilde{y}} - \\tilde{X}\\boldsymbol{\\beta})^T(\\boldsymbol{\\tilde{y}} - \\tilde{X}\\boldsymbol{\\beta}).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b81d6de",
   "metadata": {
    "editable": true
   },
   "source": [
    "If we minimize with respect to $\\boldsymbol{\\beta}$ we have then"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d6d497e",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\hat{\\boldsymbol{\\beta}} = (\\tilde{X}^T\\tilde{X})^{-1}\\tilde{X}^T\\boldsymbol{\\tilde{y}},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "772593b2",
   "metadata": {
    "editable": true
   },
   "source": [
    "where $\\boldsymbol{\\tilde{y}} = \\boldsymbol{y} - \\overline{\\boldsymbol{y}}$\n",
    "and $\\tilde{X}_{ij} = X_{ij} - \\frac{1}{n}\\sum_{k=0}^{n-1}X_{kj}$.\n",
    "\n",
    "For Ridge regression we need to add $\\lambda \\boldsymbol{\\beta}^T\\boldsymbol{\\beta}$ to the cost function and get then"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3edbdb56",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\hat{\\boldsymbol{\\beta}} = (\\tilde{X}^T\\tilde{X} + \\lambda I)^{-1}\\tilde{X}^T\\boldsymbol{\\tilde{y}}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7de9723e",
   "metadata": {
    "editable": true
   },
   "source": [
    "What does this mean? And why do we insist on all this? Let us look at some examples.\n",
    "\n",
    "This code shows a simple first-order fit to a data set using the above transformed data, where we consider the role of the intercept first, by either excluding it or including it (*code example thanks to  Øyvind Sigmundson Schøyen*). Here our scaling of the data is done by subtracting the mean values only.\n",
    "Note also that we do not split the data into training and test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "2e4a0363",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True beta: [2, 0.5, 3.7]\n",
      "Fitted beta: [2.08376632 0.19569961 3.97898392]\n",
      "Sklearn fitted beta: [2.08376632 0.19569961 3.97898392]\n",
      "MSE with intercept column\n",
      "0.00411363461744314\n",
      "MSE with intercept column from SKL\n",
      "0.004113634617443147\n",
      "Manual intercept: 2.083766322923899\n",
      "Fitted beta (wiothout intercept): [0.19569961 3.97898392]\n",
      "Sklearn intercept: 2.0837663229239043\n",
      "Sklearn fitted beta (without intercept): [0.19569961 3.97898392]\n",
      "MSE with Manual intercept\n",
      "0.00411363461744314\n",
      "MSE with Sklearn intercept\n",
      "0.004113634617443131\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_112_1.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "\n",
    "np.random.seed(2021)\n",
    "\n",
    "def MSE(y_data,y_model):\n",
    "    n = np.size(y_model)\n",
    "    return np.sum((y_data-y_model)**2)/n\n",
    "\n",
    "\n",
    "def fit_beta(X, y):\n",
    "    return np.linalg.pinv(X.T @ X) @ X.T @ y\n",
    "\n",
    "\n",
    "true_beta = [2, 0.5, 3.7]\n",
    "\n",
    "x = np.linspace(0, 1, 11)\n",
    "y = np.sum(\n",
    "    np.asarray([x ** p * b for p, b in enumerate(true_beta)]), axis=0\n",
    ") + 0.1 * np.random.normal(size=len(x))\n",
    "\n",
    "degree = 3\n",
    "X = np.zeros((len(x), degree))\n",
    "\n",
    "# Include the intercept in the design matrix\n",
    "for p in range(degree):\n",
    "    X[:, p] = x ** p\n",
    "\n",
    "beta = fit_beta(X, y)\n",
    "\n",
    "# Intercept is included in the design matrix\n",
    "skl = LinearRegression(fit_intercept=False).fit(X, y)\n",
    "\n",
    "print(f\"True beta: {true_beta}\")\n",
    "print(f\"Fitted beta: {beta}\")\n",
    "print(f\"Sklearn fitted beta: {skl.coef_}\")\n",
    "ypredictOwn = X @ beta\n",
    "ypredictSKL = skl.predict(X)\n",
    "print(f\"MSE with intercept column\")\n",
    "print(MSE(y,ypredictOwn))\n",
    "print(f\"MSE with intercept column from SKL\")\n",
    "print(MSE(y,ypredictSKL))\n",
    "\n",
    "\n",
    "plt.figure()\n",
    "plt.scatter(x, y, label=\"Data\")\n",
    "plt.plot(x, X @ beta, label=\"Fit\")\n",
    "plt.plot(x, skl.predict(X), label=\"Sklearn (fit_intercept=False)\")\n",
    "\n",
    "\n",
    "# Do not include the intercept in the design matrix\n",
    "X = np.zeros((len(x), degree - 1))\n",
    "\n",
    "for p in range(degree - 1):\n",
    "    X[:, p] = x ** (p + 1)\n",
    "\n",
    "# Intercept is not included in the design matrix\n",
    "skl = LinearRegression(fit_intercept=True).fit(X, y)\n",
    "\n",
    "# Use centered values for X and y when computing coefficients\n",
    "y_offset = np.average(y, axis=0)\n",
    "X_offset = np.average(X, axis=0)\n",
    "\n",
    "beta = fit_beta(X - X_offset, y - y_offset)\n",
    "intercept = np.mean(y_offset - X_offset @ beta)\n",
    "\n",
    "print(f\"Manual intercept: {intercept}\")\n",
    "print(f\"Fitted beta (wiothout intercept): {beta}\")\n",
    "print(f\"Sklearn intercept: {skl.intercept_}\")\n",
    "print(f\"Sklearn fitted beta (without intercept): {skl.coef_}\")\n",
    "ypredictOwn = X @ beta\n",
    "ypredictSKL = skl.predict(X)\n",
    "print(f\"MSE with Manual intercept\")\n",
    "print(MSE(y,ypredictOwn+intercept))\n",
    "print(f\"MSE with Sklearn intercept\")\n",
    "print(MSE(y,ypredictSKL))\n",
    "\n",
    "plt.plot(x, X @ beta + intercept, \"--\", label=\"Fit (manual intercept)\")\n",
    "plt.plot(x, skl.predict(X), \"--\", label=\"Sklearn (fit_intercept=True)\")\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6d3a071",
   "metadata": {
    "editable": true
   },
   "source": [
    "The intercept is the value of our output/target variable\n",
    "when all our features are zero and our function crosses the $y$-axis (for a one-dimensional case). \n",
    "\n",
    "Printing the MSE, we see first that both methods give the same MSE, as\n",
    "they should.  However, when we move to for example Ridge regression,\n",
    "the way we treat the intercept may give a larger or smaller MSE,\n",
    "meaning that the MSE can be penalized by the value of the\n",
    "intercept. Not including the intercept in the fit, means that the\n",
    "regularization term does not include $\\beta_0$. For different values\n",
    "of $\\lambda$, this may lead to different MSE values. \n",
    "\n",
    "To remind the reader, the regularization term, with the intercept in Ridge regression, is given by"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db803b77",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\lambda \\vert\\vert \\boldsymbol{\\beta} \\vert\\vert_2^2 = \\lambda \\sum_{j=0}^{p-1}\\beta_j^2,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7a9c9d8",
   "metadata": {
    "editable": true
   },
   "source": [
    "but when we take out the intercept, this equation becomes"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e08af763",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\lambda \\vert\\vert \\boldsymbol{\\beta} \\vert\\vert_2^2 = \\lambda \\sum_{j=1}^{p-1}\\beta_j^2.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10fe24e4",
   "metadata": {
    "editable": true
   },
   "source": [
    "For Lasso regression we have"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6feb3bdd",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\lambda \\vert\\vert \\boldsymbol{\\beta} \\vert\\vert_1 = \\lambda \\sum_{j=1}^{p-1}\\vert\\beta_j\\vert.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "657a0777",
   "metadata": {
    "editable": true
   },
   "source": [
    "It means that, when scaling the design matrix and the outputs/targets,\n",
    "by subtracting the mean values, we have an optimization problem which\n",
    "is not penalized by the intercept. The MSE value can then be smaller\n",
    "since it focuses only on the remaining quantities. If we however bring\n",
    "back the intercept, we will get a MSE which then contains the\n",
    "intercept.\n",
    "\n",
    "Armed with this wisdom, we attempt first to simply set the intercept equal to **False** in our implementation of Ridge regression for our well-known  vanilla data set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "9f21317d",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Beta values for own Ridge implementation\n",
      "[ 1.03032441e+00  6.28336218e-02 -6.24175744e-01  5.21169159e-02\n",
      "  2.80847477e-01  2.12552073e-01  8.13220608e-02 -1.69634577e-02\n",
      " -6.50846111e-02 -7.38962192e-02 -5.94226022e-02 -3.50227564e-02\n",
      " -9.80609616e-03  1.08299273e-02  2.41882037e-02  2.93492130e-02\n",
      "  2.64742912e-02  1.63249532e-02 -5.01831050e-05 -2.15098090e-02]\n",
      "Beta values for Scikit-Learn Ridge implementation\n",
      "[ 1.03032441e+00  6.28336218e-02 -6.24175744e-01  5.21169159e-02\n",
      "  2.80847477e-01  2.12552073e-01  8.13220608e-02 -1.69634577e-02\n",
      " -6.50846112e-02 -7.38962192e-02 -5.94226022e-02 -3.50227564e-02\n",
      " -9.80609615e-03  1.08299273e-02  2.41882037e-02  2.93492130e-02\n",
      "  2.64742912e-02  1.63249532e-02 -5.01831190e-05 -2.15098090e-02]\n",
      "MSE values for own Ridge implementation\n",
      "4.3632959111950474e-07\n",
      "MSE values for Scikit-Learn Ridge implementation\n",
      "4.363295916366933e-07\n",
      "Beta values for own Ridge implementation\n",
      "[ 1.03630548 -0.01963611 -0.37900111 -0.07062318  0.12182967  0.16343471\n",
      "  0.13003291  0.07490892  0.02365049 -0.01449782 -0.03814292 -0.04909093\n",
      " -0.05009826 -0.04389027 -0.03279636 -0.01866537 -0.00289724  0.01348565\n",
      "  0.02976145  0.04543942]\n",
      "Beta values for Scikit-Learn Ridge implementation\n",
      "[ 1.03630548 -0.01963611 -0.37900111 -0.07062318  0.12182967  0.16343471\n",
      "  0.13003291  0.07490892  0.02365049 -0.01449782 -0.03814292 -0.04909093\n",
      " -0.05009826 -0.04389027 -0.03279636 -0.01866537 -0.00289724  0.01348565\n",
