Morten Hjorth-Jensen
4995 lines
628 KiB
Plaintext
4995 lines
628 KiB
Plaintext
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"<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)\n",
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"doconce format html week39.do.txt --no_mako -->\n",
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"<!-- dom:TITLE: Week 39: Optimization and Gradient Methods -->"
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"# Week 39: Optimization and Gradient Methods\n",
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"**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University\n",
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"\n",
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"Date: **Week 39**"
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"source": [
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"## Plan for week 39\n",
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"\n",
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"**Material for the active learning sessions on Tuesday and Wednesday.**\n",
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"\n",
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" * Discussions on how to structure your report for the first project\n",
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"\n",
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" * Exercise for week 39 on how to write the abstract and the introduction of the report and how to include references. \n",
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"\n",
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" * Work on project 1, in particular resampling methods like cross-validation and bootstrap. **For more discussions of project 1, chapter 5 of Goodfellow et al is a good read, in particular sections 5.1-5.5 and 5.7-5.11**.\n",
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"\n",
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" * [Video on how to write scientific reports recorded during one of the lab sessions](https://youtu.be/tVW1ZDmZnwM)\n",
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"\n",
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"These sections summarize neatly what we have done till now and point to what is coming with respect to deep learning. \n",
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" * A general guideline can be found at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/EvaluationGrading/EvaluationForm.md>.\n",
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"\n",
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" \n",
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"\n",
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"**Material for the lecture on Thursday September 28.**\n",
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"\n",
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" * Repetition of Logistic regression equations and classification problems and discussion of Gradient methods. Examples on how to implement Logistic Regression and discussion of stochastic gradient descent \n",
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"\n",
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" * Stochastic Gradient descent with examples and automatic differentiation\n",
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"\n",
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" * [Video of lecture](https://youtu.be/bFRVuIJroHs)\n",
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"\n",
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" * Whiteboard notes TBA at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesSep28.pdf>\n",
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"\n",
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" * Readings and Videos:\n",
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"\n",
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" * These lecture notes\n",
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"\n",
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" * For a good discussion on gradient methods, we would like to recommend Goodfellow et al section 4.3-4.5 and sections 8.3-8.6. We will come back to the latter chapter in our discussion of Neural networks as well. \n",
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"\n",
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" * [Video on gradient descent](https://www.youtube.com/watch?v=sDv4f4s2SB8)\n",
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"\n",
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" * [Video on stochastic gradient descent](https://www.youtube.com/watch?v=vMh0zPT0tLI)\n",
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"\n",
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"<!-- rett opp tyrleif -->"
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"source": [
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"## Optimization, the central part of any Machine Learning algortithm\n",
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"\n",
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"The first few slides here are a repetition from last week. \n",
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"\n",
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"Almost every problem in machine learning and data science starts with\n",
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"a dataset $X$, a model $g(\\beta)$, which is a function of the\n",
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"parameters $\\beta$ and a cost function $C(X, g(\\beta))$ that allows\n",
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"us to judge how well the model $g(\\beta)$ explains the observations\n",
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"$X$. The model is fit by finding the values of $\\beta$ that minimize\n",
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"the cost function. Ideally we would be able to solve for $\\beta$\n",
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"analytically, however this is not possible in general and we must use\n",
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"some approximative/numerical method to compute the minimum."
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"source": [
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"## Revisiting our Logistic Regression case\n",
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"\n",
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"In our discussion on Logistic Regression we studied the \n",
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"case of\n",
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"two classes, with $y_i$ either\n",
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"$0$ or $1$. Furthermore we assumed also that we have only two\n",
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"parameters $\\beta$ in our fitting, that is we\n",
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"defined probabilities"
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"$$\n",
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"\\begin{align*}\n",
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"p(y_i=1|x_i,\\boldsymbol{\\beta}) &= \\frac{\\exp{(\\beta_0+\\beta_1x_i)}}{1+\\exp{(\\beta_0+\\beta_1x_i)}},\\nonumber\\\\\n",
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"p(y_i=0|x_i,\\boldsymbol{\\beta}) &= 1 - p(y_i=1|x_i,\\boldsymbol{\\beta}),\n",
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"\\end{align*}\n",
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"$$"
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]
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"source": [
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"where $\\boldsymbol{\\beta}$ are the weights we wish to extract from data, in our case $\\beta_0$ and $\\beta_1$."
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"source": [
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"## The equations to solve\n",
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"\n",
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"Our compact equations used a definition of a vector $\\boldsymbol{y}$ with $n$\n",
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"elements $y_i$, an $n\\times p$ matrix $\\boldsymbol{X}$ which contains the\n",
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"$x_i$ values and a vector $\\boldsymbol{p}$ of fitted probabilities\n",
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"$p(y_i\\vert x_i,\\boldsymbol{\\beta})$. We rewrote in a more compact form\n",
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"the first derivative of the cost function as"
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"$$\n",
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"\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}} = -\\boldsymbol{X}^T\\left(\\boldsymbol{y}-\\boldsymbol{p}\\right).\n",
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"$$"
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"source": [
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"If we in addition define a diagonal matrix $\\boldsymbol{W}$ with elements \n",
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"$p(y_i\\vert x_i,\\boldsymbol{\\beta})(1-p(y_i\\vert x_i,\\boldsymbol{\\beta})$, we can obtain a compact expression of the second derivative as"
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"source": [
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"$$\n",
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"\\frac{\\partial^2 \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T} = \\boldsymbol{X}^T\\boldsymbol{W}\\boldsymbol{X}.\n",
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"$$"
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"cell_type": "markdown",
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"source": [
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"This defines what is called the Hessian matrix."
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]
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"source": [
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"## Solving using Newton-Raphson's method\n",
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"\n",
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"If we can set up these equations, Newton-Raphson's iterative method is normally the method of choice. It requires however that we can compute in an efficient way the matrices that define the first and second derivatives. \n",
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"\n",
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"Our iterative scheme is then given by"
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"$$\n",
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"\\boldsymbol{\\beta}^{\\mathrm{new}} = \\boldsymbol{\\beta}^{\\mathrm{old}}-\\left(\\frac{\\partial^2 \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T}\\right)^{-1}_{\\boldsymbol{\\beta}^{\\mathrm{old}}}\\times \\left(\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}}\\right)_{\\boldsymbol{\\beta}^{\\mathrm{old}}},\n",
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"$$"
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"source": [
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"or in matrix form as"
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]
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"source": [
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"$$\n",
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"\\boldsymbol{\\beta}^{\\mathrm{new}} = \\boldsymbol{\\beta}^{\\mathrm{old}}-\\left(\\boldsymbol{X}^T\\boldsymbol{W}\\boldsymbol{X} \\right)^{-1}\\times \\left(-\\boldsymbol{X}^T(\\boldsymbol{y}-\\boldsymbol{p}) \\right)_{\\boldsymbol{\\beta}^{\\mathrm{old}}}.\n",
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"$$"
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"source": [
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"The right-hand side is computed with the old values of $\\beta$. \n",
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"\n",
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"If we can compute these matrices, in particular the Hessian, the above is often the easiest method to implement."
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]
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"source": [
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"## Brief reminder on Newton-Raphson's method\n",
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"\n",
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"Let us quickly remind ourselves how we derive the above method.\n",