      "  0.02976145  0.04543942]\n",
      "MSE values for own Ridge implementation\n",
      "5.194042826649355e-06\n",
      "MSE values for Scikit-Learn Ridge implementation\n",
      "5.194042826815211e-06\n",
      "Beta values for own Ridge implementation\n",
      "[ 1.04220758 -0.10931453 -0.17641709 -0.06020587  0.02208512  0.05789007\n",
      "  0.06491736  0.05785343  0.04537385  0.03196357  0.01969145  0.00934499\n",
      "  0.00107405 -0.00526348 -0.00992331 -0.01318643 -0.01531845 -0.01655318\n",
      " -0.01708852 -0.01708781]\n",
      "Beta values for Scikit-Learn Ridge implementation\n",
      "[ 1.04220758 -0.10931453 -0.17641709 -0.06020587  0.02208512  0.05789007\n",
      "  0.06491736  0.05785343  0.04537385  0.03196357  0.01969145  0.00934499\n",
      "  0.00107405 -0.00526348 -0.00992331 -0.01318643 -0.01531845 -0.01655318\n",
      " -0.01708852 -0.01708781]\n",
      "MSE values for own Ridge implementation\n",
      "2.0940821989652176e-05\n",
      "MSE values for Scikit-Learn Ridge implementation\n",
      "2.0940821989627646e-05\n",
      "Beta values for own Ridge implementation\n",
      "[ 1.01219292 -0.06043581 -0.10391807 -0.05651951 -0.01898855  0.00312361\n",
      "  0.01463049  0.01975848  0.02123176  0.02068067  0.01905883  0.01691985\n",
      "  0.01458337  0.01223198  0.00996754  0.00784393  0.00588657  0.00410387\n",
      "  0.00249435  0.00105081]\n",
      "Beta values for Scikit-Learn Ridge implementation\n",
      "[ 1.01219292 -0.06043581 -0.10391807 -0.05651951 -0.01898855  0.00312361\n",
      "  0.01463049  0.01975848  0.02123176  0.02068067  0.01905883  0.01691985\n",
      "  0.01458337  0.01223198  0.00996754  0.00784393  0.00588657  0.00410387\n",
      "  0.00249435  0.00105081]\n",
      "MSE values for own Ridge implementation\n",
      "0.00031535148309577417\n",
      "MSE values for Scikit-Learn Ridge implementation\n",
      "0.0003153514830958095\n",
      "Beta values for own Ridge implementation\n",
      "[ 8.38916861e-01  1.31276579e-01  8.97497404e-03 -1.72271878e-02\n",
      " -2.11744554e-02 -1.91492986e-02 -1.57201944e-02 -1.23002365e-02\n",
      " -9.30466214e-03 -6.81048318e-03 -4.78184120e-03 -3.15130074e-03\n",
      " -1.84923989e-03 -8.13661243e-04  7.46984697e-06  6.56636616e-04\n",
      "  1.16805821e-03  1.56912044e-03  1.88168312e-03  2.12318726e-03]\n",
      "Beta values for Scikit-Learn Ridge implementation\n",
      "[ 8.38916861e-01  1.31276579e-01  8.97497404e-03 -1.72271878e-02\n",
      " -2.11744554e-02 -1.91492986e-02 -1.57201944e-02 -1.23002365e-02\n",
      " -9.30466214e-03 -6.81048318e-03 -4.78184120e-03 -3.15130074e-03\n",
      " -1.84923989e-03 -8.13661243e-04  7.46984697e-06  6.56636616e-04\n",
      "  1.16805821e-03  1.56912044e-03  1.88168312e-03  2.12318726e-03]\n",
      "MSE values for own Ridge implementation\n",
      "0.01507238889517717\n",
      "MSE values for Scikit-Learn Ridge implementation\n",
      "0.01507238889517706\n",
      "Beta values for own Ridge implementation\n",
      "[0.37396662 0.14174745 0.0764924  0.04892055 0.03447512 0.02586427\n",
      " 0.02024962 0.01633913 0.01347916 0.0113104  0.0096208  0.00827728\n",
      " 0.00719176 0.00630331 0.00556826 0.0049544  0.00443743 0.0039987\n",
      " 0.0036237  0.003301  ]\n",
      "Beta values for Scikit-Learn Ridge implementation\n",
      "[0.37396662 0.14174745 0.0764924  0.04892055 0.03447512 0.02586427\n",
      " 0.02024962 0.01633913 0.01347916 0.0113104  0.0096208  0.00827728\n",
      " 0.00719176 0.00630331 0.00556826 0.0049544  0.00443743 0.0039987\n",
      " 0.0036237  0.003301  ]\n",
      "MSE values for own Ridge implementation\n",
      "0.2640931530791004\n",
      "MSE values for Scikit-Learn Ridge implementation\n",
      "0.26409315307910025\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_120_1.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn import linear_model\n",
    "\n",
    "def MSE(y_data,y_model):\n",
    "    n = np.size(y_model)\n",
    "    return np.sum((y_data-y_model)**2)/n\n",
    "\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",
    "n = 100\n",
    "x = np.random.rand(n)\n",
    "y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)\n",
    "\n",
    "Maxpolydegree = 20\n",
    "X = np.zeros((n,Maxpolydegree))\n",
    "#We include explicitely the intercept column\n",
    "for degree in range(Maxpolydegree):\n",
    "    X[:,degree] = x**degree\n",
    "# We split the data in test and training data\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n",
    "\n",
    "p = Maxpolydegree\n",
    "I = np.eye(p,p)\n",
    "# Decide which values of lambda to use\n",
    "nlambdas = 6\n",
    "MSEOwnRidgePredict = np.zeros(nlambdas)\n",
    "MSERidgePredict = np.zeros(nlambdas)\n",
    "lambdas = np.logspace(-4, 2, nlambdas)\n",
    "for i in range(nlambdas):\n",
    "    lmb = lambdas[i]\n",
    "    OwnRidgeBeta = np.linalg.pinv(X_train.T @ X_train+lmb*I) @ X_train.T @ y_train\n",
    "    # Note: we include the intercept column and no scaling\n",
    "    RegRidge = linear_model.Ridge(lmb,fit_intercept=False)\n",
    "    RegRidge.fit(X_train,y_train)\n",
    "    # and then make the prediction\n",
    "    ytildeOwnRidge = X_train @ OwnRidgeBeta\n",
    "    ypredictOwnRidge = X_test @ OwnRidgeBeta\n",
    "    ytildeRidge = RegRidge.predict(X_train)\n",
    "    ypredictRidge = RegRidge.predict(X_test)\n",
    "    MSEOwnRidgePredict[i] = MSE(y_test,ypredictOwnRidge)\n",
    "    MSERidgePredict[i] = MSE(y_test,ypredictRidge)\n",
    "    print(\"Beta values for own Ridge implementation\")\n",
    "    print(OwnRidgeBeta)\n",
    "    print(\"Beta values for Scikit-Learn Ridge implementation\")\n",
    "    print(RegRidge.coef_)\n",
    "    print(\"MSE values for own Ridge implementation\")\n",
    "    print(MSEOwnRidgePredict[i])\n",
    "    print(\"MSE values for Scikit-Learn Ridge implementation\")\n",
    "    print(MSERidgePredict[i])\n",
    "\n",
    "# Now plot the results\n",
    "plt.figure()\n",
    "plt.plot(np.log10(lambdas), MSEOwnRidgePredict, 'r', label = 'MSE own Ridge Test')\n",
    "plt.plot(np.log10(lambdas), MSERidgePredict, 'g', label = 'MSE Ridge Test')\n",
    "\n",
    "plt.xlabel('log10(lambda)')\n",
    "plt.ylabel('MSE')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20de82fd",
   "metadata": {
    "editable": true
   },
   "source": [
    "The results here agree when we force **Scikit-Learn**'s Ridge function to include the first column in our design matrix.\n",
    "We see that the results agree very well. Here we have thus explicitely included the intercept column in the design matrix.\n",
    "What happens if we do not include the intercept in our fit?\n",
    "Let us see how we can change this code by zero centering."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "4138ed50",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Beta values for own Ridge implementation\n",
      "[ 3.43579948e-02 -5.43330971e-01 -3.10141413e-03  2.47116868e-01\n",
      "  2.18613217e-01  1.02054837e-01 -4.25617658e-04 -5.90475506e-02\n",
      " -7.68534263e-02 -6.68929213e-02 -4.24906604e-02 -1.40927184e-02\n",
      "  1.11482289e-02  2.88529063e-02  3.67047975e-02  3.38135733e-02\n",
      "  2.02198703e-02 -3.46383926e-03 -3.63025821e-02]\n",
      "Beta values for Scikit-Learn Ridge implementation\n",
      "[ 3.43579948e-02 -5.43330971e-01 -3.10141413e-03  2.47116868e-01\n",
      "  2.18613217e-01  1.02054837e-01 -4.25617655e-04 -5.90475506e-02\n",
      " -7.68534263e-02 -6.68929213e-02 -4.24906604e-02 -1.40927184e-02\n",
      "  1.11482289e-02  2.88529063e-02  3.67047975e-02  3.38135733e-02\n",
      "  2.02198702e-02 -3.46383925e-03 -3.63025821e-02]\n",
      "Intercept from own implementation:\n",
      "1.0330308045187757\n",
      "Intercept from Scikit-Learn Ridge implementation\n",
      "1.0330308045183194\n",
      "MSE values for own Ridge implementation\n",
      "3.139255958997547e-06\n",
      "MSE values for Scikit-Learn Ridge implementation\n",
      "3.1392559585020426e-06\n",
      "Beta values for own Ridge implementation\n",
      "[-0.05807125 -0.29822833 -0.08551306  0.08156108  0.13679863  0.12333649\n",
      "  0.08251519  0.03815288  0.00111756 -0.02498832 -0.04010697 -0.04566964\n",
      " -0.04355837 -0.03562355 -0.02348765 -0.00848904  0.00831018  0.0260906\n",
      "  0.04423486]\n",
      "Beta values for Scikit-Learn Ridge implementation\n",
      "[-0.05807125 -0.29822833 -0.08551306  0.08156108  0.13679863  0.12333649\n",
      "  0.08251519  0.03815288  0.00111756 -0.02498832 -0.04010697 -0.04566964\n",
      " -0.04355837 -0.03562355 -0.02348765 -0.00848904  0.00831018  0.0260906\n",
      "  0.04423486]\n",
      "Intercept from own implementation:\n",
      "1.0411487294305088\n",
      "Intercept from Scikit-Learn Ridge implementation\n",
      "1.0411487294305226\n",
      "MSE values for own Ridge implementation\n",
      "1.9601304850035702e-05\n",
      "MSE values for Scikit-Learn Ridge implementation\n",
      "1.9601304850073734e-05\n",
      "Beta values for own Ridge implementation\n",
      "[-0.1416398  -0.14021063 -0.05383795  0.01367553  0.04784395  0.05796251\n",
      "  0.05447415  0.044613    0.03267527  0.02098261  0.01066519  0.00217499\n",
      " -0.00440346 -0.00917248 -0.01231917 -0.01405935 -0.0146081  -0.01416528\n",
      " -0.01290947]\n",
      "Beta values for Scikit-Learn Ridge implementation\n",
      "[-0.1416398  -0.14021063 -0.05383795  0.01367553  0.04784395  0.05796251\n",
      "  0.05447415  0.044613    0.03267527  0.02098261  0.01066519  0.00217499\n",
      " -0.00440346 -0.00917248 -0.01231917 -0.01405935 -0.0146081  -0.01416528\n",
      " -0.01290947]\n",
      "Intercept from own implementation:\n",
      "1.049556996627824\n",
      "Intercept from Scikit-Learn Ridge implementation\n",
      "1.0495569966278269\n",
      "MSE values for own Ridge implementation\n",
      "5.4959161509357395e-05\n",
      "MSE values for Scikit-Learn Ridge implementation\n",
      "5.4959161509366685e-05\n",
      "Beta values for own Ridge implementation\n",
      "[-0.13535942 -0.08593216 -0.03568439 -0.0036367   0.01397146  0.02229529\n",
      "  0.02503753  0.0245528   0.02228115  0.01908936  0.01549377  0.01179792\n",
      "  0.00817631  0.00472512  0.00149311 -0.00149956 -0.00424967 -0.00676387\n",
      " -0.00905423]\n",
      "Beta values for Scikit-Learn Ridge implementation\n",
      "[-0.13535942 -0.08593216 -0.03568439 -0.0036367   0.01397146  0.02229529\n",
      "  0.02503753  0.0245528   0.02228115  0.01908936  0.01549377  0.01179792\n",
      "  0.00817631  0.00472512  0.00149311 -0.00149956 -0.00424967 -0.00676387\n",
      " -0.00905423]\n",
      "Intercept from own implementation:\n",
      "1.039967668952797\n",
      "Intercept from Scikit-Learn Ridge implementation\n",
      "1.0399676689527975\n",
      "MSE values for own Ridge implementation\n",
      "7.571105947979344e-05\n",
      "MSE values for Scikit-Learn Ridge implementation\n",
      "7.571105947979412e-05\n",
      "Beta values for own Ridge implementation\n",
      "[-0.05100875 -0.04063602 -0.02723445 -0.01713366 -0.0100706  -0.00517114\n",
      " -0.00174276  0.00068734  0.00243186  0.00369758  0.00462287  0.0053018\n",
      "  0.00579953  0.006162    0.00642221  0.00660427  0.00672607  0.0068011\n",
      "  0.00683964]\n",
      "Beta values for Scikit-Learn Ridge implementation\n",
      "[-0.05100875 -0.04063602 -0.02723445 -0.01713366 -0.0100706  -0.00517114\n",
      " -0.00174276  0.00068734  0.00243186  0.00369758  0.00462287  0.0053018\n",
      "  0.00579953  0.006162    0.00642221  0.00660427  0.00672607  0.0068011\n",
      "  0.00683964]\n",
      "Intercept from own implementation:\n",
      "0.999955585168597\n",
      "Intercept from Scikit-Learn Ridge implementation\n",
      "0.999955585168597\n",
      "MSE values for own Ridge implementation\n",
      "0.0007698473260556343\n",
      "MSE values for Scikit-Learn Ridge implementation\n",
      "0.0007698473260556325\n",
      "Beta values for own Ridge implementation\n",
      "[-0.00834567 -0.00803064 -0.00673407 -0.00554552 -0.00458878 -0.0038335\n",
      " -0.00323332 -0.00274989 -0.0023548  -0.00202756 -0.00175331 -0.00152117\n",
      " -0.001323   -0.0011526  -0.00100519 -0.00087697 -0.00076495 -0.00066668\n",
      " -0.00058016]\n",
      "Beta values for Scikit-Learn Ridge implementation\n",
      "[-0.00834567 -0.00803064 -0.00673407 -0.00554552 -0.00458878 -0.0038335\n",
      " -0.00323332 -0.00274989 -0.0023548  -0.00202756 -0.00175331 -0.00152117\n",
      " -0.001323   -0.0011526  -0.00100519 -0.00087697 -0.00076495 -0.00066668\n",
      " -0.00058016]\n",
      "Intercept from own implementation:\n",
      "0.9637117593816477\n",
      "Intercept from Scikit-Learn Ridge implementation\n",
      "0.9637117593816477\n",
      "MSE values for own Ridge implementation\n",
      "0.0023813163025848865\n",
      "MSE values for Scikit-Learn Ridge implementation\n",
      "0.002381316302584885\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_122_1.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn import linear_model\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "def MSE(y_data,y_model):\n",
    "    n = np.size(y_model)\n",
    "    return np.sum((y_data-y_model)**2)/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(315)\n",
    "\n",
    "n = 100\n",
    "x = np.random.rand(n)\n",
    "y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)\n",
    "\n",
    "Maxpolydegree = 20\n",
    "X = np.zeros((n,Maxpolydegree-1))\n",
    "\n",
    "for degree in range(1,Maxpolydegree): #No intercept column\n",
    "    X[:,degree-1] = x**(degree)\n",
    "\n",
    "# We split the data in test and training data\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n",
    "\n",
    "#For our own implementation, we will need to deal with the intercept by centering the design matrix and the target variable\n",
    "X_train_mean = np.mean(X_train,axis=0)\n",
    "#Center by removing mean from each feature\n",
    "X_train_scaled = X_train - X_train_mean \n",
    "X_test_scaled = X_test - X_train_mean\n",
    "#The model intercept (called y_scaler) is given by the mean of the target variable (IF X is centered)\n",
    "#Remove the intercept from the training data.\n",
    "y_scaler = np.mean(y_train)           \n",
    "y_train_scaled = y_train - y_scaler   \n",
    "\n",
    "p = Maxpolydegree-1\n",
    "I = np.eye(p,p)\n",
    "# Decide which values of lambda to use\n",
    "nlambdas = 6\n",
    "MSEOwnRidgePredict = np.zeros(nlambdas)\n",
    "MSERidgePredict = np.zeros(nlambdas)\n",
    "\n",
    "lambdas = np.logspace(-4, 2, nlambdas)\n",
    "for i in range(nlambdas):\n",
    "    lmb = lambdas[i]\n",
    "    OwnRidgeBeta = np.linalg.pinv(X_train_scaled.T @ X_train_scaled+lmb*I) @ X_train_scaled.T @ (y_train_scaled)\n",
    "    intercept_ = y_scaler - X_train_mean@OwnRidgeBeta #The intercept can be shifted so the model can predict on uncentered data\n",
    "    #Add intercept to prediction\n",
    "    ypredictOwnRidge = X_test_scaled @ OwnRidgeBeta + y_scaler \n",
    "    RegRidge = linear_model.Ridge(lmb)\n",
    "    RegRidge.fit(X_train,y_train)\n",
    "    ypredictRidge = RegRidge.predict(X_test)\n",
    "    MSEOwnRidgePredict[i] = MSE(y_test,ypredictOwnRidge)\n",
    "    MSERidgePredict[i] = MSE(y_test,ypredictRidge)\n",
    "    print(\"Beta values for own Ridge implementation\")\n",
    "    print(OwnRidgeBeta) #Intercept is given by mean of target variable\n",
    "    print(\"Beta values for Scikit-Learn Ridge implementation\")\n",
    "    print(RegRidge.coef_)\n",
    "    print('Intercept from own implementation:')\n",
    "    print(intercept_)\n",
    "    print('Intercept from Scikit-Learn Ridge implementation')\n",
    "    print(RegRidge.intercept_)\n",
    "    print(\"MSE values for own Ridge implementation\")\n",
    "    print(MSEOwnRidgePredict[i])\n",
    "    print(\"MSE values for Scikit-Learn Ridge implementation\")\n",
    "    print(MSERidgePredict[i])\n",
    "\n",
    "\n",
    "# Now plot the results\n",
    "plt.figure()\n",
    "plt.plot(np.log10(lambdas), MSEOwnRidgePredict, 'b--', label = 'MSE own Ridge Test')\n",
    "plt.plot(np.log10(lambdas), MSERidgePredict, 'g--', label = 'MSE SL Ridge Test')\n",
    "plt.xlabel('log10(lambda)')\n",
    "plt.ylabel('MSE')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e9dfda5",
   "metadata": {
    "editable": true
   },
   "source": [
    "We see here, when compared to the code which includes explicitely the\n",
    "intercept column, that our MSE value is actually smaller. This is\n",
    "because the regularization term does not include the intercept value\n",
    "$\\beta_0$ in the fitting.  This applies to Lasso regularization as\n",
    "well.  It means that our optimization is now done only with the\n",
    "centered matrix and/or vector that enter the fitting procedure. Note\n",
    "also that the problem with the intercept occurs mainly in these type\n",
    "of polynomial fitting problem.\n",
    "\n",
    "The next example is indeed an example where all these discussions about the role of intercept are not present."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7eb252c",
   "metadata": {
    "editable": true
   },
   "source": [
    "## More complicated Example: The Ising model\n",
    "\n",
    "The one-dimensional Ising model with nearest neighbor interaction, no\n",
    "external field and a constant coupling constant $J$ is given by"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "990ff280",
   "metadata": {
    "editable": true
   },
   "source": [
    "<!-- Equation labels as ordinary links -->\n",
    "<div id=\"_auto1\"></div>\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "    H = -J \\sum_{k}^L s_k s_{k + 1},\n",
    "\\label{_auto1} \\tag{1}\n",
    "\\end{equation}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ea46b31",
   "metadata": {
    "editable": true
   },
   "source": [
    "where $s_i \\in \\{-1, 1\\}$ and $s_{N + 1} = s_1$. The number of spins\n",
    "in the system is determined by $L$. For the one-dimensional system\n",
    "there is no phase transition.\n",
    "\n",
    "We will look at a system of $L = 40$ spins with a coupling constant of\n",
    "$J = 1$. To get enough training data we will generate 10000 states\n",
    "with their respective energies."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "fa60aaab",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "import seaborn as sns\n",
    "import scipy.linalg as scl\n",
    "from sklearn.model_selection import train_test_split\n",
    "import tqdm\n",
    "sns.set(color_codes=True)\n",
    "cmap_args=dict(vmin=-1., vmax=1., cmap='seismic')\n",
    "\n",
    "L = 40\n",
    "n = int(1e4)\n",
    "\n",
    "spins = np.random.choice([-1, 1], size=(n, L))\n",
    "J = 1.0\n",
    "\n",
    "energies = np.zeros(n)\n",
    "\n",
    "for i in range(n):\n",
    "    energies[i] = - J * np.dot(spins[i], np.roll(spins[i], 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9e8214e",
   "metadata": {
    "editable": true
   },
   "source": [
    "Here we use ordinary least squares\n",
    "regression to predict the energy for the nearest neighbor\n",
    "one-dimensional Ising model on a ring, i.e., the endpoints wrap\n",
    "around. We will use linear regression to fit a value for\n",
    "the coupling constant to achieve this.\n",
    "\n",
    "A more general form for the one-dimensional Ising model is"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a578cd63",