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"\n",
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"Perhaps the most celebrated of all one-dimensional root-finding\n",
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"routines is Newton's method, also called the Newton-Raphson\n",
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"method. This method requires the evaluation of both the\n",
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"function $f$ and its derivative $f'$ at arbitrary points. \n",
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"If you can only calculate the derivative\n",
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"numerically and/or your function is not of the smooth type, we\n",
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"normally discourage the use of this method."
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"source": [
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"## The equations\n",
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"\n",
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"The Newton-Raphson formula consists geometrically of extending the\n",
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"tangent line at a current point until it crosses zero, then setting\n",
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"the next guess to the abscissa of that zero-crossing. The mathematics\n",
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"behind this method is rather simple. Employing a Taylor expansion for\n",
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"$x$ sufficiently close to the solution $s$, we have"
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"<!-- Equation labels as ordinary links -->\n",
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"<div id=\"eq:taylornr\"></div>\n",
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"\n",
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"$$\n",
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"f(s)=0=f(x)+(s-x)f'(x)+\\frac{(s-x)^2}{2}f''(x) +\\dots.\n",
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" \\label{eq:taylornr} \\tag{1}\n",
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"$$"
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"source": [
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"For small enough values of the function and for well-behaved\n",
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"functions, the terms beyond linear are unimportant, hence we obtain"
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]
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"source": [
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"$$\n",
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"f(x)+(s-x)f'(x)\\approx 0,\n",
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"$$"
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]
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"metadata": {
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"source": [
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"yielding"
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]
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"source": [
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"$$\n",
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"s\\approx x-\\frac{f(x)}{f'(x)}.\n",
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"$$"
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"source": [
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"Having in mind an iterative procedure, it is natural to start iterating with"
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"source": [
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"$$\n",
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||
"x_{n+1}=x_n-\\frac{f(x_n)}{f'(x_n)}.\n",
|
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"$$"
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]
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"source": [
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"## Simple geometric interpretation\n",
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"\n",
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"The above is Newton-Raphson's method. It has a simple geometric\n",
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"interpretation, namely $x_{n+1}$ is the point where the tangent from\n",
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"$(x_n,f(x_n))$ crosses the $x$-axis. Close to the solution,\n",
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||
"Newton-Raphson converges fast to the desired result. However, if we\n",
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||
"are far from a root, where the higher-order terms in the series are\n",
|
||
"important, the Newton-Raphson formula can give grossly inaccurate\n",
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||
"results. For instance, the initial guess for the root might be so far\n",
|
||
"from the true root as to let the search interval include a local\n",
|
||
"maximum or minimum of the function. If an iteration places a trial\n",
|
||
"guess near such a local extremum, so that the first derivative nearly\n",
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||
"vanishes, then Newton-Raphson may fail totally"
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"source": [
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||
"## Extending to more than one variable\n",
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"\n",
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"Newton's method can be generalized to systems of several non-linear equations\n",
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"and variables. Consider the case with two equations"
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]
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"source": [
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"$$\n",
|
||
"\\begin{array}{cc} f_1(x_1,x_2) &=0\\\\\n",
|
||
" f_2(x_1,x_2) &=0,\\end{array}\n",
|
||
"$$"
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]
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"source": [
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"which we Taylor expand to obtain"
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]
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},
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"id": "9c8e6fc9",
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"metadata": {
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"source": [
|
||
"$$\n",
|
||
"\\begin{array}{cc} 0=f_1(x_1+h_1,x_2+h_2)=&f_1(x_1,x_2)+h_1\n",
|
||
" \\partial f_1/\\partial x_1+h_2\n",
|
||
" \\partial f_1/\\partial x_2+\\dots\\\\\n",
|
||
" 0=f_2(x_1+h_1,x_2+h_2)=&f_2(x_1,x_2)+h_1\n",
|
||
" \\partial f_2/\\partial x_1+h_2\n",
|
||
" \\partial f_2/\\partial x_2+\\dots\n",
|
||
" \\end{array}.\n",
|
||
"$$"
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"source": [
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"Defining the Jacobian matrix ${\\bf \\boldsymbol{J}}$ we have"
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"source": [
|
||
"$$\n",
|
||
"{\\bf \\boldsymbol{J}}=\\left( \\begin{array}{cc}\n",
|
||
" \\partial f_1/\\partial x_1 & \\partial f_1/\\partial x_2 \\\\\n",
|
||
" \\partial f_2/\\partial x_1 &\\partial f_2/\\partial x_2\n",
|
||
" \\end{array} \\right),\n",
|
||
"$$"
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]
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{
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"cell_type": "markdown",
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"source": [
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"we can rephrase Newton's method as"
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|
||
"$$\n",
|
||
"\\left(\\begin{array}{c} x_1^{n+1} \\\\ x_2^{n+1} \\end{array} \\right)=\n",
|
||
"\\left(\\begin{array}{c} x_1^{n} \\\\ x_2^{n} \\end{array} \\right)+\n",
|
||
"\\left(\\begin{array}{c} h_1^{n} \\\\ h_2^{n} \\end{array} \\right),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "521c56f5",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where we have defined"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4508944b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\left(\\begin{array}{c} h_1^{n} \\\\ h_2^{n} \\end{array} \\right)=\n",
|
||
" -{\\bf \\boldsymbol{J}}^{-1}\n",
|
||
" \\left(\\begin{array}{c} f_1(x_1^{n},x_2^{n}) \\\\ f_2(x_1^{n},x_2^{n}) \\end{array} \\right).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "69b72003",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"We need thus to compute the inverse of the Jacobian matrix and it\n",
|
||
"is to understand that difficulties may\n",
|
||
"arise in case ${\\bf \\boldsymbol{J}}$ is nearly singular.\n",
|
||
"\n",
|
||
"It is rather straightforward to extend the above scheme to systems of\n",
|
||
"more than two non-linear equations. In our case, the Jacobian matrix is given by the Hessian that represents the second derivative of cost function."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "dd11ba71",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Steepest descent\n",
|
||
"\n",
|
||
"The basic idea of gradient descent is\n",
|
||
"that a function $F(\\mathbf{x})$, \n",
|
||
"$\\mathbf{x} \\equiv (x_1,\\cdots,x_n)$, decreases fastest if one goes from $\\bf {x}$ in the\n",
|
||
"direction of the negative gradient $-\\nabla F(\\mathbf{x})$.\n",
|
||
"\n",
|
||
"It can be shown that if"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ccb5e1a6",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathbf{x}_{k+1} = \\mathbf{x}_k - \\gamma_k \\nabla F(\\mathbf{x}_k),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6952b928",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"with $\\gamma_k > 0$.\n",
|
||
"\n",
|
||
"For $\\gamma_k$ small enough, then $F(\\mathbf{x}_{k+1}) \\leq\n",
|
||
"F(\\mathbf{x}_k)$. This means that for a sufficiently small $\\gamma_k$\n",
|
||
"we are always moving towards smaller function values, i.e a minimum."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f0c5476d",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## More on Steepest descent\n",
|
||
"\n",
|
||
"The previous observation is the basis of the method of steepest\n",
|
||
"descent, which is also referred to as just gradient descent (GD). One\n",
|
||
"starts with an initial guess $\\mathbf{x}_0$ for a minimum of $F$ and\n",
|
||
"computes new approximations according to"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4aeb7465",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathbf{x}_{k+1} = \\mathbf{x}_k - \\gamma_k \\nabla F(\\mathbf{x}_k), \\ \\ k \\geq 0.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "337ccfd3",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"The parameter $\\gamma_k$ is often referred to as the step length or\n",
|
||
"the learning rate within the context of Machine Learning."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7540286d",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## The ideal\n",
|
||
"\n",
|
||
"Ideally the sequence $\\{\\mathbf{x}_k \\}_{k=0}$ converges to a global\n",
|
||
"minimum of the function $F$. In general we do not know if we are in a\n",
|
||
"global or local minimum. In the special case when $F$ is a convex\n",
|
||
"function, all local minima are also global minima, so in this case\n",
|
||
"gradient descent can converge to the global solution. The advantage of\n",
|
||
"this scheme is that it is conceptually simple and straightforward to\n",
|
||
"implement. However the method in this form has some severe\n",
|
||
"limitations:\n",
|
||
"\n",
|
||
"In machine learing we are often faced with non-convex high dimensional\n",
|
||
"cost functions with many local minima. Since GD is deterministic we\n",
|
||
"will get stuck in a local minimum, if the method converges, unless we\n",
|
||
"have a very good intial guess. This also implies that the scheme is\n",
|
||
"sensitive to the chosen initial condition.\n",
|
||
"\n",
|
||
"Note that the gradient is a function of $\\mathbf{x} =\n",
|
||
"(x_1,\\cdots,x_n)$ which makes it expensive to compute numerically."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b7ce5820",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## The sensitiveness of the gradient descent\n",
|
||
"\n",
|
||
"The gradient descent method \n",
|
||
"is sensitive to the choice of learning rate $\\gamma_k$. This is due\n",
|
||
"to the fact that we are only guaranteed that $F(\\mathbf{x}_{k+1}) \\leq\n",
|
||
"F(\\mathbf{x}_k)$ for sufficiently small $\\gamma_k$. The problem is to\n",
|
||
"determine an optimal learning rate. If the learning rate is chosen too\n",
|
||