   "metadata": {
    "editable": true
   },
   "source": [
    "<!-- Equation labels as ordinary links -->\n",
    "<div id=\"_auto2\"></div>\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "    H = - \\sum_j^L \\sum_k^L s_j s_k J_{jk}.\n",
    "\\label{_auto2} \\tag{2}\n",
    "\\end{equation}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d90dcfee",
   "metadata": {
    "editable": true
   },
   "source": [
    "Here we allow for interactions beyond the nearest neighbors and a state dependent\n",
    "coupling constant. This latter expression can be formulated as\n",
    "a matrix-product"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4eec69a",
   "metadata": {
    "editable": true
   },
   "source": [
    "<!-- Equation labels as ordinary links -->\n",
    "<div id=\"_auto3\"></div>\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "    \\boldsymbol{H} = \\boldsymbol{X} J,\n",
    "\\label{_auto3} \\tag{3}\n",
    "\\end{equation}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae46a11b",
   "metadata": {
    "editable": true
   },
   "source": [
    "where $X_{jk} = s_j s_k$ and $J$ is a matrix which consists of the\n",
    "elements $-J_{jk}$. This form of writing the energy fits perfectly\n",
    "with the form utilized in linear regression, that is"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87ebb9b8",
   "metadata": {
    "editable": true
   },
   "source": [
    "<!-- Equation labels as ordinary links -->\n",
    "<div id=\"_auto4\"></div>\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "    \\boldsymbol{y} = \\boldsymbol{X}\\boldsymbol{\\beta} + \\boldsymbol{\\epsilon},\n",
    "\\label{_auto4} \\tag{4}\n",
    "\\end{equation}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "856efd3f",
   "metadata": {
    "editable": true
   },
   "source": [
    "We split the data in training and test data as discussed in the previous example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "5ae2828f",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [],
   "source": [
    "X = np.zeros((n, L ** 2))\n",
    "for i in range(n):\n",
    "    X[i] = np.outer(spins[i], spins[i]).ravel()\n",
    "y = energies\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d6201d9",
   "metadata": {
    "editable": true
   },
   "source": [
    "In the ordinary least squares method we choose the cost function"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4af380a7",
   "metadata": {
    "editable": true
   },
   "source": [
    "<!-- Equation labels as ordinary links -->\n",
    "<div id=\"_auto5\"></div>\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "    C(\\boldsymbol{X}, \\boldsymbol{\\beta})= \\frac{1}{n}\\left\\{(\\boldsymbol{X}\\boldsymbol{\\beta} - \\boldsymbol{y})^T(\\boldsymbol{X}\\boldsymbol{\\beta} - \\boldsymbol{y})\\right\\}.\n",
    "\\label{_auto5} \\tag{5}\n",
    "\\end{equation}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e8eefa3",
   "metadata": {
    "editable": true
   },
   "source": [
    "We then find the extremal point of $C$ by taking the derivative with respect to $\\boldsymbol{\\beta}$ as discussed above.\n",
    "This yields the expression for $\\boldsymbol{\\beta}$ to be"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1c0765c",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\boldsymbol{\\beta} = \\frac{\\boldsymbol{X}^T \\boldsymbol{y}}{\\boldsymbol{X}^T \\boldsymbol{X}},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c754e28b",
   "metadata": {
    "editable": true
   },
   "source": [
    "which immediately imposes some requirements on $\\boldsymbol{X}$ as there must exist\n",
    "an inverse of $\\boldsymbol{X}^T \\boldsymbol{X}$. If the expression we are modeling contains an\n",
    "intercept, i.e., a constant term, we must make sure that the\n",
    "first column of $\\boldsymbol{X}$ consists of $1$. We do this here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "ff056cf9",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [],
   "source": [
    "X_train_own = np.concatenate(\n",
    "    (np.ones(len(X_train))[:, np.newaxis], X_train),\n",
    "    axis=1\n",
    ")\n",
    "X_test_own = np.concatenate(\n",
    "    (np.ones(len(X_test))[:, np.newaxis], X_test),\n",
    "    axis=1\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "524f259e",
   "metadata": {
    "editable": true
   },
   "source": [
    "Doing the inversion directly turns out to be a bad idea since the matrix\n",
    "$\\boldsymbol{X}^T\\boldsymbol{X}$ is singular. An alternative approach is to use the **singular\n",
    "value decomposition**. Using the definition of the Moore-Penrose\n",
    "pseudoinverse we can write the equation for $\\boldsymbol{\\beta}$ as"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52be4553",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\boldsymbol{\\beta} = \\boldsymbol{X}^{+}\\boldsymbol{y},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c37ff09a",
   "metadata": {
    "editable": true
   },
   "source": [
    "where the pseudoinverse of $\\boldsymbol{X}$ is given by"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea49a105",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\boldsymbol{X}^{+} = \\frac{\\boldsymbol{X}^T}{\\boldsymbol{X}^T\\boldsymbol{X}}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf31067a",
   "metadata": {
    "editable": true
   },
   "source": [
    "Using singular value decomposition we can decompose the matrix  $\\boldsymbol{X} = \\boldsymbol{U}\\boldsymbol{\\Sigma} \\boldsymbol{V}^T$,\n",
    "where $\\boldsymbol{U}$ and $\\boldsymbol{V}$ are orthogonal(unitary) matrices and $\\boldsymbol{\\Sigma}$ contains the singular values (more details below).\n",
    "where $X^{+} = V\\Sigma^{+} U^T$. This reduces the equation for\n",
    "$\\omega$ to"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ef2c839",
   "metadata": {
    "editable": true
   },
   "source": [
    "<!-- Equation labels as ordinary links -->\n",
    "<div id=\"_auto6\"></div>\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "    \\boldsymbol{\\beta} = \\boldsymbol{V}\\boldsymbol{\\Sigma}^{+} \\boldsymbol{U}^T \\boldsymbol{y}.\n",
    "\\label{_auto6} \\tag{6}\n",
    "\\end{equation}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96bbf134",
   "metadata": {
    "editable": true
   },
   "source": [
    "Note that solving this equation by actually doing the pseudoinverse\n",
    "(which is what we will do) is not a good idea as this operation scales\n",
    "as $\\mathcal{O}(n^3)$, where $n$ is the number of elements in a\n",
    "general matrix. Instead, doing $QR$-factorization and solving the\n",
    "linear system as an equation would reduce this down to\n",
    "$\\mathcal{O}(n^2)$ operations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "5e729b1e",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def ols_svd(x: np.ndarray, y: np.ndarray) -> np.ndarray:\n",
    "    u, s, v = scl.svd(x)\n",
    "    return v.T @ scl.pinv(scl.diagsvd(s, u.shape[0], v.shape[0])) @ u.T @ y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "80b923d1",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [],
   "source": [
    "beta = ols_svd(X_train_own,y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4cf2f1a",
   "metadata": {
    "editable": true
   },
   "source": [
    "When extracting the $J$-matrix  we need to make sure that we remove the intercept, as is done here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "93be2c0d",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [],
   "source": [
    "J = beta[1:].reshape(L, L)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae869089",
   "metadata": {
    "editable": true
   },
   "source": [
    "A way of looking at the coefficients in $J$ is to plot the matrices as images."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "8d6d8152",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58739/4162706317.py:7: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.\n",
      "  cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2000x1400 with 2 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_154_1.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(20, 14))\n",
    "im = plt.imshow(J, **cmap_args)\n",
    "plt.title(\"OLS\", fontsize=18)\n",
    "plt.xticks(fontsize=18)\n",
    "plt.yticks(fontsize=18)\n",
    "cb = fig.colorbar(im)\n",
    "cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8092ac84",
   "metadata": {
    "editable": true
   },
   "source": [
    "It is interesting to note that OLS\n",
    "considers both $J_{j, j + 1} = -0.5$ and $J_{j, j - 1} = -0.5$ as\n",
    "valid matrix elements for $J$.\n",
    "In our discussion below on hyperparameters and Ridge and Lasso regression we will see that\n",
    "this problem can be removed, partly and only with Lasso regression. \n",
    "\n",
    "In this case our matrix inversion was actually possible. The obvious question now is what is the mathematics behind the SVD?\n",
    "\n",
    "Let us now \n",
    "focus on Ridge and Lasso regression as well. We repeat some of the\n",
    "basic parts of the Ising model and the setup of the training and test\n",
    "data.  The one-dimensional Ising model with nearest neighbor\n",
    "interaction, no external field and a constant coupling constant $J$ is\n",
    "given by"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d9251cde",
   "metadata": {
    "editable": true
   },
   "source": [
    "<!-- Equation labels as ordinary links -->\n",
    "<div id=\"_auto7\"></div>\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "    H = -J \\sum_{k}^L s_k s_{k + 1},\n",
    "\\label{_auto7} \\tag{7}\n",
    "\\end{equation}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "abe454c9",
   "metadata": {
    "editable": true
   },
   "source": [
    "where $s_i \\in \\{-1, 1\\}$ and $s_{N + 1} = s_1$. The number of spins in the system is determined by $L$. For the one-dimensional system there is no phase transition.\n",
    "\n",
    "We will look at a system of $L = 40$ spins with a coupling constant of $J = 1$. To get enough training data we will generate 10000 states with their respective energies."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "89f8fbd0",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "import seaborn as sns\n",
    "import scipy.linalg as scl\n",
    "from sklearn.model_selection import train_test_split\n",
    "import sklearn.linear_model as skl\n",
    "import tqdm\n",
    "sns.set(color_codes=True)\n",
    "cmap_args=dict(vmin=-1., vmax=1., cmap='seismic')\n",
    "\n",
    "L = 40\n",
    "n = int(1e4)\n",
    "\n",
    "spins = np.random.choice([-1, 1], size=(n, L))\n",
    "J = 1.0\n",
    "\n",
    "energies = np.zeros(n)\n",
    "\n",
    "for i in range(n):\n",
    "    energies[i] = - J * np.dot(spins[i], np.roll(spins[i], 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e06639d4",
   "metadata": {
    "editable": true
   },
   "source": [
    "A more general form for the one-dimensional Ising model is"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43ef0f40",
   "metadata": {
    "editable": true
   },
   "source": [
    "<!-- Equation labels as ordinary links -->\n",
    "<div id=\"_auto8\"></div>\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "    H = - \\sum_j^L \\sum_k^L s_j s_k J_{jk}.\n",
    "\\label{_auto8} \\tag{8}\n",
    "\\end{equation}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "523dc03b",
   "metadata": {
    "editable": true
   },
   "source": [
    "Here we allow for interactions beyond the nearest neighbors and a more\n",
    "adaptive coupling matrix. This latter expression can be formulated as\n",
    "a matrix-product on the form"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f389eef",
   "metadata": {
    "editable": true
   },
   "source": [
    "<!-- Equation labels as ordinary links -->\n",
    "<div id=\"_auto9\"></div>\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "    H = X J,\n",
    "\\label{_auto9} \\tag{9}\n",
    "\\end{equation}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6e00f24",
   "metadata": {
    "editable": true
   },
   "source": [
    "where $X_{jk} = s_j s_k$ and $J$ is the matrix consisting of the\n",
    "elements $-J_{jk}$. This form of writing the energy fits perfectly\n",
    "with the form utilized in linear regression, viz."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ea1084d",
   "metadata": {
    "editable": true
   },
   "source": [
    "<!-- Equation labels as ordinary links -->\n",
    "<div id=\"_auto10\"></div>\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "    \\boldsymbol{y} = \\boldsymbol{X}\\boldsymbol{\\beta} + \\boldsymbol{\\epsilon}.\n",
    "\\label{_auto10} \\tag{10}\n",
    "\\end{equation}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5551bb05",
   "metadata": {
    "editable": true
   },
   "source": [
    "We organize the data as we did above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "f5dd7795",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [],
   "source": [
    "X = np.zeros((n, L ** 2))\n",
    "for i in range(n):\n",
    "    X[i] = np.outer(spins[i], spins[i]).ravel()\n",
    "y = energies\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.96)\n",
    "\n",
    "X_train_own = np.concatenate(\n",
    "    (np.ones(len(X_train))[:, np.newaxis], X_train),\n",
    "    axis=1\n",
    ")\n",
    "\n",
    "X_test_own = np.concatenate(\n",
    "    (np.ones(len(X_test))[:, np.newaxis], X_test),\n",
    "    axis=1\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f36c807b",
   "metadata": {
    "editable": true
   },
   "source": [
    "We will do all fitting with **Scikit-Learn**,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "eb701dd4",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [],
   "source": [
    "clf = skl.LinearRegression().fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd356ada",
   "metadata": {
    "editable": true
   },
   "source": [
    "When  extracting the $J$-matrix we make sure to remove the intercept"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "ae737db8",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [],
   "source": [
    "J_sk = clf.coef_.reshape(L, L)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d152a32a",
   "metadata": {
    "editable": true
   },
   "source": [
    "And then we plot the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "8d713977",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58739/3777801602.py:7: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.\n",
      "  cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n"
     ]
    },
    {
     "data": {
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36tRJ8+bN8z/2L1VMTfDNN9/oySef1Lhx4zRgwABNnz7d30eO9MILL6iwsFC9e/fW/fffX2XhokGDBmny5MmSpHfeeSfgNknSe++9p7/85S8KCQnRP//5T40cOdJS/fr0wgsvKC8vT2eeeabuvfdetWzZ0r8tPj5eTz/9tKKiorRixQp99dVX/m1Lly5VaGiorrzyymojPrt27aqJEydKqv18FR4erttuu83/ua1pYTHT/R0AAKCxkAgFABw1BgwYoPDw8Gq/79q1qyRVmbfwq6++UklJiZKSknTCCSfUuL+LLrpIUsXCLPv27ZMknXDCCfruu+/03XffKSYmplqdkpISf3L08OHDNe735JNP/s1jWblyZbV///vf/5Sdna3TTjtNU6dO1SeffOJvY6WsrCz/I6uVC8v82uDBgxUTE+NPNEn/93p06tRJZ5xxRrU6LVq00MUXX1xnm2s6LrvtiYuLU2hoqA4cOKA777zTn+SsdMMNN+jxxx/Xueee6/9dZULu+eef18KFC6u837GxsXrppZd07733KiIios7j+PzzzyVVzP1YmdT+tcpHyZcvX17jfJhDhgyp9rvKfihVJJ7ri9vtrnF6hMokaM+ePdWnT58a61599dWSpK1bt9aYCKupL1QmOo8//njFx8dX2175h4iCgoLADuAXHTp00KxZs/Txxx/rtttuU//+/au8VwcPHtTcuXM1fPjwav2h8lgvvfRS/9y5RxozZowWLVqkV155JeD2vP/++/rzn/+s8vJyPfzww7rgggssHU99q5xvs7bPUdu2bXXqqadKqjrX6sMPP6w1a9ZoypQpNdZr1qyZpIpz16/nUZWkHj16KDIyss62mezvAAAAjYk5QgEAR43Y2Ngaf1+ZTDly4Z7KldZ37txZ6/x1viMWIdq8ebPatGlTZZ+ZmZlau3attm3bpu3bt2vTpk3asGGDf8GSmpIKkn5zZKWkKgv7lJSU6LvvvtM///lPrVu3Trt27dLpp5+utm3bVqt35AryN9xwQ637r2xj5RyYlfVSU1NrrZOWllZnm2s6LrvtadOmjSZOnKhnnnlG7733nt577z21a9dO/fv312mnnaZBgwZVG5l2zTXX6KOPPtKePXs0depUhYaG6sQTT9TAgQM1aNAg9erVK6D5IStHr9WWID9yW1lZmbZu3VrttampLx6Z1CsrK/vNdgSqZcuWNSZ3K1/Luo4jISFBUVFRKigo0JYtW5SSklJle8eOHavVqRyFW9PIwCO3+2pZxOu3JCQkaNKkSZo0aZJKSkq0Zs0aLV26VAsWLFB2drZyc3M1efJkffzxxwoLC1NxcbF27dolSVVG7x4pKipKycnJAbdh//79uuOOO/yf4co/hDSWQ4cO+RfNevrpp/Xyyy/XWK6yTOV7XykkJEQlJSX65ptvtHnzZm3fvl2ZmZlav369duzY4S9XXl5eLZEcyPnKZH8HAABoTCRCAQBHjSMfk/4tlaP4CgoKqjwyX5sjRzStXr1aM2fO9K8KXSkmJkaDBw/WTz/9pKysrFr39VsjEn8tLCxMp556qnr16qUrrrhCGzdu1Pjx4zV37twqo66kqqNeAzmuyvKVjxvXNfKrpkf4j1TTcdltjyRNmTJFaWlpevXVV7VixQrt2bNH77//vt5//32FhobqvPPO01//+lf/Y9AdO3bUggUL9Oyzz+qjjz7Srl27/AvlPPXUU+rcubOmTZums88+u842VI5kPPLx6l878rU4dOhQte2/1RftJglrUtMoaCmw45Ck5s2bq6CgoMbjqBwtWJOaRl7Wt7CwMPXt21d9+/bVDTfcoIcfflgvvviicnJy9OWXX+rcc89VXl6ev/xvjVwMVGlpqTwej84880x98sknmjlzpgYNGlTrCOFA7dmzRzfddFON2wYPHqzrrruuxm1Hjq6t7RH2Ix35OSotLdVTTz2l119/vcprFRISopSUFPXs2VMff/xxrfuqrX8dyWR/BwAAaEwkQgEATVJlgmfo0KF6/PHHA66XkZGhcePGqaioSElJSbrkkkvUrVs3de3a1T8q6vLLL68zEWpXVFSU/t//+3+65JJLlJubq/T0dL3zzjtVklWViaDo6GgtW7Ys4H1X7qOux5lrSpT9FrvtqXTOOefonHPOUUFBgX+1+K+++kqbN2/2P/7+zDPP+Mu3adNG06ZN07Rp07RhwwYtX75c3377rZYsWaLs7GzddNNNeuONN9SzZ89aYzZv3lySanzkvdKRifHK8kebQI7jyO2NdRxPPvmk3n//ffXv319///vfay0XGhqqqVOn6t///rd27tzpH7l7ZP+300dr4vF49NRTT+nUU0/V6NGjtW7dOt11112aM2eOrVXnKxUXF9f6B4EuXbrUWu/IY3z//ferjdyty1//+lfNnz9fISEh+v3vf6/f/e53Sk5OVkJCgiIiIrR06dI6E6EAAAD4P8wRCgBoko4//nhJVR/d/rXDhw9r+fLl2r59u//Rzjlz5qioqEiJiYmaN2+err76ag0cOLDKo6GVj+k2hMTERN12222SKpKyv17kpvK48vLytGfPnlr3s2LFCmVkZPgXDqpMrNQ12uzX8zIGwm57ioqKtH79en/MqKgonXnmmbrzzjv14Ycf+l+DL774wp/I27Vrl7799lv/PlJTUzV27Fg99dRT+uyzz9S5c2eVlZVp0aJFdbY5MTFRkvTjjz/WWuZ///ufJMnlctU4T+bRIJDjyMjIUGFhoaS6E3ENqby8XJmZmfr8889VWlpaZ1m32+2foqLy0fyWLVv6f1fb53n37t267LLLNGXKlN9MDFfue/DgwQoNDdWMGTMUEhKiZcuW6bXXXrNyaNXExcVpw4YNNf574IEHaq3XsmVL/1QYmzZtqrXchg0btG7dOh04cEBSxWfi3XfflSTde++9mj59ui688EJ169bNP4J7586dQR0TAADAsYREKACgSRo8eLBCQkK0efNmLV26tMYys2fP1tixY3XRRRf5Fz6qnIOva9euNT42vHTpUuXk5EhquHnxrrrqKvXt21eS9Nprr1UZYda1a1d/QuvVV1+tsf7333+vq666Suedd55WrVolqWJRHI/Hox07dmjJkiXV6hQXF+u9996z3Fa77XnzzTd10UUXaerUqTU+Vjtw4ED/f3u9Xnm9Xo0cOVLjx4/Xl19+Wa1827Zt/cne2uZurVS58Mvnn3+u7du311imco7G3r17V1m9+2hSeRxr1qypdRTi7NmzJVUsVFTX/LAN6fzzz5fb7dbu3burjO6tSeU8vB6Px78wkFSxMrxU+6rwH330kVavXq3Vq1f/5lQBv5aWlqYJEyZIkmbOnFlrn/i1YEaO1qRy4apXX321xj588OBBjR8/XiNHjtScOXMkSTk5Of7PT01zxZaXl2v+/Pn+/2cuTwAAgLqRCAUABOXgwYPav39/nf8aYn65zp0769JLL5Uk3Xrrrf6VwqWK5MDbb7+tJ598UlJF4rFyTsjKEY5Lly7VihUr/HW8Xq8WLVpUZWXmypGJ9c3lcmn69OnyeDwqLy/XX/7yF5WUlPi333zzzZKk5557Tv/617+qbFuxYoV/e+/evdW/f39JFYnCK6+8UpJ05513Vkmc5ebm6pZbbrH9uL+d9gwfPlwej0cbN27U/fff7x+1KFUsZPPoo49Kknr16qWYmBiFhobq/PPPlyTdd999WrNmTZU2/Oc///EneCuTZrUZNmyYUlNTVVxcrGuvvbbKSNiCggL95S9/0ZIlSxQaGqrbb7/d1mtiwkknnaTBgwdLkm666aYqUxOUlJTo8ccf11tvvSVJ+tOf/lTvibtAde3aVePHj5dU8Zj81KlTq416LC0t1SeffKKrr75aXq9XEyZMUKdOnfzbJ06cqPDwcK1YsULTp0/3/+FCkr7++mt/f7nmmmtstfGmm25Sly5dVFhYqGnTpgV0TqqcFqLyjyfBmjRpkiIjI/X9999r6tSp2r9/v39bdna2Jk2apNzcXLVo0UJXXXWVpIpRviEhIZKkf/3rX1Vel5ycHN18881VzmNHbgcAAEB1zBEKAAhKXSuJV/ruu+8aZNTdtGnTtGvXLn3xxReaPHmy2rdvr9jYWGVnZ/uTDEOHDtUtt9zir3P11Vdr0aJFys3N1VVXXaWEhAQ1b95cWVlZOnDggCIjI3XSSSfphx9+aNBHTrt27ao//vGPevLJJ7Vp0yY988wz/kVYzj//fGVmZuqJJ57QzJkz9eyzzyohIUH79+/3J2WOP/54Pf3001X2eeutt2rdunVavny5rrjiCv+x/fzzz/J6vUpLS9PatWv9iZVA2WlP+/btdf/992vq1Kl6+eWXNW/ePMXHx6usrEzbtm1TcXGxYmJidN999/nrTJkyRd9//71++uknXXrppercubNiYmK0e/du7d69W5J0xRVX/GYiNDQ0VE8//bSuvfZabd68WRdddJH/tah8fD8iIkJ///vf/SNzj1YPPfSQrrvuOv3www8aN26cOnfurNatW2vLli0qKChQSEiIbrnlFn8SubHccccdCgkJ0ezZs7Vw4UItXLhQ7dq1U/v27eX1erV9+3YVFhbK5XJp7Nix/qkRKiUlJenBBx/Un/70J82dO1fvvvuuEhMTtW/fPv+q6BdffLE/2W9VRESEpk+frgkTJmj58uV67bXX/MnG2vTo0UNffPGF3n//fW3YsEF9+/bV3/72N1vxpYqk5mOPPaYpU6Zo0aJF+vjjj5WUlKTS0lJlZmbK6/UqMjJSzz33XJXpA/7whz/o+eef16JFi/TVV18pPj5ehw4d0tatW+Xz+XTKKafo+++/l9fr1c6dOxUdHW27jQAAAE5HIhQA0GSFh4dr1qxZ+vDDDzV//nytXbtW69atU/PmzXXKKafo4osv1ogRI6qsjt2pUyctXLhQTz/9tL755hvt2LFDISEh6tixo0aMGKHx48crOztb48eP17Jly1RYWFhvK1n/2h//+Ed9+OG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      "text/plain": [