"small the method will take a long time to converge and if it is too\n",
|
||
"large we can experience erratic behavior.\n",
|
||
"\n",
|
||
"Many of these shortcomings can be alleviated by introducing\n",
|
||
"randomness. One such method is that of Stochastic Gradient Descent\n",
|
||
"(SGD), see below."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0a557da3",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Convex functions\n",
|
||
"\n",
|
||
"Ideally we want our cost/loss function to be convex(concave).\n",
|
||
"\n",
|
||
"First we give the definition of a convex set: A set $C$ in\n",
|
||
"$\\mathbb{R}^n$ is said to be convex if, for all $x$ and $y$ in $C$ and\n",
|
||
"all $t \\in (0,1)$ , the point $(1 − t)x + ty$ also belongs to\n",
|
||
"C. Geometrically this means that every point on the line segment\n",
|
||
"connecting $x$ and $y$ is in $C$ as discussed below.\n",
|
||
"\n",
|
||
"The convex subsets of $\\mathbb{R}$ are the intervals of\n",
|
||
"$\\mathbb{R}$. Examples of convex sets of $\\mathbb{R}^2$ are the\n",
|
||
"regular polygons (triangles, rectangles, pentagons, etc...)."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "bdbf8a07",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Convex function\n",
|
||
"\n",
|
||
"**Convex function**: Let $X \\subset \\mathbb{R}^n$ be a convex\n",
|
||
"set. Assume that the function $f: X \\rightarrow \\mathbb{R}$ is\n",
|
||
"continuous, then $f$ is said to be convex if $f(tx_1 + (1-t)x_2) \\leq tf(x_1) + (1-t)f(x_2)$\n",
|
||
"for all $x_1, x_2 \\in X$ and for all $t \\in [0,1]$.\n",
|
||
"If $\\leq$ is replaced with a strict inequaltiy in the\n",
|
||
"definition, we demand $x_1 \\neq x_2$ and $t\\in(0,1)$ then $f$ is said\n",
|
||
"to be strictly convex. For a single variable function, convexity means\n",
|
||
"that if you draw a straight line connecting $f(x_1)$ and $f(x_2)$, the\n",
|
||
"value of the function on the interval $[x_1,x_2]$ is always below the\n",
|
||
"line as illustrated below."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e02d1dac",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Conditions on convex functions\n",
|
||
"\n",
|
||
"In the following we state first and second-order conditions which\n",
|
||
"ensures convexity of a function $f$. We write $D_f$ to denote the\n",
|
||
"domain of $f$, i.e the subset of $R^n$ where $f$ is defined. For more\n",
|
||
"details and proofs we refer to: [S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press](http://stanford.edu/boyd/cvxbook/).\n",
|
||
"\n",
|
||
"**First order condition.**\n",
|
||
"\n",
|
||
"Suppose $f$ is differentiable (i.e $\\nabla f(x)$ is well defined for\n",
|
||
"all $x$ in the domain of $f$). Then $f$ is convex if and only if $D_f$\n",
|
||
"is a convex set and $f(y) \\geq f(x) + \\nabla f(x)^T (y-x)$ holds\n",
|
||
"for all $x,y \\in D_f$.\n",
|
||
"\n",
|
||
"This condition means that for a convex function\n",
|
||
"the first order Taylor expansion (right hand side above) at any point\n",
|
||
"a global under estimator of the function. To convince yourself you can\n",
|
||
"make a drawing of $f(x) = x^2+1$ and draw the tangent line to $f(x)$ and\n",
|
||
"note that it is always below the graph.\n",
|
||
"\n",
|
||
"**Second order condition.**\n",
|
||
"\n",
|
||
"Assume that $f$ is twice\n",
|
||
"differentiable, i.e the Hessian matrix exists at each point in\n",
|
||
"$D_f$. Then $f$ is convex if and only if $D_f$ is a convex set and its\n",
|
||
"Hessian is positive semi-definite for all $x\\in D_f$. For a\n",
|
||
"single-variable function this reduces to $f''(x) \\geq 0$. Geometrically this means that $f$ has nonnegative curvature\n",
|
||
"everywhere.\n",
|
||
"\n",
|
||
"This condition is particularly useful since it gives us an procedure for determining if the function under consideration is convex, apart from using the definition."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d9a72971",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## More on convex functions\n",
|
||
"\n",
|
||
"The next result is of great importance to us and the reason why we are\n",
|
||
"going on about convex functions. In machine learning we frequently\n",
|
||
"have to minimize a loss/cost function in order to find the best\n",
|
||
"parameters for the model we are considering. \n",
|
||
"\n",
|
||
"Ideally we want the\n",
|
||
"global minimum (for high-dimensional models it is hard to know\n",
|
||
"if we have local or global minimum). However, if the cost/loss function\n",
|
||
"is convex the following result provides invaluable information:\n",
|
||
"\n",
|
||
"**Any minimum is global for convex functions.**\n",
|
||
"\n",
|
||
"Consider the problem of finding $x \\in \\mathbb{R}^n$ such that $f(x)$\n",
|
||
"is minimal, where $f$ is convex and differentiable. Then, any point\n",
|
||
"$x^*$ that satisfies $\\nabla f(x^*) = 0$ is a global minimum.\n",
|
||
"\n",
|
||
"This result means that if we know that the cost/loss function is convex and we are able to find a minimum, we are guaranteed that it is a global minimum."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c3e744c2",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Some simple problems\n",
|
||
"\n",
|
||
"1. Show that $f(x)=x^2$ is convex for $x \\in \\mathbb{R}$ using the definition of convexity. Hint: If you re-write the definition, $f$ is convex if the following holds for all $x,y \\in D_f$ and any $\\lambda \\in [0,1]$ $\\lambda f(x)+(1-\\lambda)f(y)-f(\\lambda x + (1-\\lambda) y ) \\geq 0$.\n",
|
||
"\n",
|
||
"2. Using the second order condition show that the following functions are convex on the specified domain.\n",
|
||
"\n",
|
||
" * $f(x) = e^x$ is convex for $x \\in \\mathbb{R}$.\n",
|
||
"\n",
|
||
" * $g(x) = -\\ln(x)$ is convex for $x \\in (0,\\infty)$.\n",
|
||
"\n",
|
||
"3. Let $f(x) = x^2$ and $g(x) = e^x$. Show that $f(g(x))$ and $g(f(x))$ is convex for $x \\in \\mathbb{R}$. Also show that if $f(x)$ is any convex function than $h(x) = e^{f(x)}$ is convex.\n",
|
||
"\n",
|
||
"4. A norm is any function that satisfy the following properties\n",
|
||
"\n",
|
||
" * $f(\\alpha x) = |\\alpha| f(x)$ for all $\\alpha \\in \\mathbb{R}$.\n",
|
||
"\n",
|
||
" * $f(x+y) \\leq f(x) + f(y)$\n",
|
||
"\n",
|
||
" * $f(x) \\leq 0$ for all $x \\in \\mathbb{R}^n$ with equality if and only if $x = 0$\n",
|
||
"\n",
|
||
"Using the definition of convexity, try to show that a function satisfying the properties above is convex (the third condition is not needed to show this)."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "2732cf8b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Standard steepest descent\n",
|
||
"\n",
|
||
"Before we proceed, we would like to discuss the approach called the\n",
|
||
"**standard Steepest descent** (different from the above steepest descent discussion), which again leads to us having to be able\n",
|
||
"to compute a matrix. It belongs to the class of Conjugate Gradient methods (CG).\n",
|
||
"\n",
|
||
"[The success of the CG method](https://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf)\n",
|
||
"for finding solutions of non-linear problems is based on the theory\n",
|
||
"of conjugate gradients for linear systems of equations. It belongs to\n",
|
||
"the class of iterative methods for solving problems from linear\n",
|
||
"algebra of the type"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1b14ba6d",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{A}\\boldsymbol{x} = \\boldsymbol{b}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "5f271cd8",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"In the iterative process we end up with a problem like"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "eb0ce7c8",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{r}= \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "3482f635",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where $\\boldsymbol{r}$ is the so-called residual or error in the iterative process.\n",
|
||
"\n",
|
||
"When we have found the exact solution, $\\boldsymbol{r}=0$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0c88f8d2",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Gradient method\n",
|
||
"\n",
|
||
"The residual is zero when we reach the minimum of the quadratic equation"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "fe152e73",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"P(\\boldsymbol{x})=\\frac{1}{2}\\boldsymbol{x}^T\\boldsymbol{A}\\boldsymbol{x} - \\boldsymbol{x}^T\\boldsymbol{b},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "740c5860",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"with the constraint that the matrix $\\boldsymbol{A}$ is positive definite and\n",
|
||
"symmetric. This defines also the Hessian and we want it to be positive definite."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "477da242",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Steepest descent method\n",
|
||
"\n",
|
||
"We denote the initial guess for $\\boldsymbol{x}$ as $\\boldsymbol{x}_0$. \n",
|
||
"We can assume without loss of generality that"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7e2169e6",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{x}_0=0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e513c1c5",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"or consider the system"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a4a4f67c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{A}\\boldsymbol{z} = \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "96138e83",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"instead."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f843d9f8",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Steepest descent method\n",
|
||
"One can show that the solution $\\boldsymbol{x}$ is also the unique minimizer of the quadratic form"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "5702234f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"f(\\boldsymbol{x}) = \\frac{1}{2}\\boldsymbol{x}^T\\boldsymbol{A}\\boldsymbol{x} - \\boldsymbol{x}^T \\boldsymbol{x} , \\quad \\boldsymbol{x}\\in\\mathbf{R}^n.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "682a415f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"This suggests taking the first basis vector $\\boldsymbol{r}_1$ (see below for definition) \n",
|
||
"to be the gradient of $f$ at $\\boldsymbol{x}=\\boldsymbol{x}_0$, \n",
|
||
"which equals"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "302ac54a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{A}\\boldsymbol{x}_0-\\boldsymbol{b},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "dd2cbeb1",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"and \n",
|
||
"$\\boldsymbol{x}_0=0$ it is equal $-\\boldsymbol{b}$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f280370e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Final expressions\n",
|
||
"We can compute the residual iteratively as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9702a162",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{r}_{k+1}=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_{k+1},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "3a1de3f0",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which equals"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4fa494ea",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{b}-\\boldsymbol{A}(\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{r}_k),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a4f12308",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"or"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "df770c35",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"(\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k)-\\alpha_k\\boldsymbol{A}\\boldsymbol{r}_k,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b1a30174",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which gives"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6f816a49",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\alpha_k = \\frac{\\boldsymbol{r}_k^T\\boldsymbol{r}_k}{\\boldsymbol{r}_k^T\\boldsymbol{A}\\boldsymbol{r}_k}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4e5cd41c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"leading to the iterative scheme"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "91f972cb",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{x}_{k+1}=\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{r}_{k},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "97064af3",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Steepest descent example"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 1,
|
||
"id": "5af74f1d",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_15547/3838917029.py:18: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().\n",
|
||
" ax = fig.gca(projection=\"3d\")\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"<mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x128cc9730>"
|
||
]
|
||
},
|
||
"execution_count": 1,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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\n",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week39_80_2.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"%matplotlib inline\n",
|
||
"\n",
|
||
"import numpy as np\n",
|
||
"import numpy.linalg as la\n",
|
||
"\n",
|
||
"import scipy.optimize as sopt\n",
|
||
"\n",
|
||
"import matplotlib.pyplot as pt\n",
|
||
"from mpl_toolkits.mplot3d import axes3d\n",
|
||
"\n",
|
||
"def f(x):\n",
|
||
" return x[0]**2 + 3.0*x[1]**2\n",
|
||
"\n",
|
||
"def df(x):\n",
|
||
" return np.array([2*x[0], 6*x[1]])\n",
|
||
"\n",
|
||
"fig = pt.figure()\n",
|
||
"ax = fig.gca(projection=\"3d\")\n",
|
||
"\n",
|
||
"xmesh, ymesh = np.mgrid[-3:3:50j,-3:3:50j]\n",
|
||
"fmesh = f(np.array([xmesh, ymesh]))\n",
|
||
"ax.plot_surface(xmesh, ymesh, fmesh)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "db2d4ba3",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"And then as countor plot"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 2,
|
||
"id": "dbba72eb",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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vbmB/Vz2tA4bTnhfnH0JxVCrFkclMjUwmLyxelvIWYgQoikLrQD+He5o41NPIoZ4myvpaT1sM0E+tZWpkMjOjU5kVnc7UiGQCtBOri+CeJNvI7p497O7eO2xfnmh9NPOj57Igah7xAfFerNK7JJRMQC/Vv8yWzq3DzqvPCspkQfQ85kTOJlgX7MXqLiyXonCiv539XfXs72pgf3f9aUdlGpWKyWHxQ0dlKUyPTCEhMMxLFQshBhx2SvtaPN3Lkp7G0xaB06rUFEYkMjMqjZnRacyISp1Qy+m7FBfHjSfY0bWTfT0Hhq2EnRmUwb2ZXyIpINGLFXqHhJIJ6Lm659nYsZkYv2jmR81jfvQ84v3jvF3WBdNs7mNHRzW7OmvY01l32nwQvVpDUUQys6LdL2ZTI5MJ0srqi0KMVYqiUGPsYn+3++BiX1fdaeuoaFQqCsITmRebyfzYTKZFpkyY4R6b00ZJ3yF2du3iqOEYGpWaPxb/wSdXw5ZQMgG1DbTR7zCSE5w9ISaSGe1WdnfWsrOjhp0dNTR8ZMZ/oEbHtKgUdwiJSmNKRBJ+MhQjxLilKArNlj72d9Wzr7ue/V31NJh7hz0nUKNjZnQ682MzWRCbRVZI9IR4vTPYDdSa6pgWMdXbpXiFhBIx5iiKwvH+dra1VbG1vYpDPY3Dxp81KhVTI5KZH5vJvNhMpkQkoZsgR0xCiDNrsRjYM3Rwsquz5rRh2oSAMBbHZbMoLpu5sZnSHR2nJJSIMcFot7Kro4Yt7ZVsb68+baGm9OAoFsRmMj82i9nR6RNqbHmicrhcWOyDmAftmO2DWOx2bE4HNocTm8Px4W2n+7bd6cLhcuFUhq5diudjp+vcLzcqFWjUarQqNRq1Cq1ajUaldl+r1fhpNPhptfhpNPhrtfhptB9+rNMRpNMRqNMTrNfhp9FOiCPuiezkXLKT3dN9XXUMnrKwoU6lZkZ0GouGQkp2SIz8n44TEkqE1zSYetjUdoJNrcc50N0wrBvir9EyNyaTRXHZLI7LJjlIlmsebYqi0G+z0WMdoHdg6GIdwGCz0W+zYrTZ6LfZMNis9A/dNg0OuoOI3c6g8/TVb8cDtUpFoE5HkE5PoE5HqJ/fKRf/YbfD/fyJCAggIiCASH/3tV4jXbvRNuCws7erjm3tlWxrrzptqCcpMJyl8ZO4KGESs6LTJ8xclIlIQokYNU7FxeGeJja1nmBT23GqjV3DHs8IjhoKITnMjE6TeSEjQFEUeq0DdFosdJhNdJktdFhMdA5dd5kt9AxYPEHkXDvMflJatXroDV6Ln1b3kW6FBj+NFr1Gg16jcXc7hrobWpXK87FapULF2Y90XSg4XS6crpPdlqEui8uF3eXydGUGnY6hLo3Tc22x2xlw2LHYz7yH0fkK1us9ASU6MJDYoGDPdYznOojowED8tPI7PhLqTN1sbXMHlL0f6aIEafUsjM1macIkFsfl+NSS+OOBhBIxoqxOOzs7aljfUsHmthPDzpTRqtTMiEplaUIuS+MnkRrsmzsNXygnOxtN/QZaTUZajEbaTCZaTUbaTEZajUbazKbz7mAE6XREBgS6OwL+/sO6BWGn3A7R+xHi5+fpMgTp3UMi46Vz4HS5GHA4PJ0e8+Ag5sFBjIM2Tyfo1M6Q0Waj1zpAn9VKz4CFXqsV13m+LEYFBJIQHExCSAjxwSEkBJ+8DiYpNJT44BC0allQ67OwOAbZ3VnLptbjbG47Qdcpc1HUqCiOSmFZwmSWJU6WjuwYIKFEXHBGu5UtbZWsb6lgW3slllN20Q3V+bM4LoeLEiaxKDabUL2/Fysdf2wOB/WGPur7+mgy9tPYb6C530Bjfz9N/QZMg4Of6OtE+gcQHRRETGAgMYFBxAYFER0YRExQEFEBgUQGBBAZEECEf4AczX9CLkWh32alZ2Bg6GKhy2Kh02Kmw2ymy2Ie1pEaPMPmjh+lUalICAkhOSSM5LBQkkPCSAl1384IjyQqIEDmSpwHl6JQ2tvCpjZ3QKkwtA97PC8snksSJ7M8MY8cmYfiFRJKxAVhttvY0Hqc95uPsb2jethuugkBoSxLnMwlCZOZHpUqZ8p8DJei0Go0UtPbQ21fL7V9vZ7bzf39Z9lU/kPRgYEkhoQSHxxM4skj75CQoY9DiQkKGjfdi4lKURT6rFbaTEZaTEMdLeNQR2uou9XS3/+xwSVE70dmRAQZ4RFkDF1nRkSSER5BgG5irYY6EpotfWxqPc76lgr2d9cPG67MCI7isqQCLk8uICc01otV+hYJJeJTszkdbG2v5L2mUja1nhi2q25mcDTLh4448sMT5IjjDFyKQouxn8qebiq7u6ns6eZEdxfVvT3nnN8QovcjLTyclNAwUkJDSQodOnoODSUpJFTejCYIl6LQaTbT2G+gaagTdvJ2g6GPFuPZA6oKSAkNIzsyipyoKCZFRpMdFUV2RKT8fpxFr83CpjZ3QNnRUT0sEE4KjeWq5ClckVxIUlC494r0ARJKxHlxKi72dNaxuvEo61rLMdo/XMo+IziKK5ILuTQpX44sPsJos1HR3Ul5ZycVXZ2Ud3VS2dN91vChU6tJCwt3H/0OHfm6j4ilZS/cTg7l1fT2UtvXQ01vL3VDXbVeq/WMn3MyrEyOjmFydAx5MTHkRceQEjqxd+w9Xya7jc1tJ1jTdIxtHVXDOr/FkSlcmVzIZckFRPkFebHKiUlCifhYiqJQZmjj7YbDrGkqHTZRLD4glCuSC7kyuZC8sHiff2FTFIV2s4nSjnZKOzo8AaSx//RNAcEdPjIiIpkUGXXKUW0UqWHh6GSIRXxK3RaLp/NW1dPt6cb1WAfO+PxgnZ7c6GjyomMoiImlMDaOnKhoGebDvevxupZyVjeVsqez1tOd0qhUzI3J5JqUIpYlTiZQFmu7ICSUiLNqG+hnVeMR3m44QrWx03N/mC6Ay5LzuTJ5CjOiUlH7aBA5NYAcHQohpR3tdFpO36YdICE4xH10OnTJjY4mTcKHGEXdFgsnursoHwrLFV2dVHZ3n3Huil6tITc6msLYOIpi4ySoAB0DRtY0H+O9plKO9DZ77g/U6lmRmMe1qVOZHZ3us6+JF4KEEjGM2THI+pZy3m44wu7OGs9RgV6t4ZKEyVydUsSCuCyfXHzIPDjI0Y52StpaONzWxqH2VjrMpwcQjUpFdmQUhbFx5MfEkhcdw+ToaML9A7xQtRDnZnc6qenrdXf1Ojs41tnB0Y52+m22056rV2vIj4llWkIC0+LiKY5PJDk01Cc7pPWmHt5tPMI7jUeGLdaWEBDK1SlFXJNSRFZojBcrHJ8klAgUReFAdwNv1B/ig+Zjw07hnRmVxjWpRVyamO9Tp+8qikJNbw8HWls41NbKofY2TnR3nbYOhVqlImcogEwZOprMi46RyYRiXFMUhcZ+g6cL6O4EnjmoRAUEMC0+gWnxCRTHJzItPoFAH/r9VxSFQz1N7uHt5mP02z+czzMlIpEb0oq5IqnQp14/PwsJJT6s22bmjfoSXq8rof6UnXdTgyK5NtWd9H1lMSGHy0VZZwd7m5vY19LE/pbmM04WTAgOoXjoBXhqfDyFMXESQIRPUBSFBoOBQ+2t7qDe1kpZZwd2l2vY8zQqFfkxscxMTGJOUjKzk5J9pktoczrY3HaCdxqOsLW90rN1hp9ay4qkPG5Jn8GMqFSf7Cx9UhJKfIyiKOztquPl2gNsaCnHPvRHE6jRcVlyATemFVMcmTLh/2icLhdlXZ3sbKxnd1MTB1qaMdmHLzzmp9EyNS6e4gR3CJkWl0BccLCXKhZi7LE5HJR1dlAyFFIOtrXQYjSe9rzcqGjmJCUzLyWVuUkphPlP/K5Bt83MqsYjvF5XQtUpc/KyQqK5JX0G16ZOJUzvG2HtfEgo8RFGu5W3Gg7z35p91Jq6PfcXRSRxc/p0Lk8unNBbfSuKQm1fLzsbG9jR2MDupkYMtuGdkBC9n+foblZiEgWxcT49qU+IT6PZ2M/+lmb2Njext7mJ6t6eYY+rVSoKY+OYn5zK/JRUZiYm4q+duN1GRVE40tvMa3UHWd1UysDQ8LifWsuVKYXckTmb/PAEL1c5dkgomeAq+zt4qWYf7zQc9swVCdTquTplCremzyQvPN7LFY6cngEL2xvq2dZQz87GelpNpmGPB+v0zElOZl5yKnOSkpkcHYNG9hkR4oLqtJjZ19zMnuZGdjY2nBZS9BoNMxKSWJCSypK0dPJiYifs2StGu5VVjUf5X+0Bjvd/uMR9cWQKd2TOYnlSvk+eRHAqCSUTkMPlYmPrcV6q2cuerjrP/VkhMXwucxbXphQRpPPzXoEjxOFycbi9la31dWypr+Noe9uwFS/1ag3TExKZn5LKgpRUpsTFy2ZnQoyyNpORnY0Nnq5lu3n4wUJ0YCCLU9NZlJbOotQ0IgMm3i6+JyfHvlSzjw+aj3mG0aP9grg5fQa3ZswgLsD33rtAQsmE9Lkt/6KkpxFwTzq7OGEyd2TOYnZ0+oSbK9JpNrOproat9XVsb6w/7eyAydExLE5NY0FKGjMTk2RSqhBjyMmz3HY0NrC9oZ6dTQ3DVjlWAVPi4lmSls5FaRkUxcVPuG5mp9XEq3UHeKX2AB1W93wcjUrFcwvvYkZ0qperG30SSiagp49v5fmqPdycMYNb02eQEBjm7ZIuGEVRKOvsYENtDRvrajjS3jbs8TA/fxamprI4LYNFqWnEB4d4qVIhxPmyORwcbG1hS0MdW+vrqOjqHPZ4VEAAF6VncnFGJgtT0gjxmzgdX7vLyYbWCl6q2UedqZv1lz7gk0M5EkomIItjEK1KjV4zMbactzrs7GhsYGNtDZtqa2j7SLt3SmwcF6VnsGToSEqGZISYGNpNJrY21LGlrpatDXWYBj88Q06nVjMnKYWLMzK5JCOLlLCJc/DVNzhAuI+emSOhRIxJVoedzXV1vFd1nI21NcNaugFaLQtT07g4I4ul6RnEBslpukJMdHank30tzWysrWFDbTX1hr5hjxfGxHJ5ziSuyM4lLTzcKzWKz05CiRgzzhVEEoJDWJaZxcXpmcxNTsFPOzG6QL5MURQcThcDdjs2u4NBhxOH04XT5cLudOFwunC4XDiH7jsnlQqdWo1W8+FFM/SxTqPBT6vFX6/FT6tFrZ5Y86p8VU1vjyeg7G9pxnnKW5IElPFLQonwqkGnk631tbxzouK0IJIUEsoVOZO4InsSRXGyA/FYMuhw0Ge2YrBY6bNYMZgH6LNYMQ3YMNkGMVsHMVptmK2DmKyDmG3ui3XQgdVux2p3YB10nLZs/2jw02rw02nx1+vw12kJ1OsI8tcT7K8nyM/Pfe2vJ8TfjyB/PaEBfoQHBRAe6E9YkD/hgQEE++vl93EM6bZYWFtTxXuVx9nd1HhaQLlyUi5XT5pMYoi8H4x1EkrEqHMpCnubm3jneDlrqiqHLWImQcR7bHYHHQYTXUYzXUYLXf3u626Tme5+C11GM90mC31mKwOD9o//gudBrVKh12qGdTi0p3Q61GoV5/pNcCngcDpxuIY6LENdFofThd3p7sBcSFq1mtBAfyKC/IkOCSIqJIjo0MCh2x9ex4UFExboL7/Ho+hcAWV2YjLX5E7m8uxJRAT45pyNsU5CiRgViqJwrLODd46X8+6J48Mmq8YFBXPVpFyuysmVIDJCXC6Fjn4TzT0GWnqNtPcZaesz0W4w0j503WMaOK+vqVapCAv0JyzQn/Ag93VogL+n6xDsP9R18NN7rk92J/x1Q8MpOi0BOh1ajXpE/9+dLhc2uwOr3YHN7mBg0DH0sR2Lze7p7pisg5it7m6PacDd7ekf6gb1mQcwWKxY7Y7z+t7+Oi1xYcHEhYcQHx5MXFgIceHBJISHkBgZSlJkGAF6OVV9JJwMKKuOV7CnudGzbpFWrWZxajrX5E5mWWa2T20gONZJKBEjqtVo5K3jZbxZXkbVKSs5hvr5cXn2JK6ZNJnZSckTbu0BbxgYtNPQ1Ud9Zy9N3Qaae/pp7jl53Y/d6fzYr+Gv0xITGuQ50o/yHPm7j/4jQwKJCAogLNCfEH8/n5yfYbU7PAGlx2Sh2+i+dBnNnusuo4Vuo/kTB72okECSIsNIigwlOTKM5KgwUqLDSY8JJzokSIL6BdBi7Gd15XHeOV7Bsc4Oz/2BOh2XZeVwQ14Bc5NTJuxqsuOFhBJxwQ3Y7XxQXcUb5cfY0VjvOTrx02i5JCOTa3InsyQtQyarfgoul0Jzj4Hajh7qOvto6OqlrrOX+s4+2vpO3wjtVFq1mviIEJIiQokLdx+tx4eHEO85ig8hNMBP3gAvoEGHg3aDifY+E219RtoNQ9d9Jlp73WHRaLWd82sE+ulIi4kgPTqCtJhw9+2YCDLjIgn0m7j7VY2kqp5uVp2o4J3jFcPO4kkIDuH6yfnckJdPZkSk9wr0YRJKxAWhKAoH21r437FS3qs8jvmUCauzEpO4Ia+AK7InTajFjkaSoii095k40dbFiZZOqtq6qWnvobaj55zDB2GB/qRFh5MSHU5SZBjJkaEkRYWRHBlGbFgwWo10pMYag8Xq6Wi5O1wGmroNNHT10dzTf87JwAkRIWTFRZEVF8WkxGhy4qPJjIvETyeB/5NQFIWStlZeLz/G6srjw1aEnhaXwE35BVw9abK8bo0iCSXiMzENDvJWRRkvHD3Mie4uz/2poWFcn5fP9ZPzSQ0L916B44DLpVDf1UtZUwflTR2UN7svxoEzH0H7aTXuo+XYCM9Rc1pMBGnR4YQHyeS9icTucNLYbaChy90Nc3fFeqnt6KHLaDnj52jUKjJiI8lLiiUvOZa8pFgmJ8UQ7C9vrOdiczjYUFvN6+VlbK2v9UyQDdTpuDY3j89PmUpeTKyXq5z4JJSIT6W8q5MXjx7m7YoyT1fEX6vlypxcbs4vZFZikgwDnIGiKNR39XGkvpWypnbKmzqoaOnEYjv9bBatWk16bAQ58dHkJESTFR9FdnwUSZGhMgdHYLBYqW7rpqq9m6rWbirbuqhs7cJgsZ7x+ekxEZ6gUpgaT0FyHIF+MsHzTDrNZt4+Xs4rx44O29V4RkIid0yZyuXZk2T4eYRIKBGfmM3hYE1VJS8ePcSB1hbP/ZkREdwxZRo35uUT6ufvxQrHnj7zAEcb2jhS38rRhjaONrTRf4YOiL9OS25iDHnJseQPvXFkxkWilxc+cR4URaGj38zx5g6OndJ5O9N8I7VKRU5CNFNS4ylKjWdKWjyZsVE+OXn5bBRFYU9zEy8cOcTamiocQ4v4RfoHcFNBIZ8rLJJO8AUmoUR8rHaTiZdKD/PS0cN0D7jPJtCq1SzPzObzU6YyNzlFuiK4X8DqOnspqW3hYG0zh2pbqO/qO+15flqN+2g1JZ785Fjyk+NIj42Q7ocYMT0miyegHGts50hDGx0G02nPC/bXMyU1nuKMJKZnJDIlNUG6KUM6zCZeOXaUl0uP0Gpy/+xUwNL0TL44rZiFKWnyOngBSCgRZ3WorZV/HzrImqoTniOE+KBgbiss4taCKcQF+/aeM3ank/KmDk8IKaltodd8+img6TERTEmNdx+RpiUwKTEancb3dv8UY0u7wcTR+laO1LdypKGNsqZ2BgaHT6LWqFXkJcUyPTOJ6RlJTEtPJCok0EsVjw0Ol4tNtTW8cPQQ2xrqPffnREbxhanFXD85X9Y9+QwklIhhBp1O1lSdYOWhgxxub/PcPzMxibumFrM8M9tn31AdThflzR3srWpkX1UjB2ubT3sR99NqmJKWQHFGIsXpiRSlJRAWKENaYuxzOF1UtXVxqK6Vg7XNHKxppv0M3ZSsuEhmZacwOzuFWVnJPj25uqa3h/8cLuH18mOeuXWhfn7cVjCFO4uKSZL3n/M2JkPJo48+yhtvvEFFRQUBAQHMnz+f3/72t+Tm5n6iz5dQcv76rAO8ePQIzx8pocNsBkCv1nB17mS+MLWYKbFxXq5w9LlcCidaO9lb1cTeqgYO1DRjsg4Oe05YoD/FGYlMz0iiOCOR/ORYmQciJozW3n4O1DR7uoFVbd3DHlepYFJCDLOyk5mTncKMzGRCAnzvLJ9+m43Xykr5z+ESGvoNgHvOzvLMbO6dPoMZCUlernD8GJOh5LLLLuO2225j1qxZOBwOfvKTn3D06FHKysoICgr62M+XUPLJtZmMPHvwAP8tPcyAw33UHxMYxOeLpnJbYRExgR//855I+ges7Dxez7byOrZX1NFjGn7aZUiAHzMzk5mdnczsnFSy42RioPAdfeYB9lc3sbeqiX3VjaeFFI1axbT0RBbnZbAoL4Ps+CifmmfhdLnYXF/LykMH2dHY4Ll/RkIiX581lyVp6T718/g0xmQo+ajOzk5iY2PZsmULixcvPu1xm82G7ZRFb/r7+0lJSZFQcg4Nhj7+fmAfr5cdY9DlXn48LzqGe4tncuWkXPQ+MkSjKArV7d1sLatlW0UdJbXNOF0f/moH+umYkZnM7KxkZuekkJsYIxNShRjSZTSzv6qJvdWN7K1sPG1id0JEiCegzM5O8ak9fk50d/GvkgO8VVHueY0tiInl/plzuCw7R5azP4txEUqqqqrIycnh6NGjFBYWnvb4Qw89xMMPP3za/RJKTlfZ3c1T+/ew6kSFZ3GgmYlJfH3mHBb7SIp3OF2U1DazsbSaTceqae7pH/Z4ZlwkiyZnsDg/g+L0RHRa3whoQnxWTd0GtpW7A/7eygZsjg/3W/LTapg7KZWLC7NZkp/pMxNm200mni3Zz0tHP+xGZ0VEcv/M2VyTm4dWDnKGGfOhRFEUrr32Wnp7e9m2bdsZnyOdko93oruLv+zdzerK4569aJakpXP/zDnMTkr2am2jYWDQzs7j9WwsrWZLWc2wBab8tBpmZaewKC+DRXnppESFe69QISaIgUE7+6oa2Vpex7byWlp6Pwz/KhUUpydycWE2FxdmkRId7r1CR0nPgIXnDpfw3OESz3L2aWHhfH3WHK6bnC/hZMiYDyVf//rXWb16Ndu3byc5+ZO9ecqckg+dKYysyMrm67PmTvjJq8YBG5uPVbPuSBW7TtQP2zMmPNCfJQWZXFyYzbxJqT7VVhZitCmKQlVbN5uOVbOxtJpjje3DHs+Oj+KSKdksL8phUkL0hO7YGm02Xjx6mH+W7Pes+yTh5ENjOpR84xvf4K233mLr1q1kZGR84s+TUHLmMHJpVg7fnD13Qu/fcDKIfHD4BDuPN2B3ftg+TooMZWlhFhcXZlOcniib0wnhJW29Rk9A2V/d5FkHCdzr+qyYOokVUyd2QLHY7bxw5BDPHNhHj1XCyUljMpQoisI3vvEN3nzzTTZv3kxOTs55fb4vhxJFUfju2jW8fbzcZ8LIuYJIVlwky4tyWOYDR2BCjEcGi5Wt5bWsP1LJ9oo6Bk+Zh+ILAeVM4SQ1NIw/XnYlU+MTvFzd6BuToeRrX/saL730Em+//fawtUnCwsIICPj4hXp8OZQA/GjDWl45dnRChxG7w8nW8lpWHShna1ntaUHk5AtZdny0F6sUQpwPk9XGlrJa1h4+cVpAyYyL5Mrpk7l6Rh4JERPvdf3UcGJx2Nly170+tyQDjNFQcrY0/O9//5u77rrrYz/f10NJi7Efg9U6IcNIRXMHb+8rY/XBimFLumfGRXKpBBEhJoyzBRSVCuZkp3Ld7AIumZKNv25iLVZosds53NbKvJRUb5fiFWMylHxWvh5KJpo+8wCrD1bw1t5jVLR0eu6PCQ3iqumTuXJGHrmJMV6sUAgxkowDNtYfrWLV/jL2VTd57g/213PZtFyum11AUWr8hBze8TUSSsSYpCgK+2uaeW3XUdYdqfQMz+g0GpYWZnLtrALmT0qTyapC+JimbgPv7C/j7X1lw04zzkmI5qa5U7hqxmRCA2S/qfFKQokYU/rMA7y9v4zXdh2lrrPXc39eUizXzS7giuJcn94ATAjh5nIp7K9p4q29x1h7+IRnoTZ/nZZLp03iprlTmJqWIN2TcUZCifC6s3VFAvQ6rpiey81ziyhImdhrqkwUiqJgtgxiNFsxmqz0m6xDt22YLDYGrIMMWO1YrXYGbPYPb1sHGXQ4cdid2B0uHE4nDocLu8OJw+nCccqExzNRq1XotBq0Wg1ajRqtVoNO677WatUE+Onw99MR4K8jwF9/ym0dgQF6QoP9CQnyJyTYn5Agv6Frf3Q6Wc13PDBYrLx7oJzXdh8dth+PdE/GHwklwmsstkHePVDOf3ccHvZCkpcUy03zpnBl8WSC/PVerFCAO2j09Q/Q0W2kq8dEb5+FHoOZXoOFnj4LvQYzPX0W+vot9JusuFxj9qXhvAX46wgPDSAiLIjI8EAiwgKH3Y4KDyImKoSYqGD0E2zC5XikKAqH61p5dfdRPjh03NM9CdDruHpGHrctmEpOgkyEH8sklIhRV9/Zy8s7D/P23jKMVvdyywF6LVcUT+bmeVMoSIn3coW+xW530tppoKXdQEt7Hx1dRjq7TbR399PZbaKz28ig/dydio/S67XujsOp3YcgfwICdO6uxVDHIuCUjoVepz2tw6HVuD/WaNTnbMM7XS4cDndHxeEc6rAMfWx3OLHaHJ4uzYDVjnWoSzNgHcQ8MIjRZMVotg1dWzFbbJzvK1xEWCCx0SHERrpDSmx0CAmxYSTGhZEYF05osL8MJYyik92TV3cdobq9x3P/rKxkbl84jaUFWTInbQySUCJGhaIo7K9uYuXmA2wtr/Xcnxodzm0LpnLtrHxpr44gl0uhvauf2sYu6pt7aG7to7G1l6bWXjq6jR/7BqxSQWRYENFRwUSFBxEeFkhkWCCRw24HEhoSQEiQP3768d01cDpdnrDSa7AMdYXMw657DRa6ekx09JgYHHR87NcMDvQjKSGc5PhwkhMiSEmIID0lirSkSAKkIzhiTr72/HfHITaWVnt2AY8LC+bzi4q5ce4UQgL8vFylOElCiRhRLpfCxtIqnt24z7PfhUoFiyZncPvCacyflIZaLUePF4qiKLR39lPT2EVtYzd1jd2eIDJgtZ/18wL8dSTGhpEQF0Z8TCixUSHERIW4j/yjQoiOCJb5FWehKAr9JisdXUY6uo0fXncbae1wd6C6ekxn/XyVCuJjwshIiSIjJZr0lCj37eQo/PxkT6YLqa3XyP92H+H13UfpMbnXOQry03Pr/CLuXDKd6BDfW6xsrJFQIkaE3elkTclx/rlxHzVDrVN/nZZrZxVw5+Ji0mIivFzh+Odwuqhv6qaytoPK2g5O1HZQWdeByWw74/N1Wg2piRGkJUcNHam7j9iT4sOJCAuUoYURZLPZaW430Nzm7lA1t/VR3+wOjX39A2f8HI1aRWpSJDkZseRkxDIpI46c9BhCQ+Tss8/KZnfw3sEKnttywDO046fVcP2cQu6+aCaJkfK+4S0SSsQFZbU7eHNPKSs3H/CsIRAS4MfnFk7jjoXFRATLC+qn4XIp1Dd3U1bZSlllG8er26hp6DrjXA+tVk1aYuTQEXc0GSlRpCdHkZQQIWPoY1CvwUJtYxd1Td3UDnW2zhVW4qJDmJQZR35OAnnZ8eRlxxMUKMMPn4aiKGwtr+WZ9Xs5Ut8KgFat5orpk7nn4plkxkV5uULfI6FEXBBm6yAv7zzMf7YcpMdkASAqJJAvLJ7OLfOLCPaXF83z0d1rHgog7kt5VRuWgcHTnhcYoCcn/eSRtPs6PTlKhlrGOUVR6O41c6K2nRO1HVQNdcJa2g2nPVelgrSkKPInJZCfk0BBTgIZqdESQM/DyXkn/9iwl10nGgD3z/WSwmzuvWS2LEkwiiSUiM/EbB3kvzsOsXLzAQwWKwCJEaHcvXQm180umHD7UowERVFoau3jcHkTR8qbOFzeTHNb32nP8/fTMjkrnvycBCZnx5ObGUdCbJjMyfEhJrONqroOKqrbKa9yB9bWjv7Tnhfgr6MwN5GpeckU5SVRkJMg81M+odKGNp7duI8NR6s8912Un8lXV8yVcDIKJJSIT+VMYSQ9JoJ7L5nFFdMno9PIkfrZuFwK1fWdlBxr5EhFM0fKm+jpswx7jkoFGSnR5OckeC7pKVFy9CtO09Nnpqyy7ZSuWitmy/CumlarZnJWPEWTk5ian8zUvGSCg6R7eS5VbV08u2Efa0qO4xp6u5NwMvIklIjzYrEN8tL208PIl5fP4fJpufKmeRZtHQb2HKpj/5F6So41njZfQK/TkJedQFFeEkV5SUzJTZI3DfGpuFwKNQ1dwzpvHz37R6NWkZsVz4wpqcyels6U3ES0WjmQOJPajh6eWb+H9w4ODydfu3QeeckTbyd2b5NQIj4Rh9PFG3uO8re1u+k2uo/qJYyc3aDdwaFjTewuqWVPSS31zT3DHg/w11GUl8S0/BSK8pKYnBU/7tf2EGOToii0dhg4XO7uypWUNtL0keHBwAA9M6akMrc4g7nTM4iLltfNjzpTOLm8OJdvXr6A5KgwL1c3cUgoER9re0Udj7+zxXPqXEpUGPdfOk/CyEf0GwfYeaCG7fur2VNSO2xdEI1aRf6kRGZPTWNGURr52fFyZCq8pq2znwNH69l/pIF9h+tO69xNyohl4exsFs3KJjs9Rk4XP0VtRw9Prd3NmpLjAOi1Gj6/qJj7ls2WCf0XgIQScVZVbV08/s5WdhyvByA80J+vrpjLLfOK0MkbKgAt7X1s31fNtr1VHClv8qwWCRAdGcy86RnMmZbBjKJUQoJkxVox9rhcCidq29lTUsfuklqOnWgZtn9RXHQIC2dls3BWNsUFyRKmh5Q3dfDEu1vZU9kIQGRwAF+/bD43zC6Ug7XPQEKJOE230cLfPtjFa7uP4lIUtBo1dyx0HwmEBcoba31TN5t2nWDTrhNU13cOeywrNdpzhJmbFSdHmGLc6TVY2HWghm37qth7qA7bKUvoBwf6sWBWFkvn5TJ7WprPb0J4cp2Tx9/ZSl1nLwDZ8VE8eM0S5uemebm68UlCifAYdDh4YWsJ/9iwF5PVPXt/2ZRsvnPVIlKiw71bnJd5gsjO41Q3dHnu16hVFOUls2h2NgtmZpEUH+69IoW4wGw2O/uONLB9XxU79lfTa/jwLLGgQD0LZ2VLQMG9gvX/dh7hqbW7PScALJyczoPXLJYF2M6ThBIBwNayGn779hYauvoAyE+O5cFrljAzK9m7hXlRU2sv67dXnB5ENGpmFaWxdP4kFs3KlmW/hU9wOl2Unmhh084TbN59YtgZPUGBehbOzObiBbnMmZbus0M8BouVv6/bw3+3H8LhcqFVq7l94TTuXzFXNv37hCSU+LiGrj5++9Zmz869MaFBfOuKBVw9I98nF+XqNVjYuKOCD7aWU1bZ6rlfgogQH3K5lKGAcpxNu4YHlLCQAC5ZkMuKxfkUTErwySHM+s5eHl+1lc3HagD36tYPXLGQa2b65uvq+ZBQ4qNsdgf/2LCXf23cj93pRKtRc+fi6Xxl2RyCfGwbdYfDya6Dtby74Si7D9Z4Jquq1SpmFqVxyYJcCSJCnMXJgLJxx3E27qwYthBgUnw4Vywt5IqlBcREhXixSu/YXlHHb9/a7JlvUpSWwC9uXsakhGgvVzZ2SSjxQQdqmnjof+s9fygLJqfzg2uXkBEb6eXKRldrh4G31x5mzaZjdPeZPfdPzopjxeJ8LlkwmagI2cpciE/K4XRx8GgDH2wtY+ueSs9p8Wq1irnFGVyzfCrzpmeg8aGzU+wOJy9uK+Gpdbux2Oxo1WruvngmX1k2Bz8fnodzNhJKfIjJauP3727j1V1HAYgOCeRH1y9leVGOz7RYXS6FvYfreGNNCbsO1nDytzgiLJDLluRz5SVTSE+WiWlCfFYD1kE2767k3fVHOVze5Lk/ITaUa1dM5cqLpxARFujFCkdXu8HEb97YyMbSasC9+OTDtyxnemaSlysbWySU+IhdJ+r5xf/W0dprBODGuYV8+8pFPnOKb79xgNWbSnnrg8PDNrubNTWN61ZMZcHMLJ+dnCfESGto7uGd9UdYvbEUo8l9dopep2Hp/FxuuKyY/Jx4nzkwWn+kkkfe2EiX0YJKBXcsKuably8gQC8bJoKEkgnPZLXxxKptvLbb3R1Jigzll7euYHZ2ipcrGx2VtR28+t5B1m+vYHBovYXgQD8uX1rA9ZdOIzXJt4ashPAmm83O+h0VvPH+IY5Xt3vuz82K44bLprFsYZ5PbLfQP2Dlsbe38ta+YwCkRYfzy1tXSNcECSUT2ke7I7cvmMYDVy4g0G9iT2R1uRR2HazhlVX7OVja6Lk/Oz2GGy4rZvmiyQT42GReIcYSRVEor2rjjfdL2LjjOIN2J+AeRr3hsmlcd+k0nxja2VZey0OvrqfDYJKuyRAJJRPQmbojv7p1BbMmeHfEarOzZtMx/rf6AI0t7km8GrWKi+blctMVxRTmJvpMi1iI8aKv38K7G47yxppDdHS7D6D0Og2XLsnnlqtmkJEysc9U6R+w8vg7W3lzr3RNQELJhDPocHD9Y897FkHzhe5Id6+Z1947yNtrD9M/NF4dHOjHNcuLuPGKYtnxVIhxwOFwsnl3JS+/s4+KU4Z25hSnc9vVM5lZlDahDyo+2jX53eev4LJpud4ua9RJKJmA/vbBLt7ZXzbhuyO9BjMvvLmXNz847JkvkhgXxi1XzeCKpYUEBkzcICbERKUoCkcqmvnfqgNs3VvpOUMuPyeB+25fyMyi1AkbTk52TXadaOCN793pk6vASiiZgOwOJ3anc8J2R/qNA/z3nf289t5BzzoIhbmJ3H7tLBbOzPKpNRCEmMia2/p4dfVBVq0/4tkYcFpBMvfdtpCp+RN3CwyDxeozZ0Z+lIQSMW6YLTb+9+4BXl61H7PFvWHg5Kw47rt9IbOnpU/YoychfF13r5kX3tzDWx8cxu5wT4qdPS2d+25fQF52gperExeShBIx5g1YB3l9TQkvvbXPM2ckKy2G+25fwIKZWRJGhPAR7V39/Of1Pby74ShOpwuAhbOyuOe2BeSkx3q5OnEhSCgRY5bD6WL1hqP865WdnmXgUxMjuee2+SydlysbWwnho5rb+lj56i4+2FqGa2ivqksX53Pf7QuIjw3zcnXis5BQIsYcRVHYsb+ap57fSn1zD+BemvpLty5g+aI8tDJnRAgB1Dd1889XdrJx53EAdFoNN15RzBdumCMbaI5TEkrEmHLsRCt/+88Wz14ZocH+3HXzPK67dCp62bzK5yiKgtPhwm53nPN5arUanV6DWi2B1RdVVLXxt+e3eBZLDA7y4ws3zuXGy4t9YoXYiURCiRgT2jr7+etzm9m06wQAer2WW66czh3XzyYkyDdnoU8EVssgPV1Gujv66e0xYzRYMPUPYOq3YuofwNg/gKl/ALPRinXAjn3QweCgg0Gbw33b5uB8Xmp0Og06Py06nRa9n/ui02sJCvYnOMSf4NAAgkMDCAkLGLrtT1h4EFGxIURGhxAaESjBZpxSFIXdJbU89fxWahq6AIiLDuFrX1jCxfNzZe7ZOCGhRHiVw+ni1dUH+OfLO7DaHKhUcPnSQu69bQGxUSHeLk+cg8PupKOtj7amXlqbemhr6qWro5+ejn56ukx0d/ZjMdm8XeZ50WjVREQFExUT6gkqcYkRxCdHEJ8cSUJyBMGhMiwwljmdLj7YUsY//rudzh4TADOL0njwK8tJig/3bnHiY0koEV5TUd3G755ay4naDgCK8pL49r2XyCz6MURRFDrbDDRUd1Bf3UFTXZcngHS0GXANnQFxLv4BeqJiQ4iICiYkLJDg0FM6FkPdiqCQAAIC9ej17s7GyQ6H3k+LXq9Fq9Oc80jX6XR5uisnOyzujoudQZsDs9GKyWgd6tJ82KEx9Q9g6LXQ02mkr8f8iboywaEBJKS4A0piShSpWTGkZsaSkhGDn7/v7lky1thsdl56ex/Pv7GHQbsTP72WL906n1uvmiE7go9hEkrEqLMMDPLPV3bw6uqDuFwKIcH+fP0LS7jy4kJpsXqRoddMVXkLdZXt1Nd00FDVQUNNJxbz2bsdej8t8UnuLkJ8UgSxCeFExrg7DZExIUTGhBAY5Dcu/l8ddie93SZ6Oo2eIaeujn7am3tpbeqlramHvh7zWT9frVYRnxxJWlYsaVmxpGbFkJmbQEpGjCzo50WNLb08/sw6DhxtANwbc/7g/hWyvskYJaFEjKpdB2t44pn1tHX2A7Bs4WS+efdSIsODvFyZbzH0mqksa6HyWDOV5S1UlTXT0Wo443M1WjVJadGkZsaQmhlDYkoU8ckRJCRHEhEd7FNzMAYsNtqaemlrdg9ZNdV1ebpIRsPAGT/Hz19HVl4COXlJ5OQnkp2fKEFllCmKwvubj/HnlZvpN1lRqeCmK6Zz3+0LZTuKMUZCiRgVPX1m/vivTWzYUQFAfEwo3/3yMuZNz/RyZROf0+Gk5kQ7x0rqOVZSz/GjjWcNIElp0WTmxpOaGUNadhxpWbEkpkaikzOfzklRFHq7TZ6A0lDdSV1VOzXHWxkYWn34VH7+OrLzEikoTiV/Whr501IJDQ/0QuW+pddg4S8rN/PB1jIAYqND+O59y1gwM8vLlYmTJJSIEaUoCuu3V/CHZzfQb7KiVqu4+crp3HPrAjlCGSEDFhsVR5o8IaTiSOMZ3xiT0qLJyU8kp8B9BJ81OYGgYDnT6UJyOl0013dRWdZCVVkLlWXNVFecOaikZsVSMC2VguI0CqanEZ8UMS6GvcajvYfqeOzv62jtcIfz5YvyeOCeiwmTtU28TkKJGDE9fWYe+/s6tu2tAiAnI5Yf3L+CyVnxXq5sYnE6nJQfaaRkdzUle6qpONJ02gTUoBB/8qemUlCcSt60VLLzEiWAeMnJoFJxtImyknqOlTTQWNt52vNi4sMonptF8ZwsiudmER4V7IVqJy6rzc6/XtnJy6v243IpRIYH8uBXVrBodra3S/NpEkrEiNhTUsuv/vQeff0DaDRq7rppLnfeMEdmvV8gRoOF/dsr2bP1OPt3VGLqHz6fITYhzH3EPXRJy471qbkf401fj5nyww2UHqyn7FA9lcdacAxtPAegUqnInZLM7MWTmLN4Mpm58dJFuUCOnWjl0b+uoa7JvXr0NcuL+NbdS/HzkzOpvEFCibigHA4n//jvDl58ay/g3jjvp9+8XE7zvQB6uozsWF/GtnWllB6o8+z5ARASFuA+qp6bTfGcTOKTI71YqfisrAODHCupp2R3NQd3VVFzvG3Y49FxoSxcVsCiFYXkTU2RwPkZ2QYd/POVHfz37X0oCmSmRvPL715NenKUt0vzORJKxAXT1mHgoSdXU3q8BYDrL5vG//viRbLM82dwahA5ur9u2Doa6dlxzF6Sy5zFuUwuSpGzOSawrvZ+9m47zt6txynZXY3Navc8Fh0bysLlBSy+dAqTi5IloHwG+w7X86s/raanz4K/n5bv3LuMy5cWSFdqFEkoERfEjv3V/PrPazCarAQH+vHDr13KRfMmebusccnQa2bb2lK2rj09iOQWJrNoRSELl+VLN8RH2ax2Du6qYtu6UnZvrhi2au7JgLLksiImFyXLm+mn0N1r5ld/eo/9R+oBuHRJPg9+ZTn+MpwzKiSUiM/E6XTxz1d28p/XdwOQlxPPw9++isS4cO8WNs7Y7Q72bTvB+ndK2Lv1xLD5BJ4gsryA+KQIL1YpxppBm50DO88cUJLTo1l29TQuuXoaMbK8+nlxuRReeHMPz768A5dLISs1mke+fy3JCfL3N9IklIhPra/fwsNPrmbfYfcRxU1XFPP1L1yETieTWT8JRVGoLGth/TslbF5zhP4+i+ex7LxELrq8SIKI+MROBpSta0vZuaHMM8SjUqmYOiuDZdcUs2BZPgGBfl6udPwoOdbIL36/ip4+C8GBfvz0m5ezcJacnTOSJJSIT6WsspWfPv4OHV1G/P20fP/+S1mxKM/bZY0Lhl4z694uYe3bB2mo7vDcHxkTwsVXTmXZ1cWk58R5sUIx3lnMNravP8b6d0o4sq/Wc79/gJ6Fywu4/MaZ5E9LleGdT6Crx8TPnljF0YpmAO68YQ733LYArczhGhFjMpRs3bqVxx57jAMHDtDa2sqbb77Jdddd94k/X0LJyFq1/gi//8cG7A4nyQkR/Ob715CZGuPtssa8qvIW3nh+B9s+KMVudw/P6P20zFuax/Jriimem4VGTpkWF1hbcy8b3j3EhlWHaGno9tyfnhPHtZ+bxyVXTUUv8yXOyeFw8tf/bOHV1QcBmDEllV9992pCZbG1C25MhpI1a9awY8cOpk+fzo033iihZIxwuRSeeWkbL7zpPt138Zwcfvz1ywgOknbw2SiKwsFdVby2cjslu6s99+fkJ3LFTbNYfOkUgkJkETMx8hRFofxwI++/sZ8t7x/1DO9ERAVz7R3zuPKW2YSEypvsuazfXsFvn/qAAaud1MRIHv/pDTJ/7gIbk6Fk2DdSqSSUjAF2u5Pf/PV91m0rB+DuW+bxpVvmS/v3LJwOJ1s+OMprK7d71phQa9QsXlHI9XfOJ7cw2csVCl9m7B9g7ZsHePOFnXS1uzfH9A/Qc/mNM7n+zvnEJoR7t8AxrLq+kwcfeYOObiMRYYE89pMbZJXqC2hChBKbzYbN9uGs8/7+flJSUiSUXCAD1kF+8tg77D1Uh0aj5gdfXcEVFxd6u6wxyelwsnH1YV56ZjOtje4VIv0D9Fx2wwyu+/x8mbQqxhSH3cnm94/w2srt1FW2A6DValhx/XRuvWcxcYny+3omnd1GHvzNG1TVdRLgr+P/fng9M6akerusCWFChJKHHnqIhx9++LT7JZR8dgbjAA8+8gZlla34+2n59YPXMrc4w9tljTlnCiNhEYFcd8d8rrp1NiFhsgOsGLsUReHAzipe/ddWDg9NjJVwcm5mi40f/fYtDpY2otNq+MUDV8raTBfAhAgl0ikZGR3dRr7zy1epa+ohJNifx358A4W5id4ua0w5Wxi56a5FXH3rHPwDZSdkMb6UHqjjhac3cmhPDSDh5Fxsgw5++eRqtuypRK1W8b0vL+ea5UXeLmtcmxCh5KNkTslnV9/Uzbd/9RodXUZiIoN54mc3kZka7e2yxgyn08Wm1Yd58e+bJIyICels4eT2+y4iJj7My9WNHU6ni8efWceq9UcB+PLnFnLnDXNkvt2nJKFEnKa8qpXv/foNDMYBUhIj+MPPbiI+Vl6EwN3m3rvtBP9+ci11Ve4xeAkjYiL7aDjR+2m57o553PylxXK2zhBFUXjmpe08/8YeAG6+cjrfuGsparUEk/M1JkOJyWSiqqoKgOLiYn7/+9+zdOlSIiMjSU39+MlEEko+vdITLXz74VcZsNqZnBXHYz+5kQiZDwFAa1MPf31kFft3VAIQHBrALV9axDW3zZUwIia80gN1rPzzOkoPuldwDosI5N7vXMaya4qlKzDklVX7+fPKzQBcvWwKD35lhQST8zQmQ8nmzZtZunTpafd/8YtfZOXKlR/7+RJKPp3K2g6+8fNXMFlsTC9M4f9+eD2BAfJma7c7eH3ldl56ZjODNgc6nYZr75jHrfcukSNF4VMURWHv1uP88w8f0FDTCcCUmel882fXkpIhCygCrNl8jEf/+j4ul8LNV07nm3cvldB2HsZkKPmsJJScv+a2Pu7/yUv09FmYMjmJ3//sRgL8JZAc3V/Ln3/9jucFeNqcTP7fT64hOV3m1wjf5bA7efP5nbzw9EZsVjtarYabv7SI2+5dgp+/rA67ZlMpj/zlfQDuu30hX7xprpcrGj8klAi6e83c/5OXaGk3kJ0ew19+eZvPr9JqNll59on3WfP6fgDCI4P48oOXs/SKqXLUI8SQtuZe/vbou+zdehyAxNQovvPw9RTOSPduYWPAa+8d5Ml/bgTgwa8s59oVU71c0fggocTHmcw2/t/PX6aqrpPEuDCeeuRzREUEebssrzqws5InH3qLzjYDAFfcPIu7v7VChmqEOANFUdi5sZynHn2Xro5+VCoV19w+l7u/udzn51o989J2/vP6btRqFb/67tUsmSvrmHwcCSU+zDbo4Lu/fo1Dx5qIDA/kqUc+R1J8uLfL8hqzyco/Hl/D+28cACAhJZLvPHw9U2bKYnFCfByz0co/nhj+9/PdX97g010TRVH43dPrWLX+CDqthid+diPTC2Xl13ORUOKjHE4XP3v8HbbtrSIoUM+fH76VSZlx3i7Laz7aHbn2c/PkSE+IT+HUvyXpmrjXMfn5E6vYsqeSwAA9f/mlb7/WfhwJJT7o1PSu12l4/Ke+m96tlkH+/th7nrkj0h0R4rM7U9fkwd/cRP5U33ydsQ06+N6vX6fkWCMRYYE8/Rvf7kqfy6d9/1aPYE1ihL2+poRV64+gVqv4xQNX+mwgaWvq4YE7/+4JJNd+bh5Pvfr/JJAI8RkFhfjzwEPX88jTXyQmPozWxh4evPtZVr28x9uleYWfXsujP7iOnIxYeg0WfvTbtxiwDnq7rAlFQsk4daSi2bO4z9fuXOKzE69KD9TxrTuepq6ynYioYH77zy9x/w+v9NkWsxAjYcb8HJ5+/RssuWwKToeLv/5mFX95ZBUOu9PbpY264CA/HvvJDUSFB1HT0MXvnl7HGB5wGHcklIxDPX1mfvb4OzidLi5ZkMutV8/wdkle8cGbB/jhff/G0GshJz+RP7/8NabOyvR2WUJMSEEh/vzwt7fwpQdWoFKpePeVPfz0a89h7B/wdmmjLjoimF9+92o0GjXrtpXzxpoSb5c0YUgoGWecThe//ON7dPeaSU+O5Af3X+pz6204nS7+8fga/vCLN3E4nCxaUchj/76X6DiZdyTESFKpVNzypcX8/MnP4R+g59CeGh644+801XV5u7RRNzU/ma9/YQkAf3luCxVVbV6uaGKQUDLOPP/mHvYfqcffT8uvvneNzy0fbzZZefhbL/L6f3YAcMdXl/Kj392Cv4/9HITwpnlL8/j9f+4jNiGM5vouHrjjaQ7urvJ2WaPu5iuns3hODnaHk589sQqj2ertksY9CSXjyMHSBv71yk4AvnvfMjJSfGuJ9LamHr5z5zPs3XocvZ+WH/3uVu782iWo1fJrLMRoy8xN4I8v3U/e1BRMRis/vf8/PjcBVqVS8aOvX0pCbCitHQZ++7cPZH7JZySv5uNEr8HMw0+uxuVSuGJpAZcvLfR2SaOq9KB7Qmt9dQeRMSE89u97WXLZFG+XJYRPi4gK5rfPfolLrpqGy/nhBFinw3cmwIYE+fPL716NVqtm8+5KmV/yGUkoGQcUReGRP78/NI8kim/fe4m3SxpVB3dV8aMvr/RMaP3TS/eTW5js7bKEEIDeT8f3Hrlx2ATYR3/wP58KJnnZCXz9CxcB8OfnNlNV1+ndgsYxCSXjwIYdx9ldUotep+GX373ap3b9LTvUwMPfehH7oIM5SybLhFYhxqCTE2B/+vvb0ek0bF93jCcffguXy+Xt0kbNTVcUs3BWFg6Hi989vRaXS4ZxPg0JJWNcv8nKn/7t3qHyCzfOJTPVd+aR1Bxv5Wdf/w82q52ZC3L46e9vkwmtQoxhCy7J54e/uxW1Rs26t0t45rE1PjPHQqVS8d37lhEYoKesspW31x72dknjkoSSMe7vL26jp89CWlIkn7tulrfLGTVNdV38+CsrMRutFBSnDR2Bab1dlhDiYyy4JJ/vPHw9AG+9uIsXn97k5YpGT0xUCF/53EIAnn5xK129Ji9XNP5IKBnDjlY0e9L2g19Zjt5H3pQ7Wvv40Zf/TV+PmazJCfzyL3dKh0SIcWTZNcXc/8MrAXjhqY28+fxOL1c0eq67dBp52fGYLYP86V++E8guFAklY5TD4eSxv68D4MqLC5lWkOLlikZHX7eJH315JZ1tBpLTo3nkqS8SFOLv7bKEEOfp2s/N4wv/zz0p/++Pvcfatw54uaLRodGo+f5XV6BRq9i48zi7DtR4u6RxRULJGFVR005zWx/hoQF8bWjVwInO1D/AT+5/jub6LmITwnj0mbsIjwr2dllCiE/p9vsu4sYvLADgyYfeYvu6Y16uaHTkZMRy81Xu7T827Tru5WrGF5UyhmchfdqtjyeK5rY+WtoNzJqa5u1SRpx1YJAff3UlZSUNREQF8/jKe0lK851JvUJMVIqi8ORDb/HBmwfQajU8/JfPM2N+jrfLGnGWgUF27K9m2cLJPrcVCHz692/plIxhSfHhPhFIAJ55fA1lJQ0Eh/jzyN/vkkAixAShUqn45s+vZdGKQhwOJ49+/390thm8XdaICwzQs3xRnk8Gks9CQonwul2bynnv1X0A/PiJ28icFO/lioQQF5JGo+b7j95ETkESpv4BnvjZ6z61hon45CSUCK/q6TLy5ENvAnDDFxYwfW62lysSQowEnU7L939zE37+Og7tqfGpM3LEJyehRHiNoij84edvYui1kDEpnru+udzbJQkhRlBKRgxffvByAFb+aR01x1u9XJEYaySUCK9Z9coe9m0/gU6v5QeP3oxe7xvrsAjhy664aRZzlkzGbnfy2x++is1q93ZJYgyRUCK8or66g2efeB+Aex5YQXpOnJcrEkKMBpVKxbcfuo7wyCDqqzv415NrvV2SGEMklIhRZ7c7+N2PXmXQ5mD6/Gyu+dxcb5ckhBhF4VHBfOdXNwDw9ku72L+j0ssVibFCQokYdS8+vYnqilZCwwP57q9uRK2WX0MhfM3sRblcfdscAJ742euYjVYvVyTGAnk3EKOqq72fN/6zA4Bv/PQaomJCvFyREMJb7v3OZSSlRdPbZeL1/2z3djliDJBQIkbVi3/fyKDNQUFxGguXF3i7HCGEF/n567j7W+6z7t74z056u2VXXV8noUSMmqa6Lj548yAAd39ruax0KIRgwSX5TCpMwjowyMv/2OLtcoSXSSgRo+b5v23A5XQxe3EuhdPTvV2OEGIMUKlU3P3NFQCs/t9e2pp7vVyR8CYJJWJU1FW1s/WDUgDu+sYyL1cjhBhLiudmMW1OJg6Hk1eelW6JL5NQIkbFf5/ZjKIoLFxeQGZugrfLEUKMMZ+//2IA1r59ULolPkxCiRhxp3ZJ7vjKUi9XI4QYiwqnp1M8NwunwyXdEh8moUSMuDef3+npkmTIDsBCiLO446vug5a1bx+kv8/i5WqEN0goESPKYXeyY0MZgGehJCGEOJPC6elk5sbjdLjYubHM2+UIL5BQIkbUoT3VmPoHiIgKljNuhBAfa/GKQgC2rT3m5UqEN0goESNq6zr3XJIFywrQaOTXTQhxbouGQknJnmoZwvFB8i4hRozD7mTnhnIAFq2Q1VuFEB8vKS2azNx4XE4ZwvFFEkrEiJGhGyHEpyFDOL5LQokYMTJ0I4T4NGQIx3fJO4UYEQ67k10bZehGCHH+ZAjHd0koESOioaYDo2GAoBB/GboRQpy3uRdNBqD0YL2XKxGjSUKJGBH11R0ApGXHytCNEOK8ZU5yb0fRUNPh5UrEaJJ3CzEiPKEkK9bLlQghxqPUrBgAGqo7cblcXq5GjBYJJWJENHhCSZyXKxFCjEeJKVFotRqsA4N0tBq8XY4YJRJKxIior+4EPjzaEUKI86HVaUhOjwZkCMeXSCgRF9ygzU5rYzcgnRIhxKd38qCmvkpCia+QUCIuuKa6LlwuheAQfyKjg71djhBinDo5J+3kHDUx8UkoERdcU10XACmZMahUKi9XI4QYr1Iz3aHk5GuKmPhGJZT87W9/IyMjA39/f2bMmMG2bdtG49sKLxm0OQAIDPL3ciVCiPEsMNgPAPugw8uViNEy4qHklVde4YEHHuAnP/kJJSUlLFq0iMsvv5yGhoaR/tZCCCGEGEdGPJT8/ve/55577uHee+8lLy+PJ598kpSUFJ566qnTnmuz2ejv7x92EUIIIYRvGNFQMjg4yIEDB1ixYsWw+1esWMHOnTtPe/6jjz5KWFiY55KSkjKS5QkhhBBiDBnRUNLV1YXT6SQubvhpoXFxcbS1tZ32/B/96EcYDAbPpbGxcSTLE0IIIcQYoh2Nb/LRMzAURTnjWRl+fn74+fmNRklCCCGEGGNGtFMSHR2NRqM5rSvS0dFxWvdECCGEEL5tREOJXq9nxowZrFu3btj969atY/78+SP5rYUX6f11AJhNVi9XIoQYz8xG92uI3m9UmvpiDBjx/+nvfOc73HnnncycOZN58+bxzDPP0NDQwFe/+tWR/tbCS1JO2a/ibEN1QgjxcU6u5JqSIXto+YoRDyW33nor3d3d/PKXv6S1tZXCwkLee+890tLSRvpbCy9JSo9GrVFjMdno7jASHRfq7ZKEEONQvWe38VgvVyJGy6is6Pq1r32Nuro6bDYbBw4cYPHixaPxbYWX6