       "<Figure size 2000x1400 with 2 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_172_1.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(20, 14))\n",
    "im = plt.imshow(J_sk, **cmap_args)\n",
    "plt.title(\"LinearRegression from Scikit-learn\", fontsize=18)\n",
    "plt.xticks(fontsize=18)\n",
    "plt.yticks(fontsize=18)\n",
    "cb = fig.colorbar(im)\n",
    "cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ede30c18",
   "metadata": {
    "editable": true
   },
   "source": [
    "The results agree perfectly with our previous discussion where we used our own code.\n",
    "\n",
    "Having explored the ordinary least squares we move on to ridge\n",
    "regression. In ridge regression we include a **regularizer**. This\n",
    "involves a new cost function which leads to a new estimate for the\n",
    "weights $\\boldsymbol{\\beta}$. This results in a penalized regression problem. The\n",
    "cost function is given by"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eac772e9",
   "metadata": {
    "editable": true
   },
   "source": [
    "<!-- Equation labels as ordinary links -->\n",
    "<div id=\"_auto11\"></div>\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "    C(\\boldsymbol{X}, \\boldsymbol{\\beta}; \\lambda) = (\\boldsymbol{X}\\boldsymbol{\\beta} - \\boldsymbol{y})^T(\\boldsymbol{X}\\boldsymbol{\\beta} - \\boldsymbol{y}) + \\lambda \\boldsymbol{\\beta}^T\\boldsymbol{\\beta}.\n",
    "\\label{_auto11} \\tag{11}\n",
    "\\end{equation}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "b66675f0",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58739/438060758.py:10: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.\n",
      "  cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2000x1400 with 2 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_175_1.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_lambda = 0.1\n",
    "clf_ridge = skl.Ridge(alpha=_lambda).fit(X_train, y_train)\n",
    "J_ridge_sk = clf_ridge.coef_.reshape(L, L)\n",
    "fig = plt.figure(figsize=(20, 14))\n",
    "im = plt.imshow(J_ridge_sk, **cmap_args)\n",
    "plt.title(\"Ridge from Scikit-learn\", fontsize=18)\n",
    "plt.xticks(fontsize=18)\n",
    "plt.yticks(fontsize=18)\n",
    "cb = fig.colorbar(im)\n",
    "cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71aa37b5",
   "metadata": {
    "editable": true
   },
   "source": [
    "In the **Least Absolute Shrinkage and Selection Operator** (LASSO)-method we get a third cost function."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b70ef66",
   "metadata": {
    "editable": true
   },
   "source": [
    "<!-- Equation labels as ordinary links -->\n",
    "<div id=\"_auto12\"></div>\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "    C(\\boldsymbol{X}, \\boldsymbol{\\beta}; \\lambda) = (\\boldsymbol{X}\\boldsymbol{\\beta} - \\boldsymbol{y})^T(\\boldsymbol{X}\\boldsymbol{\\beta} - \\boldsymbol{y}) + \\lambda \\sqrt{\\boldsymbol{\\beta}^T\\boldsymbol{\\beta}}.\n",
    "\\label{_auto12} \\tag{12}\n",
    "\\end{equation}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "079981ff",
   "metadata": {
    "editable": true
   },
   "source": [
    "Finding the extremal point of this cost function is not so straight-forward as in least squares and ridge. We will therefore rely solely on the function ``Lasso`` from **Scikit-Learn**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "c8d4a180",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_58739/3544313922.py:9: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.\n",
      "  cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2000x1400 with 2 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_179_1.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "clf_lasso = skl.Lasso(alpha=_lambda).fit(X_train, y_train)\n",
    "J_lasso_sk = clf_lasso.coef_.reshape(L, L)\n",
    "fig = plt.figure(figsize=(20, 14))\n",
    "im = plt.imshow(J_lasso_sk, **cmap_args)\n",
    "plt.title(\"Lasso from Scikit-learn\", fontsize=18)\n",
    "plt.xticks(fontsize=18)\n",
    "plt.yticks(fontsize=18)\n",
    "cb = fig.colorbar(im)\n",
    "cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57839941",
   "metadata": {
    "editable": true
   },
   "source": [
    "It is quite striking how LASSO breaks the symmetry of the coupling\n",
    "constant as opposed to ridge and OLS. We get a sparse solution with\n",
    "$J_{j, j + 1} = -1$.\n",
    "\n",
    "We see how the different models perform for a different set of values for $\\lambda$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "0e3bbb4e",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "  0%|                                                                                                                                                                                    | 0/10 [00:00<?, ?it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_coordinate_descent.py:628: 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\n",
      "  model = cd_fast.enet_coordinate_descent(\n",
      "\r",
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      " 30%|███████████████████████████████████████████████████▌                                                                                                                        | 3/10 [00:02<00:05,  1.32it/s]"
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      "\r",
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      "\r",
      " 50%|██████████████████████████████████████████████████████████████████████████████████████                                                                                      | 5/10 [00:03<00:03,  1.48it/s]"
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      "\r",
      " 60%|███████████████████████████████████████████████████████████████████████████████████████████████████████▏                                                                    | 6/10 [00:04<00:02,  1.55it/s]"
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    {
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      "\r",
      " 70%|████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████▍                                                   | 7/10 [00:04<00:01,  1.50it/s]"
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    {
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     "output_type": "stream",
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      "\r",
      " 80%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████▌                                  | 8/10 [00:05<00:01,  1.52it/s]"
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     "output_type": "stream",
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      "\r",
      " 90%|██████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████▊                 | 9/10 [00:06<00:00,  1.50it/s]"
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     "output_type": "stream",
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      "\r",
      "100%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 10/10 [00:06<00:00,  1.52it/s]"
     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\r",
      "100%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 10/10 [00:06<00:00,  1.47it/s]"
     ]
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    {
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     "output_type": "stream",
     "text": [
      "\n"
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      "text/plain": [
       "<Figure size 3200x5400 with 30 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_181_13.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lambdas = np.logspace(-4, 5, 10)\n",
    "\n",
    "train_errors = {\n",
    "    \"ols_sk\": np.zeros(lambdas.size),\n",
    "    \"ridge_sk\": np.zeros(lambdas.size),\n",
    "    \"lasso_sk\": np.zeros(lambdas.size)\n",
    "}\n",
    "\n",
    "test_errors = {\n",
    "    \"ols_sk\": np.zeros(lambdas.size),\n",
    "    \"ridge_sk\": np.zeros(lambdas.size),\n",
    "    \"lasso_sk\": np.zeros(lambdas.size)\n",
    "}\n",
    "\n",
    "plot_counter = 1\n",
    "\n",
    "fig = plt.figure(figsize=(32, 54))\n",
    "\n",
    "for i, _lambda in enumerate(tqdm.tqdm(lambdas)):\n",
    "    for key, method in zip(\n",
    "        [\"ols_sk\", \"ridge_sk\", \"lasso_sk\"],\n",
    "        [skl.LinearRegression(), skl.Ridge(alpha=_lambda), skl.Lasso(alpha=_lambda)]\n",
    "    ):\n",
    "        method = method.fit(X_train, y_train)\n",
    "\n",
    "        train_errors[key][i] = method.score(X_train, y_train)\n",
    "        test_errors[key][i] = method.score(X_test, y_test)\n",
    "\n",
    "        omega = method.coef_.reshape(L, L)\n",
    "\n",
    "        plt.subplot(10, 5, plot_counter)\n",
    "        plt.imshow(omega, **cmap_args)\n",
    "        plt.title(r\"%s, $\\lambda = %.4f$\" % (key, _lambda))\n",
    "        plot_counter += 1\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14711abd",
   "metadata": {
    "editable": true
   },
   "source": [
    "We see that LASSO reaches a good solution for low\n",
    "values of $\\lambda$, but will \"wither\" when we increase $\\lambda$ too\n",
    "much. Ridge is more stable over a larger range of values for\n",
    "$\\lambda$, but eventually also fades away.\n",
    "\n",
    "To determine which value of $\\lambda$ is best we plot the accuracy of\n",
    "the models when predicting the training and the testing set. We expect\n",
    "the accuracy of the training set to be quite good, but if the accuracy\n",
    "of the testing set is much lower this tells us that we might be\n",
    "subject to an overfit model. The ideal scenario is an accuracy on the\n",
    "testing set that is close to the accuracy of the training set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "9ff29a72",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2000x1400 with 1 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_183_0.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(20, 14))\n",
    "\n",
    "colors = {\n",
    "    \"ols_sk\": \"r\",\n",
    "    \"ridge_sk\": \"y\",\n",
    "    \"lasso_sk\": \"c\"\n",
    "}\n",
    "\n",
    "for key in train_errors:\n",
    "    plt.semilogx(\n",
    "        lambdas,\n",
    "        train_errors[key],\n",
    "        colors[key],\n",
    "        label=\"Train {0}\".format(key),\n",
    "        linewidth=4.0\n",
    "    )\n",
    "\n",
    "for key in test_errors:\n",
    "    plt.semilogx(\n",
    "        lambdas,\n",
    "        test_errors[key],\n",
    "        colors[key] + \"--\",\n",
    "        label=\"Test {0}\".format(key),\n",
    "        linewidth=4.0\n",
    "    )\n",
    "plt.legend(loc=\"best\", fontsize=18)\n",
    "plt.xlabel(r\"$\\lambda$\", fontsize=18)\n",
    "plt.ylabel(r\"$R^2$\", fontsize=18)\n",
    "plt.tick_params(labelsize=18)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c10be56",
   "metadata": {
    "editable": true
   },
   "source": [
    "From the above figure we can see that LASSO with $\\lambda = 10^{-2}$\n",
    "achieves a very good accuracy on the test set. This by far surpasses the\n",
    "other models for all values of $\\lambda$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "efce3b63",
   "metadata": {
    "editable": true
   },
   "source": [
    "## Exercises and Projects\n",
    "\n",
    "The main aim of this project is to study in more detail various\n",
    "regression methods, including the Ordinary Least Squares (OLS) method,\n",
    "The total score is **100** points. Each subtask has its own final score.\n",
    "\n",
    "We will first study how to fit polynomials to a specific\n",
    "two-dimensional function called [Franke's\n",
    "function](http://www.dtic.mil/dtic/tr/fulltext/u2/a081688.pdf).  This\n",
    "is a function which has been widely used when testing various\n",
    "interpolation and fitting algorithms. Furthermore, after having\n",
    "established the model and the method, we will employ resamling\n",
    "techniques such as cross-validation and/or bootstrap in order to perform a\n",
    "proper assessment of our models. We will also study in detail the\n",
    "so-called Bias-Variance trade off.\n",
    "\n",
    "The Franke function, which is a weighted sum of four exponentials  reads as follows"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef5a4df0",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\begin{align*}\n",
    "f(x,y) &= \\frac{3}{4}\\exp{\\left(-\\frac{(9x-2)^2}{4} - \\frac{(9y-2)^2}{4}\\right)}+\\frac{3}{4}\\exp{\\left(-\\frac{(9x+1)^2}{49}- \\frac{(9y+1)}{10}\\right)} \\\\\n",
    "&+\\frac{1}{2}\\exp{\\left(-\\frac{(9x-7)^2}{4} - \\frac{(9y-3)^2}{4}\\right)} -\\frac{1}{5}\\exp{\\left(-(9x-4)^2 - (9y-7)^2\\right) }.\n",
    "\\end{align*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b085eff4",
   "metadata": {
    "editable": true
   },
   "source": [
    "The function will be defined for $x,y\\in [0,1]$.  Our first step will\n",
    "be to perform an OLS regression analysis of this function, trying out\n",
    "a polynomial fit with an $x$ and $y$ dependence of the form $[x, y,\n",
    "x^2, y^2, xy, \\dots]$. We will also include bootstrap first as\n",
    "a resampling technique.  After that we will include the cross-validation technique. As in homeworks 1 and 2, we can use a uniform\n",
    "distribution to set up the arrays of values for $x$ and $y$, or as in\n",
    "the example below just a set of fixed \n",
    "values for $x$ and $y$ with a given step\n",
    "size.  We will fit a\n",
    "function (for example a polynomial) of $x$ and $y$.  Thereafter we\n",
    "will repeat much of the same procedure using the Ridge and Lasso\n",
    "regression methods, introducing thus a dependence on the bias\n",
    "(penalty) $\\lambda$.\n",
    "\n",
    "Finally we are going to use (real) digital terrain data and try to\n",
    "reproduce these data using the same methods. We will also try to go\n",
    "beyond the second-order polynomials metioned above and explore \n",
    "which polynomial fits the data best.\n",
    "\n",
    "The Python code for the Franke function is included here (it performs also a three-dimensional plot of it)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "5056dccb",
   "metadata": {
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    {
     "ename": "TypeError",
     "evalue": "gca() got an unexpected keyword argument 'projection'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[30], line 9\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mrandom\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m random, seed\n\u001b[1;32m      8\u001b[0m fig \u001b[38;5;241m=\u001b[39m plt\u001b[38;5;241m.\u001b[39mfigure()\n\u001b[0;32m----> 9\u001b[0m ax \u001b[38;5;241m=\u001b[39m \u001b[43mfig\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgca\u001b[49m\u001b[43m(\u001b[49m\u001b[43mprojection\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43m3d\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m     11\u001b[0m \u001b[38;5;66;03m# Make data.\u001b[39;00m\n\u001b[1;32m     12\u001b[0m x \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39marange(\u001b[38;5;241m0\u001b[39m, \u001b[38;5;241m1\u001b[39m, \u001b[38;5;241m0.05\u001b[39m)\n",
      "\u001b[0;31mTypeError\u001b[0m: gca() got an unexpected keyword argument 'projection'"
     ]
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    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import cm\n",
    "from matplotlib.ticker import LinearLocator, FormatStrFormatter\n",
    "import numpy as np\n",
    "from random import random, seed\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.gca(projection='3d')\n",
    "\n",
    "# Make data.\n",
    "x = np.arange(0, 1, 0.05)\n",
    "y = np.arange(0, 1, 0.05)\n",
    "x, y = np.meshgrid(x,y)\n",
    "\n",
    "\n",
    "def FrankeFunction(x,y):\n",
    "    term1 = 0.75*np.exp(-(0.25*(9*x-2)**2) - 0.25*((9*y-2)**2))\n",
    "    term2 = 0.75*np.exp(-((9*x+1)**2)/49.0 - 0.1*(9*y+1))\n",
    "    term3 = 0.5*np.exp(-(9*x-7)**2/4.0 - 0.25*((9*y-3)**2))\n",
    "    term4 = -0.2*np.exp(-(9*x-4)**2 - (9*y-7)**2)\n",
    "    return term1 + term2 + term3 + term4\n",
    "\n",
    "\n",
    "z = FrankeFunction(x, y)\n",
    "\n",
    "# Plot the surface.\n",
    "surf = ax.plot_surface(x, y, z, cmap=cm.coolwarm,\n",
    "                       linewidth=0, antialiased=False)\n",
    "\n",
    "# Customize the z axis.\n",
    "ax.set_zlim(-0.10, 1.40)\n",
    "ax.zaxis.set_major_locator(LinearLocator(10))\n",
    "ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))\n",
    "\n",
    "# Add a color bar which maps values to colors.\n",
    "fig.colorbar(surf, shrink=0.5, aspect=5)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f5e72aef",
   "metadata": {
    "editable": true
   },
   "source": [
    "### Exercise: Ordinary Least Square (OLS) on the Franke function\n",
    "\n",
    "We will generate our own dataset for a function\n",
    "$\\mathrm{FrankeFunction}(x,y)$ with $x,y \\in [0,1]$. The function\n",
    "$f(x,y)$ is the Franke function. You should explore also the addition\n",
    "of an added stochastic noise to this function using the normal\n",
    "distribution $N(0,1)$.\n",
    "\n",
    "*Write your own code* (using either a matrix inversion or a singular\n",
    "value decomposition from e.g., **numpy** ) or use your code from\n",
    "homeworks 1 and 2 and perform a standard least square regression\n",
    "analysis using polynomials in $x$ and $y$ up to fifth order. Find the\n",
    "[confidence intervals](https://en.wikipedia.org/wiki/Confidence_interval) of the parameters (estimators) $\\beta$ by computing their\n",
    "variances, evaluate the Mean Squared error (MSE)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ba33237",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "MSE(\\hat{y},\\hat{\\tilde{y}}) = \\frac{1}{n}\n",
    "\\sum_{i=0}^{n-1}(y_i-\\tilde{y}_i)^2,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f9af2ef",
   "metadata": {
    "editable": true
   },
   "source": [
    "and the $R^2$ score function.  If $\\tilde{\\hat{y}}_i$ is the predicted\n",
    "value of the $i-th$ sample and $y_i$ is the corresponding true value,\n",
    "then the score $R^2$ is defined as"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77d5b0f2",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "R^2(\\hat{y}, \\tilde{\\hat{y}}) = 1 - \\frac{\\sum_{i=0}^{n - 1} (y_i - \\tilde{y}_i)^2}{\\sum_{i=0}^{n - 1} (y_i - \\bar{y})^2},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c1f9df9",
   "metadata": {
    "editable": true
   },
   "source": [
    "where we have defined the mean value  of $\\hat{y}$ as"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d06102c",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\bar{y} =  \\frac{1}{n} \\sum_{i=0}^{n - 1} y_i.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8fb40b08",
   "metadata": {
    "editable": true
   },
   "source": [
    "Your code has to include a scaling of the data (for example by\n",
    "subtracting the mean value), and\n",
    "a split of the data in training and test data. For this exercise you can\n",
    "either write your own code or use for example the function for\n",
    "splitting training data provided by the library **Scikit-Learn** (make\n",
    "sure you have installed it).  This function is called\n",
    "$train\\_test\\_split$.  **You should present a critical discussion of why and how you have scaled or not scaled the data**.\n",
    "\n",
    "It is normal in essentially all Machine Learning studies to split the\n",
    "data in a training set and a test set (eventually  also an additional\n",
    "validation set).  There\n",
    "is no explicit recipe for how much data should be included as training\n",
    "data and say test data.  An accepted rule of thumb is to use\n",
    "approximately $2/3$ to $4/5$ of the data as training data.\n",
    "\n",
    "You can easily reuse the solutions to your exercises from week 35 and week 36."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1701de47",
   "metadata": {
    "editable": true
   },
   "source": [
    "### Exercise: Bias-variance trade-off and resampling techniques\n",
    "\n",
    "Our aim here is to study the bias-variance trade-off by implementing the **bootstrap** resampling technique.\n",
    "\n",
    "With a code which does OLS and includes resampling techniques, \n",
    "we will now discuss the bias-variance trade-off 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 and basically all Machine Learning algorithms. \n",
    "\n",
    "Before you perform an analysis of the bias-variance trade-off on your test data, make\n",
    "first a figure similar to Fig. 2.11 of Hastie, Tibshirani, and\n",
    "Friedman. Figure 2.11 of this reference displays only the test and training MSEs. The test MSE can be used to \n",
    "indicate possible regions of low/high bias and variance. You will most likely not get an\n",
    "equally smooth curve!\n",
    "\n",
    "With this result we move on to the bias-variance trade-off analysis.\n",
    "\n",
    "Consider a\n",
    "dataset $\\mathcal{L}$ consisting of the data\n",
    "$\\mathbf{X}_\\mathcal{L}=\\{(y_j, \\boldsymbol{x}_j), j=0\\ldots n-1\\}$.\n",
    "\n",
    "Let us assume that the true data is generated from a noisy model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15110cdf",
   "metadata": {
    "editable": true
   },
   "source": [
    "$$\n",
    "\\boldsymbol{y}=f(\\boldsymbol{x}) + \\boldsymbol{\\epsilon}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33046595",
   "metadata": {
    "editable": true
   },
   "source": [
    "Here $\\epsilon$ is normally distributed with mean zero and standard\n",
    "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",
    "The parameters $\\boldsymbol{\\beta}$ are in turn found by optimizing the means\n",
    "squared error via the so-called cost function"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84527747",
   "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": "da2f876d",
   "metadata": {
    "editable": true
   },
   "source": [
    "Here the expected value $\\mathbb{E}$ is the sample value. \n",
    "\n",
    "Show that you can rewrite  this as"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1845a7dc",
   "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": "d2f1d7d7",
   "metadata": {
    "editable": true
   },
   "source": [
    "Explain what the terms mean, which one is the bias and which one is\n",
    "the variance and discuss their interpretations.\n",
    "\n",
    "Perform then a bias-variance analysis of the Franke function by\n",
    "studying the MSE value as function of the complexity of your model.\n",
    "\n",
    "Discuss the bias and variance trade-off as function\n",
    "of your model complexity (the degree of the polynomial) and the number\n",
    "of data points, and possibly also your training and test data using the **bootstrap** resampling method.\n",
    "\n",
    "Note also that when you calculate the bias, in all applications you don't know the function values $f_i$. You would hence replace them with the actual data points $y_i$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e898c902",
   "metadata": {
    "editable": true
   },
   "source": [
    "### Exercise:  Cross-validation as resampling techniques, adding more complexity\n",
    "\n",
    "The aim here is to write your own code for another widely popular\n",
    "resampling technique, the so-called cross-validation method.  Again,\n",
    "before you start with cross-validation approach, you should scale your\n",
    "data.\n",
    "\n",
    "Implement the $k$-fold cross-validation algorithm (write your own\n",
    "code) and evaluate again the MSE function resulting\n",
    "from the test folds. You can compare your own code with that from\n",
    "**Scikit-Learn** if needed. \n",
    "\n",
    "Compare the MSE you get from your cross-validation code with the one\n",
    "you got from your **bootstrap** code. Comment your results. Try $5-10$\n",
    "folds.  You can also compare your own cross-validation code with the\n",
    "one provided by **Scikit-Learn**."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d23dc734",
   "metadata": {
    "editable": true
   },
   "source": [
    "### Exercise: Ridge Regression on the Franke function  with resampling\n",
    "\n",
    "Write your own code for the Ridge method, either using matrix\n",
    "inversion or the singular value decomposition as done in the previous\n",
    "exercise. Perform the same bootstrap analysis as in the\n",
    "Exercise 2  (for the same polynomials) and the cross-validation  in exercise 3 but now for different values of $\\lambda$. Compare and\n",
    "analyze your results with those obtained in exercises 1-3. Study the\n",
    "dependence on $\\lambda$.\n",
    "\n",
    "Study also the bias-variance trade-off as function of various values of\n",
    "the parameter $\\lambda$. For the bias-variance trade-off, use the **bootstrap** resampling method. Comment your results."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39a35330",
   "metadata": {
    "editable": true
   },
   "source": [
    "### Exercise: Lasso Regression on the Franke function  with resampling\n",
    "\n",
    "This exercise is essentially a repeat of the previous two ones, but now\n",
    "with Lasso regression. Write either your own code (difficult and optional) or, in this case,\n",
    "you can also use the functionalities of **Scikit-Learn** (recommended). \n",
    "Give a\n",
    "critical discussion of the three methods and a judgement of which\n",
    "model fits the data best.  Perform here as well an analysis of the bias-variance trade-off using the **bootstrap** resampling technique and an analysis of the mean squared error using cross-validation."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44d9e821",
   "metadata": {
    "editable": true
   },
   "source": [
    "### Exercise: Analysis of real data\n",
    "\n",
    "With our codes functioning and having been tested properly on a\n",
    "simpler function we are now ready to look at real data. We will\n",
    "essentially repeat in this exercise what was done in exercises 1-5. However, we\n",
    "need first to download the data and prepare properly the inputs to our\n",
    "codes.  We are going to download digital terrain data from the website\n",
    "<https://earthexplorer.usgs.gov/>,\n",
    "\n",
    "Or, if you prefer, we have placed selected datafiles at <https://github.com/CompPhysics/MachineLearning/tree/master/doc/Projects/2021/Project1/DataFiles>\n",
    "\n",
    "In order to obtain data for a specific region, you need to register as\n",
    "a user (free) at this website and then decide upon which area you want\n",
    "to fetch the digital terrain data from.  In order to be able to read\n",
    "the data properly, you need to specify that the format should be **SRTM\n",
    "Arc-Second Global** and download the data as a **GeoTIF** file.  The\n",
    "files are then stored in *tif* format which can be imported into a\n",
    "Python program using"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "0a4e6d7e",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [],
   "source": [
    "scipy.misc.imread"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16a73292",
   "metadata": {
    "editable": true
   },
   "source": [
    "Here is a simple part of a Python code which reads and plots the data\n",
    "from such files"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "168356a4",
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "import numpy as np\n",
    "from imageio import imread\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from matplotlib import cm\n",
    "\n",
    "# Load the terrain\n",
    "terrain1 = imread('SRTM_data_Norway_1.tif')\n",
    "# Show the terrain\n",
    "plt.figure()\n",
    "plt.title('Terrain over Norway 1')\n",
    "plt.imshow(terrain1, cmap='gray')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.show()\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e9ec3e68",
   "metadata": {
    "editable": true
   },
   "source": [
    "If you should have problems in downloading the digital terrain data,\n",
    "we provide two examples under the data folder of project 1. One is\n",
    "from a region close to Stavanger in Norway and the other Møsvatn\n",
    "Austfjell, again in Norway.\n",
    "Feel free to produce your own terrain data.\n",
    "\n",
    "Alternatively, if you would like to use another data set, feel free to do so. This could be data close to your reseach area or simply a data set you found interesting. See for example [kaggle.com](https://www.kaggle.com/datasets) for examples.\n",
    "\n",
    "Our final part deals with the parameterization of your digital terrain\n",
    "data (or your own data).  We will apply all three methods for linear regression, the same type (or higher order) of polynomial\n",
    "approximation and cross-validation as resampling technique to evaluate which\n",
    "model fits the data best.\n",
    "\n",
    "At the end, you should present a critical evaluation of your results\n",
    "and discuss the applicability of these regression methods to the type\n",
    "of data presented here (either the terrain data we propose or other data sets)."
   ]
  }
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