PVaklKjAKivbvdyNUKI8aqhxr3buIQS3yF734gRkZrpbrc2VHd6uRIhxHhktztornfveZMqocRnSCgRIyIt++TuntIpEUKcv+b6bpwOF4FBfsTEh3m7HDFKJJSIEZGW5T7lW7YcF0J8GieHblJlt3GfIqFEjIiTwzf1VR04HU4vVyOEGG9qKloBGbrxNRJKxIhIzYwhLCIQi9nG4f213i5HCDHO7NpUDkDhjHTvFiJGlYQSMSI0Wg3zL8kHYNvaUi9XI4QYTxpqOqiv7kCr1TB/aZ63yxGjSEKJGDGLVhQCsHNDmQzhCCE+sZMHMsXzsggODfByNWI0SSgRI2bqzAzCIgIx9FpkCEcI8Ylt/cAdShYPHdgI3yGhRIwYjVbD/ItlCEcI8cmdOnQzT4ZufI6EEjGiFl0qQzhCiE9Ohm58m4QSMaJkCEcI8UkpiiJDNz5OQokYURqthgXLCgB456XdXq5GCDGWHdlXS311BzqdDN34KgklYsRd//n5qNUqdm+uoLKsxdvlCCHGqBee2gjAZTfOlKEbHyWhRIy4lIwYLrqiCIAXn97o5WqEEGPR4X01HD1Qh06n4ZYvyU7yvkpCiRgVt993kadbcuJYs7fLEUKMIYqi8PxfNwDuLolswOe7JJSIUZGSEcPSK6YCsPJPa71cjRBiLNm/vZLSg/Xo9Frpkvg4CSVi1Nz5tYvRajUc3FXNoT3V3i5HCDEGuFwuVv55HQDX3D5XuiQ+TkKJGDXxyZFccfMsAP79x3UoiuLlioQQ3rb1g1KqK1oJDPbj1nukS+LrJJSIUXX7ly/Cz1/H8dImNr132NvlCCG8aMBiY+Wf3F2Sm+5aSGh4oJcrEt4moUSMqoioYG4ZOhr662/epaO1z7sFCSG85unfvkdbcy8x8WFc//n53i5HjAESSsSou+2exUyekozZaOWxn7yG0+nydklCiFG2Y0MZH7x5AJVKxYO/uYmAQD9vlyTGAAklYtRptBq+/+jN+AfoObq/jjee2+HtkoQQo6i7o58nH3oTgJvvXkjRzAwvVyTGCgklwisSU6P46g+uAOC5v6yXlV6F8BEul4snfv4GRsMAWZMTuPPrl3i7JDGGSCgRXnPp9TOYf0k+DoeT3/3oVawDg94uSQgxwt55aTcHd1ah99Pyg/+7GZ1O6+2SxBgioUR4jUql4oFfXEdkTAiNtZ08+/sPvF2SEGIE1Z5o459PuhdPvO+7l5OaGevlisRYI6FEeFVoeCDf/dUNALz7yh72bKnwckVCiJFgs9r57Y9exT7oYNaiSVx162xvlyTGIAklwutmzM/hujvmAfB/P/gfx0ubvFyREOJCctid/ObBV6irbCcsIojv/PIGVCqVt8sSY5CEkjGstrGLnQd8Yzn2L337UqbNzmTAMshP73+Ouqp2b5ckhLgAXC4XT/zsdfZsqUDvp+WnT9xGRFSwt8sacWaLjXfWHZElD86ThJIx6mhFM3d/7z/86k9r6DWYvV3OiNPrtfz8j3cweUoyRsMAP/7KSlqberxdlhDiM1AUhb/95l02vXcEjVbNT564nSk+cvrvP/67nd89vZZf/3mNt0sZVySUjFF5OQlkpkRjNFn5y8ot3i5nVAQG+fGrv32B9Ow4ejqN/Oi+f9PV3u/tsoQQn9K//7SOd/+3171A2iM3MWdxrrdLGhXlVa28vqYEgCsvLvRyNeOLhJIxSqtR8/2vrkCtVvHB1jL2Ha73dkmjIiQskEf+fhcJKZG0Nffy46+uxNA78TtFQkw0r/xzC//751YAvvGza7jo8iIvVzQ6HE4Xv3t6HYoCly7JZ2ZRmrdLGlcklIxhk7PjueGyYgCeeGYdNpvdyxWNjqiYEB595m6iY0NpqO7gp1/7D2aT1dtlCSE+odX/28u//+jeaO+eb1/KFTfN8nJFo+e11QeprO0gNNif//fFi7xdzrgjoWSMu+/2BcREBtPU1sd/3tjj7XJGTXxSBL955i5CwwOpPNbMQ998AZvVN0KZEOPZptWH+csjqwC47d4l3Hz3Ii9XNHraOgw8+/J2AL72hSVEhMmux+dLQskYFxToxwP3updhfvGtvZyo8Z2zUlIzY3nk6S8SGOTH0f11PPTNF6RjIsQYtuHdQzz209dRFIWrbp3DF7+xzNsljRqXS+F3f1+H1eZgWn6yzCX5lCSUjAOLZ2ezeE4ODoeLnz+xCrPF5u2SRk1OfhIP//nz+PnrKNldzXfufEbOyhFijHG5XKz88zoe+/FruJwull09ja/96EqfWovkpbf3svdQHXq9lu99ZblP/dsvJAkl44BKpeKH968gLjqEprY+fvf0WhRF8XZZo2bKzAweX3kvUbEh1Fd38MAdT1N6oM7bZQkhAKtlkEe++zIv/8N9luAtX1rEd351A2q177y9HC5v4h8vuYdtvn3PxaQnR3m5ovHLd35rxrnQkAAe/s7VaDRqNuw4zttrD3u7pFGVk5/EH1+8n5yCJAy9Fn5437/54M0D3i5LCJ/W2dbHd+/6Bzs2lKHTafjer2/kSw9c6lOBpK/fwkO/fxenS2HF4jyuumSKt0sa13znN2cCKMxN5Kufd08a+9O/N/nU/BKA6LhQHvvXPSy+tBCHw8kffvEmzzy+RlZMFMILKo408s3PPU11RSthEUH89p/3sOyaYm+XNapcLoVf/2kNnT0mUhMj+d6XZdjms5JQMs7cdvVMFszMYtDu5OdPrMJk9p35JQD+AXp+9Ltb+fz9FwPwxn92yARYIUbZptWHefBL/6S3y0R6Thx/+u9XyZ+W6u2yRt2Lb+1ld0kter2WX33vagID9N4uadyTUDLOqFQqfvL/LvPML/n1n9/D5fKd+SXg/hl8/v6L+fHjt+Hnr2PfthMyAVaIUeByuXjuL+s9u/3OvWgyv//Pl4lLjPB2aaNu3+F6/vFf9zyS79xzCVlpMV6uaGKQUDIOhYYE8MiD16LTati+r5rnfWj9klMtXlHIY//+cALsN29/ij1bj3u7LCEmJEOvmYe/+SL/fWYz4J7Q+vMnP0dgkJ93C/OCtg4DD/3hXVwuhasumcJVy2QeyYUioWScmpwdz3fuc69f8o//bmft1jIvV+QdkwrcE2AnFSZhNAzwi//3PL//xRuY+ge8XZoQE8b29cf4yvV/Ys/W4+j0Wp+c0HqSwTjA9x55HYNxgNysOL49tI6UuDB87zdqArl6WRE3XzkdgEf+8j67S2q9XJF3RMeF8vjK+7j+8/NRqVSsffMgX73hz+zbdsLbpQkxrhl6zTz6/Vf49Xf+S1+PmbSsWP7w/Jd9bkLrSQPWQb7/mzeoa+ohJjKYRx68Fj+91ttlTSgqZQwveNHf309YWBgGg4HQ0FBvlzMmuVwKv/zjatZvr8DfT8uTD91C4aREb5flNaUH6/j9z9+kpaEbgBXXT+fL372c4NAAL1cmxPiyff0x/vLrd+jrMaPWqLnl7kV87qtL0fvom7DD4eQH//cme0rqCAn252+/vo2MlGhvlzVmfdr3bwklE4Dd7v5j2XuojtBgf/7q438s1oFBnvvzet56cReKohAdG8q3fnEdsxZN8nZpQox5hl4zf3v0Xba8fxSAtKxYvvvrG5lUkOTlyrzH5VL49Z/fY+3Wcvz0Wv740C0U5vruwd8nIaHExw1YB/nWQ69SVtlKbFQIT/3mduKifftn9tGuydIrivjyg1cQERXs5cqEGHsURWHDqkP844k1GHot0h0ZoigKf165mf+9ewCNRs3//fA65k3P9HZZY56EEoHBOMDXf/pf6pp6SEuK5K+/vo3wUN/epfKjXZPgEH/ufmAFl9840ycn6QlxJo21nfz51+9wZJ97Xlp6dhzf+dUNPt0dOen5N/bw9xe3AfCzb17BpUvyvVzR+CChRADQ3tXP/T/+Lx3dRnKz4vjjL24h2AdP2fuoE8ea+dMv36aqvAWAyUUpfPPn15I5Kd7LlQnhPTarnZef3cKr/9qGw+HEz1/HHV9dyg13LkCr03i7PK974/0Sfv+PDQB8466LuPXqmV6uaPyQUCI86pq6+X8/e5m+/gEKcxP53Y9vIDTY39tleZ3T6WLVy3v4z1/WYzHbUGvUXHHTLO746lIZ0hE+xeVysfWDUlb+aR1tzb0AzF6cy9d+dBXxSb63ENqZvPXBIR5/Zj0Ad94wh6/cscjLFY0vEkrEMJW1HXzjF69gMtvITI3m9z+7iehIeeMF6Grv5+nfrWb7umOAe+n6G74wn+vvXECInKUjJjBFUTiwo5Ln/rKeyjJ31zA6NpSv/vBKFlySL/u24P4ZPffabp59eQcAN185nW/evVR+NudpTIaSRx55hNWrV3Po0CH0ej19fX3n9fkSSj6b6vpOvvOr1+juNZMQG8rvf3YzKT64HPTZHNlfyz9//wHHS5sACAz24/o75nPdnfMlnIgJ5WQYeeGpjVQcHfp9D/LjprsXcsPnF+AfKHu2gPssmz/9eyOvvVcCwF03zeWe2xZIIPkUxmQo+cUvfkF4eDhNTU3885//lFDiBa0dBr798Ks0tfURERbI4z+9kdzMOG+XNWYoisKO9WW88PRG6irduy5LOBETxZnCiJ+/jitvmc0tX1pMeGSQlyscO+x2J7/56/us21YOwLe+dLFncUpx/sZkKDlp5cqVPPDAAxJKvKTXYOa7v3qdE7UdBAbo+b8fXMf0Kb63o+e5uFwudm4ol3AiJoSzhZGrbpnNTXcvkjlUHzFgHeSnj7/DnpI6NBo1P/nG5axYlOftssa1CRFKbDYbNpvN83F/fz8pKSkSSi4As8XGD//vLUqONaLTanjo21eyZK4sJvZRZwsnV90ym2vvmE9UTIiXKxTi7JxOFzs3lPHqym2cKG0GJIx8nH7jAN9/9E1Kj7fgp9fy6wevkXVILoAJEUoeeughHn744dPul1ByYdgGHTz85Gq27qlErVbxrS9dzI2X++YeFh/nTOFEp9Ow9Kqp3PTFhaRmxnq5QiE+ZLPaWff2QV7/zw5aG3sACSOfREt7Hw8+8gb1zT2EBPvz2I9vkJVaL5BRCyVnCw6n2rdvHzNnfng+t3RKxg6n08UT/1jPO+uOAHDbNTO5//OL0WhkIbEzcblc7NlynNdWbudYSb3n/jlLJnPDnfMpmpUhk+CE1/R0GVnz2j7e+e8eDL1mAELCArj6tjlcc9tcwiWMnFV5VSs/ePRNevosxEaF8PhPbyQz1Xe357jQRi2UdHV10dXVdc7npKen4+//4boYMqdkbFEUheff2MMzL20HYPbUdH7x7SsJC5F5E+dSdriB11ZuZ9fGck7+2SSnR3P5TbO4+MqpcjQqRoXT6aJkdzUfvHmAnRvLcDpcAMQlhnPDFxZw6XUz5Gyaj/Hu+qP8/tn1DNqdZKfH8NiPbyAmSoZmL6QJMXzzURJKRta6beX8398+wDboIC46hEcevJbJ2bLC6cdpquvized3snH1IQYsgwCoNWpmLchh2TXFzLlosk/vFSJGRl1VO+vfKWHj6sP0dBo99+dNTeHaz81j0fICNFpZhfVcbIMO/vDsBt7d4N5scMHMLH7xwJUEBkiIu9DGZChpaGigp6eHd955h8cee4xt29z7B2RnZxMc/PFHlRJKRl51fSc/+d3bNLX1odNq+Pa9l3D1sikyJPEJmE1WNr93hLVvHfSsdQIQHBrAkkunsOyaYiYXJcvPUnxqhl4zm9ccYf07JZ7FzsA9RHPR5UVcfuNMMnMTvFjh+NHaYeAnj73DiZp21GoV992+kDuum41aLX+fI2FMhpK77rqL55577rT7N23axEUXXfSxny+hZHSYzDYe+fMatu2rAuCKiwv57r2X4Oen83Jl40dDTQfrVx1i46pDdHX0e+5PTo/mosuLWLSikLQsmRwrPp7FbGPP5gq2ri1l37YTOBxOADRaNbMWTmLZNcXMXpwr3bjzsLukll8+uZp+k5Xw0AB+8cBVzJqa5u2yJrQxGUo+Kwklo8flUnjxrb3847/bcbkUstJi+OV3riItOcrbpY0rTqeLw/tqWP9OCTvWl2Gz2j2PpWbFsmh5AYtWFJKeLQvYiQ+dDCLb1pWyb3sl9kGH57HsvESWXVPMRZcXyWJn58nhdPHPl3fwwpt7UBTIy47nV9+7hvgYeT8ZaRJKxAWx/0g9Dz+5ml6DBX8/Ld+9bxmXLy30dlnjksVsY+eGMratLeXAzirPES9AamYMi1YUsnBZAek5cTLE44PMRit7tlawbe0x9u8YHkSS0qJZtKKAiy4rIj1HAuyn0dbZz8N/eJejx93DXtddOpVv3r0UvU46TKNBQom4YLp7zfzyj6s5cLQBgMsuyuc79y6TyWCfgal/gN2bK9i2tpSDu6qw2z8MKLGJ4cxZnMucJZMpmpmOXobNJqymui72bD3O3i0VlJbUe86cAXcQWXxpIYtWFJIhQfUz2b6vikf+8j5Gk5WgQD0/uP9SLp6f6+2yfIqEEnFBOZ0unn9zD/96ZScul0JKYgQ/+cblFE6ShYU+K7PRyq7N5Wz7oJSDu6uHHSH7B+iZMjOd6XOzKZ6bRVp2rLw5jWPG/gEO763h0O5qDu6upqWhe9jjKRkxLBwa0pMg8tlZBgZ56oWtvPn+IQAmZ8Xx8HeuJik+3Kt1+SIJJWJEHDrWyMNPrqazx4RareK2q2dyz20L8JNJdheE1TLIob017Nlawd6tx+nuMA57PDQ8kPxpqRQUp1EwPY3svESZ4DhGKYpCR2sfx0rqOXawgWOH6qmv6uDUl1itVkPRrHRmL57M7MWTSEyROVsXysHSBh796we0dhgAuPXqGXz1jsXodHKatDdIKBEjpt84wB//vYkPtpQBkJoYyQ/uX8HU/GQvVzaxKIpC7Yk2Du6qpmR3NaUH64ZNlAXQ6bXkFiZRUJxG/rRUcgqSiIyWRZ+8YXDQQe2JNo4fbXIHkZJ6utr7T3teSkYMxfOyKJ6TRdGsDIKC/c/w1cSnZTLbePrFrbz1wWEA4qJD+OHXLpOza7xMQokYcdv3VfPY02vp7nMvZ33N8iLuv3MxIUHyIjsS7HYHVWWtlB2qH3rTa/AsJX6qqNgQsvOSyMlPJCc/kez8JNk48AIbtNmprWynqqyFyrJmKstaqKtqHzYnBNyn7WZPTiS/eKi7VZwmK/2OoC17KvnDsxvo6jEBcO2KqXztzsUEBfp5uTIhoUSMin6Tlaee38qq9e69c6LCg/jWPRezdN4kGQ8fYYqi0Fzf7TkqrzjaRFNtJy7X6X/CkTEhZE6KJzUrlrShS2pWLIFB8mJ9Lk6ni/bmXuqrO6ivaqe+ptN9Xd1xWgAB9/BaTn4SBdNTKZiWRm5hsizxPgo6uo384dkNbNvrXlspOSGC739lOdOnpHq5MnGShBIxqg4da+R3T6+jocW9I+n8GZl898vLiIuW/6fRNGCxUV3ROnQE30JlectZgwpAbEIYqZnugJKQHElCcgTxyZHEJob7zFwVRVHo6zHT2tRDW1MPrU29NNV10VDdQWNtJ4M2xxk/LzQ8kOz8RCblJ5E91JWKTQiXMD6KnE4Xb609zN9f3IZlYBCNRs3nr5/NF26cK/PcxhgJJWLUDdodPP/GHp5/Yw8Oh4sAfx1f/twibrhsmuw67EUDFhs1x9uGjvY7qK9up6Gmc9h+KR+lUqmIjgslPjmChORIYuLDiIwJISomdOg6hPDIoDG/t4qiKFhMNnq6jHR39NPdaaSn0327rbmXtqZeWpt6Tpurcyq9n5aUjJhhXabM3HgJIF5WXd/J755ey7ETrQAUTErgB/evIDM1xsuViTORUCK8praxi989vY6jFc0A5GbF8e17L5HTh8cYo8FCfXUHDTWdNNZ2et6g25p6sQ4Mfuznq9UqwiKDiIwOISQ0gODQAIJD/YeuAzz3+Qfq0ek16PVa9H46dDoNej8tej8tOp0WzvbGrig4nS7sgw4GBx0M2tzX9kEHdpsDm82B2WTF1D8wdLFiNFjc1/0DGHrN9HQazxk4TlKpVMTEhxKfHEl8cgSJKVGeABKXFCGhegwxW2w899puXnn3AE6ni8AAPV+5YxHXXzpN9q0ZwySUCK9yuRTeWX+Ep5/fisliA2DpvEl85Y5FJCdEeLk6cS6KomDoMdPa1EtbUw8tTT3uLkOHkZ4uIz2d/fR2mc46JDQWBYX4Exnt7vBEDHV64hIjSEhxD1nFJPjOcNV4Zbc7eWfdYf796i76+gcAWDQ7m2/fewmxUTKRe6yTUCLGhJ4+M0+/uI01m0pRFNBo1Fy3Yip33TyXiDDZt2O8cjpdGHrNdHcY6e02ftip8HQt3B+b+gewWu3u7sbJbofN4fn41JVsz0StVqHTa4d1VvR+Ws99gUH+BIf6e7oyIWEBnk5NWHggkTEhREaHyGTTcUxRFDbtOsHfX9xGc1sfACmJEXzjrouYPyPLu8WJT0xCiRhTquo6efqFrewuqQUgMEDPHdfN5parphPgL28YvuqTvNzIvA3fdehYI399fgvllW0ARIYH8qVb5nPVJVPQjvH5TGI4CSViTDpwtIG/Pb+F49XtAERFBPHFm+Zy1SVTZGMsIQQAJ2raefblHew8UANAgL+O26+dxW1Xz5Q9t8YpCSVizHK5FDbsqOCZl7Z7loCOjwnlrpvncdlFBWhlUqEQPqmmoYt/vbKDzbsrAdCoVVy9vIi7b55PVIQM945nEkrEmDdod/DuhqP85/U9nhUYk+PD+dKt87lkwWQ540EIH9HY0su/X93Jum3lKIr7hKzli/K4++b5pCTKxPiJQEKJGDdsNjtvrT3M82/s8cyqT0+O4t7bFrBkbo7MKRBigmrrMLDytd2s2VSKc+hsrovm5vClWxeQmRrt5erEhSShZAKy2R1Y7Q7CAifm3jKWgUFeX1PCi2/txWR2n0aclRbD7dfM5JIFk2V3TyEmiJqGTl5ZdYAPtpbhGFquf/6MTO65bQG5mXFerm7kdPWbiQ71zWEoCSUT0JOrt7Nqfxm/uHkZi/MzvV3OiDGarfxv1QFeefcAlqFFvKIigrjpiulcu7yI0JAAL1cohDhfiqKw91Adr6w6wN7DdZ77Z0xJ5b7bF1KYO3EXV+wxWfjNG5s4UNPEW9//4oQ9sDwXCSUTzKDDwc2/f5GadvfeMtfMzOf71y6Z0L/c/cYB3l53hNfXlHjmnPjptVy+tIBbrppBamKklysUQnwcm83O2m3lvLLqAHVN3YB7/Zklc3K49eqZEzqMAKw9fIJH3thIj2kAjVrFY3deyfKiHG+XNeoklExAA4N2/vL+Tp7fehBFgdjQoAnfNQH3So4bdx7n5VX7qazt8Nw/f0YmN10xnZlFabK8tBBjTEe3kXfWHuattYc9c8UCA/RcfckUbrpyOgmxYV6ucGSd7I58cPgEADkJ0fz6thXkJ0/c4alzkVAygZXUNvOzl9dS39UH+EbXBNzt35Jjjbyy6gA79ld77k9OiOD6S6dy+dJCQoMn9s9AiLFMURQOljbyxpoStu+r8kxejYsO4eYrZ3DVJVMIDvLzcpUj76PdkXsuns1Xl89B58MLvkkomeDO1DX5+c3LWDLBuyYnNbT08MaaQ6zZXIrZ4p534qfXsnxRHjdcNo1JE3iynBBjjcls4/0tx3jz/UPUN/d47p+Wn8z1l01jydxJPrH+ULfRwqNvSnfkTCSU+IiPdk0un5bLD667iKiQQO8WNkosA4Os3VbOm2tKqG7o8txfMCmB6y6dxtJ5k/D303mxQiEmruM17byz7ghrt5YxMLQbc4C/jkuX5HPDZdPITI3xcoWjQ1EU3tlfxmPvbMVgsUp35AwklPiQgUE7f31/F89vPYhLUQgL9Od7Vy/m2ln5PrPGh6IoHKlo5o01h9i8+wROp/s0w6BAPcsX5nHVJVPIzYrzmZ+HECOl32Rl/fZy3l1/lBOnzPFKT47k+suKuWxJPkGBE3+I5qTG7j5++eoGdlc2AJCbGMPDtyynIEW6I6eSUOKDjjW28dD/1lPR0gnA9IxEfnT9UiYnxXq5stHV3Wvm3Q1HeXfDUc8y9gBpSZEsX5zHikV5JMaFe69AIcYZ26CDXQdq+GBrGbsO1njWFtFpNSyek821y6dSXJjiU6F/YNDOPzfu49+b9jPocOKn1XD/pfP4wpLp6DTSHfkoCSU+yu508vyWgzy9bjcDgw7UKhU3z5vCNy5fMOEnwn6Uy6VwsLSBdzccZeveKgYHHZ7HpuQmcsnCyVw0dxLRkcFerFKIscnhcHLgaAMbdx5ny+5KTBab57Hs9BiuvHgKKxbnEeZj6wYpisK6I5U8vmorrb1GAOZkp/Czmy4hLUaWxD8bCSU+rq3XyOOrtnomXIUF+vP/LpvPTXOn+MSEs48yW2xs3VPJB1vLOXC0npO/5SoVFE1OZun8SRJQhM87NYhs21tFv8nqeSw2KoTli/JYsTiPrDTfmCvyUcdbOnnsnS3sqWwEID48hAevWczyItkO4+NIKBEA7K1q5NE3N1HV5l60KDMuku9dvZiFk9N99o+oq8fExp3H2bTzOEePt3juPzWgLJmTQ0xUiBerFGJ02O1ODpaeOYhEhAWyZG4OF8/PZVp+is+uB9TVb+Yv7+/kzb3HcCkKeq2Gu5fO5J6LZxGgl4n0n4SEEuHhcLp4bfdR/vbBLnrN7kWM5k9K47vXLGZSgm9vetXe1c+W3ZVs3Hmc0lMCCsDkrDgWzs5m0axsMlOjfTbEiYnHaLay+2At2/dVsbuk1nNaPZwSROblMjU/2ad367baHTy/5SDPbtyLxeY+u+jSqZN44MqFJEdN7MXfLjQJJeI0/QNWnl2/lxe2HcLudKJWqbhhTiFfv2we0SG+uUnUqdq7+tm86wSbdp3g2IkWTv1LSIgNY+GsLBbNyqYoP9knh8DE+NbWYWD7/mq27a3iUFmT5ww1gMjwQBbPkSBykqIorCk5zpPvbffMGylMieP71y6hOCPJy9WNTxJKxFk1dvXxh9XbWXekEoAgPz33XjKLOxYVSytySHevmZ0H3C/g+482DJskGxLsz+ypacyZlsHs4nSiI2Qeihh77HYnR483s6ekjt0ltVTXdw57PD05koWzslk4O5v87ASfHZr5qJLaZh5/ZytHGtoA97yRB65cyOXTcuVn9BlIKBEf62BNM797ZwvHGtsBiA0L5ivLZnP97EJZ8OcUA9ZB9h6uZ8e+KnYeqPHs43FSdnoMs4rSmFGUxtS8JAL89V6qVPgyRVGoa+rmwNEGDhxp4EBpg2eXbXBvgjclN4mFs7NYODOblEQ5U+RUFc0d/PWDXWw+VgNAgF7HvZfM4s7F0+Vg7QKQUCI+EZdLYXVJBX9Zs5OW3n7AfWRw37LZXD+rQMLJRzidLo5VtrKnpJY9JbVUVLcPe1yrVZOfk8DUvGSK8pKYkpvkE3t9iNHncinUNHRxuLyJI+VNHCprorvXPOw54aEBzJmWwZzpGcyemkZ4qG+s9Hw+Kpo7eGrtbjaWuvfT0qhVXDe7gK9fOo+YUOmCXigSSsR5GXQ4eHXXUf61cR8d/e4XNgknH6/XYGbf4Xr2H23gwJF62ruMwx5Xq1VkpcUwNS+JorxkpuYlExUh83fE+bPbnVRUtw2FkGaOVDRjMtuGPUev1zIlN5GZRWnMKkpjUmacDDmcxUfDiEoFl0+bzFeWzyEzLtLL1U08EkrEp2KzO3h9Tyn/3LB3WDj50tKZXD+nEH+d1ssVjl2KotDc1sehY03uN46KZprb+k57XkJsKPk5CeRlJ5A/KYHcjFj8ZH8ecQpFUWhpN3CsspXyylbKKluprO1g0O4c9rwAfx2FuYkUTU5ial4yBbmJ+Onlb/RcShvaeGb9XjYd+2gYmU1mXJSXq5u4JJSIz+RM4SQyOJAvLJnOrfOLCPaXIYlPoqvH5DmyPVzeRHV9Jx/9C9No1GSlxZCfHU9eTjyTMuJIT45Cp5PulC9QFIXuXjMnats5Xt1OWWUr5VVtp81dAvdwjLvj5g4h2RmxcibYJ6AoCvuqm/jH+r2ePWokjIwuCSXigrDZHbyxp5SVmw945pyEBPhx+4JpfH5RMRHBvrXE9GdlMtuoqG6jbOjot6yylZ4+y2nP02rVZKZEk50Ry6SMWHIyYslJjyUwQCbRjmcul0JTWy+VtR2cqOlwX9e2nzGA6LQasjNiKMhJIH/okhQfLuvlnAeXS2FreQ3/2LCPI/WtgHvOyJXT87jn4lkyTDOKJJSIC8rudLKm5DjPbthHbUcPAAF6LTfOncIXl8wgPlxWP/00FEWhvcvoCSjHq9uprO0Yts/IqRJiw8hIiSI9JYqMlGgykqNIS46UM37GGJdLoa3TQF1TN7WN3dQ2dlHX2E1dUzdWm+O056vVKlITI5mUGesZ2svJiEEvw6WfisPpYu3hEzy7cR+VrV0A6LUabphTyF0XzSApUhY+G20SSsSIcLkUNpZW8Y8Neylrcm9brlWruWJ6Ll9YMoPcRN/cE+NCUhSF1g4DlXWdVNa0c6LWfUTd2WM64/NVKoiPCSM9OZLkhAj3JT6c5IQI4qJD0Mok5RGhKAoG4wDNbQaa23ppbO2lua2PhuYe6pt7GLDaz/h5fnotWWkx7u7XUCcsKzVa5hVdABbbIG/uPcbzWw/S3OPu7Ab56bl1fhF3Lp5OdKhMMvcWCSViRCmKwq4TDfxjw172Vzd57p+ZlcztC6aytDBLtu++wPr6LcOOuk/ePlPr/yS1WkVcdAiJceHERYcQGxVCTFQIsUO3Y6NDCA70kyGBM7DbnXT1mujoMtLRbaSz233d3mWktcNAS7th2DogH6XTakhNjCA9JZqMlKihSzSJ8eEyD+QCq+vs5ZUdh3lr3zFMVvf/SURQAHcsKub2hVMJDfCtHdLHIgklYtSUNrSxcvMB1h+txOly//rEhgVzy7wibpo7hagQWRthJPUaLNQ1dVPf3ENzay9NrX00tvbS0mEYthLt2QT464iJDCEyPJDwsEAiwwKJDA8adjs0xJ/QYH+Cg/zH7RuqoigMWO30m6wYTVZ6DRZ6DRZ6DGZ6+4auDRZ6+yx095rpMZhPm5R8JtGRwSQnhJMcH0FyQjgpCRESPkaB0+Vie0Ud/91+iB3H6z33p0WH84Ul07l6Zr4sejaGSCgRo66tz8iru47y2u6j9Jjckzd1Gg3LirK5ee4UZmYlyxH5KHK5FHr6zDS399HSbqCj68Oj/Y5uIx1dxmE7wn5SgQF6QoL8CAn2JyTIn5BgfwL8dAT46/D31512W6/XotVq0GnV6LQaNBr3tU6rQaNVo+LMvxMKCi6XgsPhwuFwYnc4cTg/vG13uLBa7VhtdizWwVNu27Fa7ZgHbBhNNoxmdwgxmm3D9nv5JHRaDTFRwZ7OUkxkCLFRwSTEhZEYF05CTKgMu4yyrn4zb+07xmu7j3qGaFQqWJyXwe0LpjFvUpqszTIGSSgRXjPocLD2cCX/3XHYM+MdID0mgpvmTuGamfly1s4YYbXZ6eg20tVjcncN+ixDHQQzPX0fdhH6TdZzDlWMJzqthpBgP8JDA4kY6gRFhJ28HUhkWBAR4YHERYcQHhooQXoMcLkUdlc28NruI2wqrcHhcofL0AA/bphTyC3zi0iJCvdukeKcJJSIMaGsqZ3Xdh9l9cEKz9bf0j0ZnxxOFyaz9bTug8lsZcBmZ2CoQ+G+7e5cWKx27HbnGTod7muH49ydC5Va5emqaLVqT8dFq3F/HOCvw3+oMxPgrz/lto5Af/1QN2eoqxPsHoLy02vld26cOFNXBGBqWgI3z5vCiqmTZIhmnJBQIsYUs3WQ90oqeG33Uc9ZO+Ae/71udgFXz8wnLkz2mRDC19mdTraX1/HWvmNsLav1dEVC/P24akYeN82bwqSEaC9XKc6XhBIxZh1rdHdP3iv5sHuiVqmYl5vGdbPyWVqQhZ+szyCET6ls7eLtfWWsOlDumZMG7q7ITXOncOk06YqMZxJKxJhntg6y9vAJ3tp3jIO1LZ77QwP8uLx4MldNn8zU9ARptQsxQXUbLbx/6DirDpRzrPHDHbcjgwO5asZkrp1VIF2RCUJCyQTUaDDQaTEzPSHR26VccPWdvby9v4x39pXRbvhwkbCEiBCWF+Vw6dRJTEmNl4AixDjXY7Kw/mgVaw+fYF9VE66htxytWs3i/Ayum1XAwrz0CbfOUb/NysHWVi5Kz/B2KV4hoWQC+t7aNbxRUcbi1HS+OWfehAwnTpeLPZWNvHugnA2lVZ7hHZCAIsR4dbYgAlCQEseV0ydzRfHkCbmmUb/Nyr9KDvLvQwexOR1s+eK9xAX73vy5T/v+LQP5Y5SiKPhptWjVarY21LG1oW5ChhONWs383DTm56ZhtTvYXl7L2sOVbC6robXXyH+2HOQ/Ww56AsolhdlMTU9Ao5ZFqoQYSzoMJjYfq2btkcrTgkheciyXTp3EiqIcUqLDvVfkCDo1jBgH3XtZTYqKptNi9slQ8mmNWKekrq6OX/3qV2zcuJG2tjYSExP5/Oc/z09+8hP0+k+2mZivd0oAGgx9/G3fHt6oKPPMSp+I4eSjPhpQBgY/7KBEBgdwUX4WF0/JYm5OqkySFcJLatp72FhaxabSao40tA17zBeCCJw9jHxz9jwuy85B7aMd3jE3fPP+++/zyiuvcPvtt5OdnU1paSn33Xcfd955J48//vgn+hoSSj50pnCyKDWNr8+ay+ykZC9XN7Ksdgc7KupYd6SSrWW1GK0f7qgboNexcHIaSwuzWZyXQVig7HkhxEhxulwcbWhjU2k1G0urqevsHfZ4UVoCFxdmTfggAtAzYGHloRKeO1wiYeQMxlwoOZPHHnuMp556ipqamk/0fAklpztTOJmZmMTXZs5hSVr6hJ93YXc62V/dxMahF8WOUybJqlUqpqUnsCgvg0V5GUxKiJ7wPw8hRprBYmXX8Xq2lteyvaKOXvOHG0JqNWrm5KRycWEWSwsyiQmd+MMU7SYT/zi4n/+WHmbA4d5rSsLI6cZFKPnpT3/K+++/z/79+8/4uM1mw2b78Ci4v7+flJQUCSVn0Ggw8PeD+3jtWCmDLicABTGx3D9zjs/8YSiKQllTOxtKq9lUWk1VW/ewx+PDQ1iUl87ivAxmZ6cSKHuWCPGxFEWhqq2breW1bC2v5XBdi2fjTYBgfz2LJmdwcWEWC/PSCfb382K1o6fB0MffD+zj9bJjntfcwphY7p81h0uzfOM193yM+VBSXV3N9OnTeeKJJ7j33nvP+JyHHnqIhx9++LT7JZScXbvJxD9L9vNS6REsdve8i/TwCL40bTo35BUQqPOdN+LmHgPbyuvYVl7LnsoGbA6n5zGtRk1RWgKzs5KZnZPK1LR49FqZiyKEoig0dRvYW9XI3qom9lU30tlvHvacrLhIFg91IKdlJE6403fP5XBbK8+W7GdNVaVn8u6sxCS+Pmsui1LTpBt7FqMWSs4WHE61b98+Zs6c6fm4paWFJUuWsGTJEp599tmzfp50Sj693oEBVh4+yHOHS+gf+hmG+flza0EhdxYVk+RjPz+r3cHeqka2ldeyrbx22D4aAH5aDdPSE5mVncKc7BQKUuN86oVW+LbW3v5hIaS11zjscT+thtk5qUNBJJ2kyDAvVeodg04n71edYOWhEg61f7jJ6OLUdL42a86En8d3IYxaKOnq6qKrq+ucz0lPT8ff3z3hsKWlhaVLlzJnzhxWrlyJ+jxO5ZQ5JefPPDjIq2WlrDx0kIZ+A+Cea7E8M5u7p01nVmKSzyV7RVFoPHkkWNnI3upGuo2WYc/x12kpSkugOCOR6RlJTE1LIMj/k50lJsRY5nIp1HR0c7C2hYM1zZTUttDSOzyka9VqpqTGMzsnhdnZKUxNS/DJs9q6LBZeLj3CC0cP0WF2d4v0ag1X507mS8UzyIuO8XKF48eYHL5pbm5m6dKlzJgxgxdeeAHNeR6JSij59JwuF5vravn34YPsbGzw3J8XHcNd06ZzzaTJ+Pno8IWiKNR29LC3qom9VQ3sq2qiz2Id9hy1SkVuUgwzMpIozkikKC2B+PAQL1UsxCdntTsob2qnpLbFfalrwfCR32+NWkVBchyzst0hZFp6ok/PuTrW0c7KwyWsOlHBoNM97BsTGMTni6ZyW2ERMYFB/7+9+wyO67zvPf7d3hsWZdE7SJBgpyiSlizRYmQpSiQ5Lte+iS07Za40ske6niRKnIzLTDJKMpnrGduxY0/mSk5cZDu2imUrV4wlUbJpiqREECBYQPRetmJ7O+e+2MUCy06KwAK7z2dmZxdnF+BzCGDxe/5POQVu4fqz5kLJ4pBNQ0MD//7v/54XSFwu13V9DRFKbo1+j5vvnjrJ8+fOEMvOFnfo9Xx0Uxf/c8s2Gmz2wjawwCQpE1LeHc70It8dnrxkuAeg0mpiS2M1WxpcbG2sZnNdJUadqKYIhSNJMqNuH71jM/SMTtMzNsOFKXduZd4ig1bN1oZsJbCllq0NohIYT6V4ZeAC3+/t5p3ppWtxbaty8entO7m/rQOtGNK9aWsulDz77LN85jOfuexz1/tPilBya/ljUX7cd5p/7znJVDAzhqwA3t/YxB9t2c7dTc1ip9SsGX+Q7uEp3h2e4uTwJBdm3HkrECBTTWlzOdnS4KKzrpLO2ko6airQl2DZW1h5siwz5VvgzMQcZyfm6BufpXd8hmA0fslryy1GtjZWs7Ollp3NtWysrRBzprLGAn5+cLqH/+w7jTeWWd6sViq5v62Dz2zfyXZXdYFbWBzWXCi5FUQoWRkpSeKNkSG+33uKw6MjueM1Fguf6NrKxzZvEeXKi0TiSc5OztI7OkPP2Ay9YzPM+IOXvE6lVNBS5aSztpJNdZlbe3V5ySybFG6NtCQx5vZzfnKeMxOznJnMBJGFywQQnVrFproqtjRmKnhbG1y47JaSmzt2NYvD2d/rPcWbo8Ms/tGrNpv5RNc2Pra5i0pT8e+xsppEKBFuyqjfzw9Pn+LHZ07jj2XGnTVKJQdb2vjIps3c2dCEWlRPLmsuEKJ3bIa+idls73UWbyh62ddWOyy0u8ppry6n1eWkrcpJc1WZqKqUOFmWmfYFGZz1MDjj4cKMhwszboZmPHlL2hepVUraq8vZlA29XQ0u2qvLRRXkCsYDAX52ro+fnDmdqw5DZjfsP9qynQPNLeL9bYWIUCK8J/FUil9e6Od7vd2cnFlaAldhNPHQho38QedmNoqZ51clyzJzC2HOTsxydmKOMxNznJmcy9t1djmFAmrLbDRWOGiqsNNY7sg+duCyW1AqRU+3WASjccbcPkbm/YzO+xiZ9+Xul18Zezm9Rp0JINmhwU11VbS5nGjUIoBcTTAe55WBfn529gzHpiZyx+3ZeXSf6NpKk91RwBaWBhFKhFvm7PwcPzlzmpfOn8uNuQJsKq/gDzo38+CGTsqNxXfJ8ZUSiMS4MO3mwrSbgRkPA9le8cUrIpbTqVXUl9upc9oytzIbtWVWasts1JbZSnqlxFqUliTmAiEmvAtMegJMegNMeheY9AYYdfsvWYK+nFqppKnSQUtVGW1VTtqrMxW1OqdNzPG6TmlJ4sj4GD8918ergwO5Cf0KYH99Ax/u7OK+tjb0avF7s1pEKBFuuUQ6zeGRYX56ro/Xh4dIZmf0qxQK7mho5KENnRxsacN8nVd9FpbIsownFGF4LtNjztz8jLp9jLn9pNLSVT+/zGygxmHFZbdQZTfjslmosltw2c1U2SxU2EyipH+LyLLMQjTOjD/IrD/IjD/ITCDErD/ErD/ItD/IlG/hmt+zcosxVwlrrHDkKmT15XbxvboJsizTMzfLS+fP8nL/eeYjS7vQtjrK+IPOTTy8YRPVFrGUvxBEKBFWlC8a5ef95/jZuTP0zC5dolyvVnOwuZUHN2zk/Y3NYgndLZBKS0z7Fxid9zOR63UHmPAuMOEJXHa1xcUUCnCYjJRbjJRbTDgtmcdOq4lyi4kyswG70YDdpMdmNGDQqktqYmQqLbEQjeEPxwhEonhDUTyhCJ6FMO5gBHcwc+8JhvEEI8SSqWt+TbVSSbXDkqlmOa3Z6paNhnI7jRV2Mdn5FhnyeXnx/FleOn+O0YA/d9ym0/P7HRv4cOdmtla5SurneS0SoURYNUM+Ly+dP8dL/ecY8S9dutym03N/Wzu/17GRPbV1YgLZClmIxpj0LDDlW2A2EMr24EPMBDI9+dlA6Jq99otp1SrsRj02kwG7UY/FoMOs12LW6zDptZh1Wsx6LSZ95rheo0anUWPQatBp1OiXPdaqVLd8Powsy6QkiXgyRSyRIpZMEUsmiSdTRLMfRxNJQrEEoVicUCxBOJYgFI8TimaOBSIx/JEYgXCMYOzawe5iDpMhU5mymZdVpcy47JkgUmU3i+GWFTIZXOCVC/281H+O03OzueN6tZqDLa081NHJnY1NolO0hohQIqw6WZbpnZvlpfPnePnCudy2zABOg4EPtnXwu20dIqCsMkmS8YYjeIIR3Ath3Nne/mIFwBuM4AlF8Iej+COxGw4w10OhALVShVqlRK1UZu5VSlRKJVfqwMoySLJMKi2RSqdJS/LSvXTr2whgMeiwG/U4TAacFhPlViNOs5HybEXJaTbitBiptJlLctv1QloMIq8M9OdNvlcpFNzZ2MSDHZ38TksrJjF8vCaJUCIUVFqSeHtygpfOn+XVoYHc8mIQAWUtk2WZSDyJPxLNDmXE8IejuWpDKJ4gFE0Qji+vPiSyFYpMpSKWva1EuLkchSKzMkWvWarSLFZqzAYdZp02U93RZ+4teh1GnRabUY/dqMduygxbWQ161Crxs7iWXCmIKIDbaup4oGMDv9vWgVNMtF/zRCgR1oxkOs3RiXF+ceH8JQGlTG/g7qZmPtDcwp0NTVh0Ypy9WKTSErFkkmRKIiWlSadlklI6W/mQSEvSNYOLQqFArVKiUSlRq1SolUpUy6oteo0arVol5gsUCUmW6Zuf47XhQX41PJQ3NLMYRH63vYP72trF5mbrjAglwpp0tYCiVirZU1vHB5pauKe5lUa7vXANFQRhVUSSSY6Mj/La8BCvjQzlDfuKIFI8RCgpQsFkDKVCiUldHGOmyXSad6en+NXwIK+NDDHk8+U93+oo40BTM3c2NrGnpq5kr2IsCMVElmVGAn7eHB3m8OgIvx0fJ55eWs1k0mi4o6GJDzS3cHdTc9Fc4kKWZeZiQaoMpfe3C0QoKUrfOPsG3x04yocat/GJ5ttotpQXukm31LDfl+ktDQ9xfGoibzKjXq1mb109dzU28f7GZppsdlGyF4R1IpxIcHRinMOjw7w5OsLYQiDv+TqrlXuaW/lAUwt7aourAxJLJ/nF+Gl+MHycmUiA1+/732hVxXN+10uEkiL0qbee5bh7NPfx/soW/rBlD3e52lEpimuC3kI8zq/HRjg8OsKboyPMhvO3Zm+w2rizsYn31Teyr64em15foJYKgnCxtCTRNz/HkfEx3hob5cTURG6zRchcT2t3TR3vb2zkQFML7WXOoutkTIR9/HD4BD8dOUkgmdkJW6tU8ewdj7DDWV/g1q0+EUqKkCTL/HZuiO8PHeONmf7clS1rjDY+3rybjzTuxKErvlnosixz3uPmzdFMSLn4DU4BdFVWsb++gffVN7K7pkZsHy0Iq0iWZYb9Pn4zPsaR8TGOTowTiOdfNqHeauOuxibuamxmb119US7dlWSZI3ODfH/oOIcveo/+RPNtfLhxR1G+R18PEUqK3FIKf5dAMvPLr1Wq+GDtJj7WtItdzoai63ksWiwFvzk2wpHxMQZ93rzntSoVu6pr2FfXwJ7aOrZVuYqqHCwIhSbLMuMLAY5NTvD25ARHxkeZDuVXM81aLXtr63lfQ0PRD7l64mGeH+3mJyPvMBZemhv3vspW/mfLbUVZzb5RIpSUiGgqyS8nTvP9oWOcDSxt995qqeB/NO/i9+q2FH0ynwkF+e34OL8ZH+XI+BgzFw31aFUqdriq2VNbx201dexwVRdlL00QVookywx6vbwzPcnbkxMcmxy/JIRolSp21dSwv76B/XUNbKlyFfUeRJIsc8w9wk9G3uXQ5BmScqZ6a1brinbe33shQkmJkWWZ0/4pfjT8Dr+cOE00nbn8uUap4p7qjXy4cTv7KluKPq0vlpF/PTaa68V5ovlXZFUpFHSWV7DdVc0OVw3bXC6a7Y6i7cUJwo1aiMc5NTvNqZkZTs5Mc3JmKm/5PmSW8G+trGJPbT376uvZXV2LQVP8w6aTET8vjJ3i+dFuJiP+3PEtjho+1rSL363rwlgkKyRvJRFKSlgwGePn473858i7edWTSr2F36vfwkMN2+iwVhawhatHlmWGfN5M725qgnemppgMLlzyOrtez7YqF9td1Wyvqmaby4VdbyhAiwVhdaUkiQseNydnpumenaZ7eppBn5eL/xDo1Wq2V1Wzu6aWPbV17KyuwVgCIQQgnIzz6tRZXhw7xdvukdxxs1rHA/VdfKxpF5vs1YVr4DogQokAwBn/ND8bPcnL4725uScAnTYXDzVs44G6Lsr1pbUh0VRwgXenp+iemeHU7DS9c7Mk0ulLXldntdJVUcWWqiq6KqvYUlklgoqwriXTaQa8HnrnZjk9N8vpuTnOuufz9glZVG+1ZUK6q5odrmo2VVSW1AXu0rLEb+eGeGm8h0NTZ4kt+z/aU97Ehxt38Ds1nRjEpPrrIkKJkCeRTnF49gIvjvXw5kx/bvxTpVBwR2UbDzZs5YBrQ0n+giXSac655+memaZ7ZpqTM9N5l0BfbjGobKqopLO8go0VFdSYLWLoR1hzwokE5z1uzrnnOeuep+8qAcSs1V5UKaymvASvJyPLMucXZvn5WA8/n+hlPrY0b6bJ7OThhm38Xv0Wao32wjVynRKhRLgiXzzCLydP89JYDz2+ydxxo0rDPTUbeaBuC/srW9AoS6dXdLGFeIzTc3PZ3uQsvXOzVwwqVp2Ojc4KOisq2FieubU5ysRkWmFVSLLMxEKAfo+bs+55zs5nQshYwH/JEAxkAkhXRRVdlZWZCmCVi0abHWUJB+uxkJdfTJzmFxO9DAbdueM2jYEH6rt4qH4bWxw1ovPxHohQIlyX4aCbF8d7+MV4LxPLJm3ZtQY+WLuJB+q2sMvZUNJvWIsWg0rf/GzujX/Q583beXa5WouVdqeTjjInbWVO2p3lIqwIN20xfFzweOj3uhnwerngcTPg8xJLXVr9AKgwmnIVvU3lFSKALDMXC/LKRB+/nDid1znTKlXc5ergwfqtvN/VjraEO2e3kgglwg2RZZlTvkl+Md7LK5N9eOJLF8WqNlj5YO0m7qvdzFZHregtLBNPpRj0efN6qP0e9yUrfparNptpspfR4nDQbHfQ4iij2e6g1mot6iWUwvXxx6IM+3wM+X2Ze5+XYb+PEb//skMvkPlD2lJWxkZnea5i11leWZJDMFfjjYc5NHWW/5o8w7H5EaRsLUmJgn2VLTxQ18XBmo1YNGKH6FtNhBLhpqUkibfdw/xi/DSHps4SSsVzz1UbbBys2cDB6k52OhvEH9Er8EYjDHi99HvcDHg9XPB66Pd4rhpWtEoVdTYr9VYbtVYb9VYrdRYbdTYbdRYrZQaDCIRFIJ5KMRlcYGJhgfGFABO52wJjAT++i5beLrcYPtrLnHQ4sxW4MicNNrv4XbyC6UiAX02f47+nznHcPZoLIgDby+p4oK6L+2o3l9yE/9UmQolwS8TTKd6cvcD/mzzD6zP9RFKJ3HMOrZEDrg4O1mxkX2ULelXpTZK9Ub5olGG/j2F/tgec7RGP+H2XXQG0nFGjodpswWU2U22xUG22ZD+2UG2x4DKZsep0IrgUUDyVYj4SZjoUZDoYZCYUyjwOZR8Hg8xHwtf8Oi6TmWZHGc0OBy12B83Zqlqd1SbCxzXIssxg0M1r0+c4NHWO0/6pvOc326v5YO0m7q/dTJ3JUaBWlh4RSoRbLpZOcmRuiENTZ3l9uj93kSkAvUrNvooWDlRv4C5XO5V6SwFbuv5IssxUcIGxQIDxhQCTeb3ohUsuSHglWpWKCqOJSpOJCqOJcpOJSqOJCpMJp8GAw2DAaTDi0Buw6fVibsF1iCaTeGNRvNEovmgUbzSCOxJhLhxiPhJhLhzGHQkzFw5fcr2XKzFqNNQtVsOstuwtUyVrtNnFvKMblJTSvOMZ47Xp87wx08/4sq3eFcCOsnp+p6aTe2o2Ui+CSEGIUCKsqJQkccIzyn9PneW16fNMR/M3JNviqOFuVwcfqN7ABmuV6L2/R4sl/8We90woyNSynvhMKHjJjpvXolQocOj1OPQG7AYDNp0Oq06PVafL3pYem7VaTBotRo0Gk1aLSaPBqNGu+X0rJFkmkkwSSSYIJ5NEEpn7UCJBMBFnIZ65BeMxAvHFj2MEYrFcELnSJNIr0SpVuMzmpQqW2bxU1bJYqLVYcOjFUNx7FUhEeWt2gNemz/PruQGCyaVhZo1Sxd6KZg5Wb+RA9QYqxNBMwYlQIqyaxbX9r0/388ZMf95MdoAqvYU7q9q4s6qd/ZUtmDW6ArW0uMVSSdyRCPPhMHORMPPhMPPZ+7lwGF/2j6w3GiWYiF/7C14HjVKJUaNFp1ahU6nRq9XoVCp0ajValRqdWoVWqUKlVKJSKlArlKiUStTK7L1CccU/zrIsI8kyaVkmJUmkJYmUnL2XZFJSmngqTTydIp5OE08t3SfSKaKpFJFk8pacp1apoixbaXIYDJQbjbkKVMWy+0qTCZtOLwLHCpBkmbOBGd6avcBbMwN0eyfy5oeUaY3c7erg7uoO9le2YhJbva8pIpQIBTMXC3J45gJvTPdzZH4wbydEtULJDmc9d1a18f6qdjqsleINvAAS6TT+ZUMSvlg0VzXIVQuWPQ5nKwyLFYdrzX9Za5QKRabKs1jt0WiwLKsEXa5KtDjcVWYwYtJoxM9pAQQSUX4zN8hbswP8enYAdzx/Pk67tZIDrg7udnWwtay26K/ttZ6JUCKsCfF0iuPuEd6cHeCt2QFGQp685yv1FvZXtrC/soV9FS1iBvw6kUyniaYywyCRbEhZXqlYrF7EUilSkrRU6ZAk0rK07NjV324UikwpXqVUZKorivwqy/KKjC7vXo1epc4NNenVahEq1oGklKbHO8mR+UGOzA3R453Mq4YY1Vr2VTTnKq81RlsBWyvcCBFKhDVpPOzjzWz59W33cF4VBWCDtSoXUnY6G8TVNgWhiC2ulDk6P8SRuSGOuUcIL1vhB9BqqeCuqjbudLWz09kgNjNbp0QoKUITkUm8CS+bbZtQKdb/L2Y8neIdzxhH5jK9ouVXNAbQKJR0OWrZXd7AbmcjO50NYj6KIKxjkiwzsDDHcc8oJ9xjnHCP4o7nryyzaw3sq2jJdk5ai6YaMh93MxweZk/ZbYVuSkGIUFKE/u/wsxyefwubxsY+5+3sd+6jwVhfNGVpTzzM0blMj+m388NMRwN5zytR0Gl3sdvZyO7yRnY5G3DoxI6VgrBWpSSJs4FpTrgzIeQdz2je1coBdEo1O5z17K9oYX9VK502V9EsVQ+nIhz3nuCI57ecD/ajUqj42vb/g1lTesPUIpQUof8c/xmvzx8mlFrqWdQZatlfvo99zr2UaYtn/b0sy0xE/Nk3s1FOeEYZW7b3wKJms5MdZfVsd9azs6yeZkt50byhCcJ6409EOeWd4KR3nG7POD2+SaLp/BVQRpWGHc4Gdpc3sMvZyDZHLVqVukAtvvVSUorewGl+4/kt3b5uknJmiFqBgk7rBj7Z+EfUGKoL3MrVJ0JJkUpJKXoCpzniPkK3/9RFP/Ab2eu8nd2OnZjUpgK39NabjS5wwjOWCyoDwflLXmPT6NlWVs8OZx3bHHVscdSKIR9BWAFpWWI46KHHN8FJzzgnveN5V9hdZNXo2eVsYHd5I7udjXTaXUV3BXJJlhgIDXLU8zbHvMcJLus41hpqeJ9zH/vK91KmLStgKwtLhJISkCkNHuc3nt/SH7yQO65SqNhq28Je5x522LejUxXnH2VfPMIp3wTdnnFOeifo8U1cMnFWAbRYytnqqGOLo4atjlo6bFVF96YoCCttNrpAj2+SXt8kPd5JTvunLpmUCtC0WL0sq2Ons4GWIq1eyrLMWGSMo55jvO09hifhzT1n01jZW3Y77yvfR4OxoWiG2N8LEUpKzHx8nqOeYxz1HGMiOpE7rlPq2GHfzl7nHrbYulAri6dMerGklOZ8YJaT3nHe9YzT65tkMuK/5HVapYpN9mo226vZlL21WipEUBGErPlYiD7/FGf805zxz3DaN8lsLHjJ6wwqDZvtNWwvq2OHMxNEynTFV6VdbiY2y1HP2xz1HGM6Np07rlfq2V22k71lt7PJ1lkUixFuJRFKSthEZJKj3rc56nmb+fhSOdWoMrLTsZ3bynbTZd1c1AFlkScepseb6d0t3i6eaAeZoLLBVsUmWyakdNpdtFsrxUUGhaImyzJTkQDnAjOcCUzT55vmTGCa+dil11pSoqDDVskWRy1bs7cWS0VJXCBwJjbLce8JjnmPMxYZzx3XKNRss29jr3MP2+xb0SrFFgZXIkKJgCzLDIWHc+Oc/uTSahajysh2+zZ2l+2ky7q5aId4LibLMqNhL6d9mV5gn3+aM/5pQqlLt11XoqDJ7KTDVkmbtZIOayXt1krqTQ6xc6Sw7gQSUfoX5riw7Na/MJt3zZhFShQ0W8pz1cTF+1LZN0iWZSajk5zwvcs7vnfzgogSJZttm9jrvJ1djh0YVIYCtnT9EKFEyCPJEv3BCxz3nuCE7528gKJVatli62KHfRvb7NuwakrrCr+SLDMR9uUCSp9/mnOBGXyJyGVfr1epaTaX02wpp8VSTqulnBZLBU2msqJaRSCsP7IsMx8LMRicZyjoZijkZijoZjA4f9nqB2T2A2qxVOSFjw22qpIJIIvScpqB0CAnfd286zvJbHwu95wSJZusnexx3sYu+46SXNL7XolQIlyRJEtcCA3wjjfTC3AnlrZ+V6CgzdzKDsd2dti3U613leQkLVmWmY+H6A/M5vUuBxbmiUuXv2qsEgV1JgctlnIaTWU0mstoMjtpNDtxGaxFOdlPKIxQMs5oyMNI2MtoyMNoyMtIyMNQ0H3Zqt+iGqONdkslHbZM1a/DWkWzpbxkd0mNpqOcDvRx0neKU4GevO0WNAo1m22b2eXYyU77dhFE3iMRSoTrsjiD/F1fNyf93YxGxvKer9JVscOxje32bbSb20piHsrVpGWJ8bAv1/scDnpyvdKr/THQKdXUmxw0mp00mBzUmuzUGR3UmxzUGu3oRIVFWEaSZdyxEBMRHxNhP+MRH5NhP2PZEHLxhemWU6KgPhuOM5W8ity9WB6f2Vm1x9/DSf8pzi6cIyUvdTJMKhPb7FvZ4djGFluXGJq5hUQoEW6KJ+6l29/NSf8pziycJS0vXQ3WoDKw2bqJbfYtbLVtwa61F66ha8zysvlIyMNItvc6GvYyEfaRkqWrfn6F3ky9MRNWqg02XAYr1UYbNQYbLoMNi0ZXkhWrYpWU0sxFg0xFA8xEA0xHAkxFA0xFAkyG/UxG/FesyC1y6kzZipyTRnOmMieGES+VklJcCA1wyt/DqUAvU9GpvOerdJW5ynC7pU2smlkhIpQI79ny0mZPoJdgKn9JYKOxga32LWyzbaXF3Cx+ma8gJUlMRfyMZnu5E2E/ExE/E2EfExHfZfd6uJhJrcWVDSuVeguVejMVBkv2ceZWrjeLZc0FJssygWSMuViQ+WiQudiyW/bjmegC87Eg13qjVSkUuAw26ox26kwO6kx26k1lNJnKaDCXYdHoV+Wc1iNvwktvoI8efw+nA2eISUsr7pQoabO0st22lR2OHSU7RL3aRCgRbilJlhgJj+Z6G8Ph4bznjSoDm6yddNm62GLbTLmuvEAtXV9kWcafiObK9FMRP9PRANORhcx9NIA/Eb3ur2fT6HHqzJTpTDh1Jpx6U+6xQ2vEpjVg1xqwaQzYtUb0KrV4Q76KlCSxkIwSSETxZ2+BRARvIoInFsITj+BNhPHEw3hiIbzxMMlrVMUWaZQqqg1Wqg02qo22XIWs3uSgzuTAZbCKkHmdElKC8wv99AZOc3qhj8mLqiFWtZWt9i622rbSZdtUlDter3UilAgrKpAM0Bvo45S/h75AH+F0/koVl76KLbYuuqyb2WDtEGOz70EklWAmmgkp+b3vUK737Y4Fr/uP4XJapQq71ohVo8ei0WPW6LBo9FjUutxjs1qHSa3FoNZiUGmW7pc91ipVaFRqNAplQUNOWpZIpNMkpBTxdIpoOkk0nSCaSmYepxJE00kiqQShVJxgMkYoGc8+jhNKxghmj/sTkcsul70eNo2ByrxKVqayVaGzUG3MBJEynUlMfr5JkiwxEZ2kL3CG3sBp+oP9uUtuQGbCfrOpKVfJbTI1ohTL+AtKhBJh1UiyxHB4JNNLCfQxGBpCYukPpAIFTaYmOi0b2GjdQIelXYSUW0ySZQKJKJ54GG8823OPh/I+Xt7TDySiNxVirkVBpgKgU6nRKtVolSrUShUqhRKVQpG9V6Jc9vhKf5bl7HlJSKRlmbQkkZYXb3ImgEgpEuk0SSlFXEqRXqG3L4tGh11rzFaYDDh0Jpw6I06dGaduqRq1+FhMXL61FkPIuYXznAue59zCecLp/Mm+ZVoHXdmO0GZrp1gts8aIUCIUTCQV4czCOU4v9NEXOMPcsvX+kB9SNlg7aDe3Y1IbC9Ta0iTLMpFUAn8yE1QWEtFMpSAVW6oYJOMEU5lKQmRZhSGWXqw6ZKoQCSl97X+wAJQoMKjzKzp6lQZj9rFZo8Os1l2mQqTHqtFnhrm0BqwaQ0nsWrqWSLLEeGSC88H+K4YQnVJHh6WdLdkh42p9tRiKXMNEKBHWDE/cm3ljyb65XC6k1Bpq2WBpp93SToe5HaeudK+mud6kZYmklCaRThOXUnnVi4SUJimlkbKVjZQsIeXuZVLS1as1SxUVBSqlMlddUWerLYvVGK0qe69U5x6rCzyUJFy/hJRgKDRMf+gC/cELDIQGiabz51IthpCN2Yprk7Gx5LcoWE9EKClCSSmMSqFFqVjf12PJhZSFc5wPXmA2PnvJa8q1Ttot7bSb22gzt1JnrBWrewShSASSAQZCgwyEBukPDjAcHs7bfgBAr9TRZm6j07qxaEJIIh1Aq7IVuhkFIUJJETrr/Q4Dge9RbTpAnekglca96z6gAPgTAS6ELtAfHKA/2M9oZAz5ogWTOqWOFlMzbeZW2syttJpbsJTYdviCsB6lpBTj0QkGQoMMZoPI8guFLrJpbHRkK6UbLO3UGeuKoiMSSowyEf5vJkOHiKXmuL/pVZSK9R2ubsaaDCUPPvgg3d3dzM3N4XA4OHjwIP/4j/9ITU3NdX1+qYeSt6b+F/PRY7mPNUpL0QUUyOyPMhQa5nywn4HQIEPh4UtKuZDZ9KjF3EyzqZkWUzONpgZxlU5BKCBZlpmLzzMcHmY4PMJQaJiRyCgJKX8vnsyQbQ2t5lY6zG20W9qp1FUUzXDb8iASSJzPHVeg4kDd97DrNhawdYWxJkPJV7/6Vfbt20d1dTWTk5P8+Z//OQBHjhy5rs8v9VAiy2k8sW4mQoeYDP+KeHqpt5EJKHdTYzpAlWEfKmXxbKwkyRJT0alcuXcgNMR0bPqS1ylRUmespdnURIupmWZTE7WG2nVf8hWEtUiWZXxJPyPh0bwQcvGEVMhclbzV3JKrdLaYmjEW0eR2WZYJJoeYCr/GZOhXlwSRCsMeas0HqTEdQKdyFLClhbMmQ8nFXnrpJR5++GHi8TgazaW9/Hg8Tjy+tE9AIBCgoaGB8fHxkgwly8lyGm+sh8nw68yEDxNLL11UT6XQ876ab2HXtRewhSsrnAozEhplJJK5jYZHCSQXLnmdSqFiv3Mff9T0iQK0UhCK01BomG8O/CvB1KVXHlYr1NQZa2kyNtJkbqLJ2ECVvqqo9wl5e+YvmY0sda4VqCg37KLadDfVpjtLNogst7CwQH19PX6/H5vt+ufVrFoo8Xq9PPbYY0xOTvLrX//6sq/58pe/zFe+8pXVaI4gCIIgCCtsfHycurq66379ioeSp556im984xtEIhH27t3Lyy+/jNPpvOxrL66USJKE1+tFo9GUXMVkMWWW0jmDOO9SOu9SPGcozfMuxXMGcd5nzpxhw4YNKG9g358bDiXXU804fvw4u3fvBsDtduP1ehkdHeUrX/kKNpuNl19++YYmOJXi3JJSPGcQ511K512K5wyled6leM4gzvtmzvuGZwR+9rOf5eMf//hVX9PU1JR7XF5eTnl5OR0dHXR2dlJfX8/Ro0fZt2/fjf7TgiAIgiAUsRsOJYsh42YsFmWWD9EIgiAIgiDATYSS63Xs2DGOHTvGHXfcgcPhYGhoiC9+8Yu0trbecJVEp9PxpS99CZ1Ot0KtXXtK8ZxBnHcpnXcpnjOU5nmX4jmDOO+bOe8Vm+ja29vLE088walTpwiHw1RXV3Pffffxt3/7t9TW1q7EPykIgiAIwjq2preZFwRBEAShdBTv7jaCIAiCIKwrIpQIgiAIgrAmiFAiCIIgCMKaIEKJIAiCIAhrwroNJfF4nO3bt6NQKOju7i50c1bcgw8+SENDA3q9nurqaj75yU8yNTVV6GatmJGREf7kT/6E5uZmDAYDra2tfOlLXyKRSFz7k9e5v//7v2f//v0YjUbsdnuhm7NivvnNb9Lc3Ixer2fXrl289dZbhW7SinrzzTf5/d//fWpqalAoFLzwwguFbtKKe/rpp7ntttuwWCxUVlby8MMPc/78+Wt/4jr3rW99i61bt2K1WrFarezbt49XXnml0M1aVU8//TQKhYInn3zyhj5v3YaSv/zLv6SmpqbQzVg1Bw4c4Mc//jHnz5/npz/9KYODg3zkIx8pdLNWzLlz55AkiW9/+9v09fXx1a9+lX/913/lC1/4QqGbtuISiQQf/ehHeeyxxwrdlBXzox/9iCeffJK/+Zu/4eTJk9x5553cf//9jI2NFbppKyYcDrNt2za+8Y1vFLopq+bw4cM8/vjjHD16lEOHDpFKpbj33nsJh8OFbtqKqqur4x/+4R84ceIEJ06c4AMf+AAPPfQQfX19hW7aqjh+/Djf+c532Lp1641/srwO/fKXv5Q3btwo9/X1yYB88uTJQjdp1b344ouyQqGQE4lEoZuyav7pn/5Jbm5uLnQzVs0zzzwj22y2QjdjRezZs0d+9NFH845t3LhR/qu/+qsCtWh1AfLzzz9f6Gasurm5ORmQDx8+XOimrDqHwyH/27/9W6GbseKCwaDc3t4uHzp0SL7rrrvkJ5544oY+f91VSmZnZ/mzP/sz/uM//gOj0Vjo5hSE1+vl+9//Pvv370ej0RS6OasmEAhQVlZW6GYI71EikeCdd97h3nvvzTt+7733cuTIkQK1SlgNgUAAoKR+j9PpNM899xzhcLgkrvn2+OOP88ADD3Dw4MGb+vx1FUpkWebTn/40jz76aO4qxKXkqaeewmQy4XQ6GRsb48UXXyx0k1bN4OAgX//613n00UcL3RThPXK73aTTaaqqqvKOV1VVMTMzU6BWCStNlmU+//nPc8cdd9DV1VXo5qy43t5ezGYzOp2ORx99lOeff55NmzYVulkr6rnnnuPdd9/l6aefvumvsSZCyZe//GUUCsVVbydOnODrX/86CwsL/PVf/3Whm3xLXO95L/qLv/gLTp48yauvvopKpeJTn/pU7iKH68WNnjPA1NQU9913Hx/96Ef50z/90wK1/L25mfMudgqFIu9jWZYvOSYUj89+9rP09PTwwx/+sNBNWRUbNmygu7ubo0eP8thjj/HII49w5syZQjdrxYyPj/PEE0/wve99D71ef9NfZ01sM+92u3G73Vd9TVNTEx//+Mf5+c9/nvfGlU6nUalU/OEf/iHf/e53V7qpt9T1nvflvsETExPU19dz5MiRdVUSvNFznpqa4sCBA9x+++08++yzKJVrIkffsJv5Xj/77LM8+eST+P3+FW7d6kokEhiNRn7yk5/woQ99KHf8iSeeoLu7m8OHDxewdatDoVDw/PPP8/DDDxe6Kavic5/7HC+88AJvvvkmzc3NhW5OQRw8eJDW1la+/e1vF7opK+KFF17gQx/6ECqVKncsnU6jUChQKpXE4/G8565kxa4SfCPKy8spLy+/5uu+9rWv8Xd/93e5j6empvjgBz/Ij370I26//faVbOKKuN7zvpzFLBmPx29lk1bcjZzz5OQkBw4cYNeuXTzzzDPrNpDAe/teFxutVsuuXbs4dOhQXig5dOgQDz30UAFbJtxqsizzuc99jueff5433nijZAMJZP4v1tv79Y2455576O3tzTv2mc98ho0bN/LUU09dVyCBNRJKrldDQ0Pex2azGYDW1lbq6uoK0aRVcezYMY4dO8Ydd9yBw+FgaGiIL37xi7S2tq6rKsmNmJqa4u6776ahoYF//ud/Zn5+Pvecy+UqYMtW3tjYGF6vl7GxMdLpdG4fnra2ttzP/Hr3+c9/nk9+8pPs3r2bffv28Z3vfIexsbGinjMUCoUYGBjIfTw8PEx3dzdlZWWXvLcVi8cff5wf/OAHvPjii1gsltycIZvNhsFgKHDrVs4XvvAF7r//furr6wkGgzz33HO88cYb/Nd//Vehm7ZiLBbLJXOFFudA3tAcolu6FmiVDQ8Pl8SS4J6eHvnAgQNyWVmZrNPp5KamJvnRRx+VJyYmCt20FfPMM8/IwGVvxe6RRx657Hm//vrrhW7aLfUv//IvcmNjo6zVauWdO3cW/TLR119//bLf10ceeaTQTVsxV/odfuaZZwrdtBX1x3/8x7mf7YqKCvmee+6RX3311UI3a9XdzJLgNTGnRBAEQRAEYf0O0guCIAiCUFREKBEEQRAEYU0QoUQQBEEQhDVBhBJBEARBENYEEUoEQRAEQVgTRCgRBEEQBGFNEKFEEARBEIQ1QYQSQRAEQRDWBBFKBEEQBEFYE0QoEQRBEARhTRChRBAEQRCENeH/A32m0EKAuoNVAAAAAElFTkSuQmCC\n",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week39_82_0.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"pt.axis(\"equal\")\n",
|
||
"pt.contour(xmesh, ymesh, fmesh)\n",
|
||
"guesses = [np.array([2, 2./5])]"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8290c8f1",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Find guesses"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 3,
|
||
"id": "ce55e78a",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"x = guesses[-1]\n",
|
||
"s = -df(x)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0fa3681b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Run it!"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 4,
|
||
"id": "a5aee074",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[ 0.69230769 -0.38461539]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"def f1d(alpha):\n",
|
||
" return f(x + alpha*s)\n",
|
||
"\n",
|
||
"alpha_opt = sopt.golden(f1d)\n",
|
||
"next_guess = x + alpha_opt * s\n",
|
||
"guesses.append(next_guess)\n",
|
||
"print(next_guess)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8f8ed4d2",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"What happened?"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 5,
|
||
"id": "30855606",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"[<matplotlib.lines.Line2D at 0x129deef10>]"
|
||
]
|
||
},
|
||
"execution_count": 5,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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\n",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week39_88_1.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"pt.axis(\"equal\")\n",
|
||
"pt.contour(xmesh, ymesh, fmesh, 50)\n",
|
||
"it_array = np.array(guesses)\n",
|
||
"pt.plot(it_array.T[0], it_array.T[1], \"x-\")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "fcd5a0c8",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Note that we did only one iteration here. We can easily add more using our previous guesses."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "acdc3658",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Conjugate gradient method\n",
|
||
"In the CG method we define so-called conjugate directions and two vectors \n",
|
||
"$\\boldsymbol{s}$ and $\\boldsymbol{t}$\n",
|
||
"are said to be\n",
|
||
"conjugate if"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7e07632f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{s}^T\\boldsymbol{A}\\boldsymbol{t}= 0.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "356d5fe1",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"The philosophy of the CG method is to perform searches in various conjugate directions\n",
|
||
"of our vectors $\\boldsymbol{x}_i$ obeying the above criterion, namely"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "2033af61",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{x}_i^T\\boldsymbol{A}\\boldsymbol{x}_j= 0.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0a85c783",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Two vectors are conjugate if they are orthogonal with respect to \n",
|
||
"this inner product. Being conjugate is a symmetric relation: if $\\boldsymbol{s}$ is conjugate to $\\boldsymbol{t}$, then $\\boldsymbol{t}$ is conjugate to $\\boldsymbol{s}$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6c19d77d",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Conjugate gradient method\n",
|
||
"An example is given by the eigenvectors of the matrix"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f42364fb",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{v}_i^T\\boldsymbol{A}\\boldsymbol{v}_j= \\lambda\\boldsymbol{v}_i^T\\boldsymbol{v}_j,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c841e7d3",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which is zero unless $i=j$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "297492ba",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Conjugate gradient method\n",
|
||
"Assume now that we have a symmetric positive-definite matrix $\\boldsymbol{A}$ of size\n",
|
||
"$n\\times n$. At each iteration $i+1$ we obtain the conjugate direction of a vector"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4963a2d8",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{x}_{i+1}=\\boldsymbol{x}_{i}+\\alpha_i\\boldsymbol{p}_{i}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4a39d88b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"We assume that $\\boldsymbol{p}_{i}$ is a sequence of $n$ mutually conjugate directions. \n",
|
||
"Then the $\\boldsymbol{p}_{i}$ form a basis of $R^n$ and we can expand the solution \n",
|
||
"$ \\boldsymbol{A}\\boldsymbol{x} = \\boldsymbol{b}$ in this basis, namely"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "83a86148",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{x} = \\sum^{n}_{i=1} \\alpha_i \\boldsymbol{p}_i.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c691f06b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Conjugate gradient method\n",
|
||
"The coefficients are given by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d4df90e8",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathbf{A}\\mathbf{x} = \\sum^{n}_{i=1} \\alpha_i \\mathbf{A} \\mathbf{p}_i = \\mathbf{b}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "bf3217ad",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Multiplying with $\\boldsymbol{p}_k^T$ from the left gives"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b43b4b20",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{p}_k^T \\boldsymbol{A}\\boldsymbol{x} = \\sum^{n}_{i=1} \\alpha_i\\boldsymbol{p}_k^T \\boldsymbol{A}\\boldsymbol{p}_i= \\boldsymbol{p}_k^T \\boldsymbol{b},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d82bb554",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"and we can define the coefficients $\\alpha_k$ as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "dde5ed03",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\alpha_k = \\frac{\\boldsymbol{p}_k^T \\boldsymbol{b}}{\\boldsymbol{p}_k^T \\boldsymbol{A} \\boldsymbol{p}_k}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "65ecffe4",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Conjugate gradient method and iterations\n",
|
||
"\n",
|
||
"If we choose the conjugate vectors $\\boldsymbol{p}_k$ carefully, \n",
|
||
"then we may not need all of them to obtain a good approximation to the solution \n",
|
||
"$\\boldsymbol{x}$. \n",
|
||
"We want to regard the conjugate gradient method as an iterative method. \n",
|
||
"This will us to solve systems where $n$ is so large that the direct \n",
|
||
"method would take too much time.\n",
|
||
"\n",
|
||
"We denote the initial guess for $\\boldsymbol{x}$ as $\\boldsymbol{x}_0$. \n",
|
||
"We can assume without loss of generality that"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "65a1b4c0",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{x}_0=0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "41dec06b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"or consider the system"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7d1da8a1",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{A}\\boldsymbol{z} = \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c4850b28",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"instead."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ff91db7e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Conjugate gradient method\n",
|
||
"One can show that the solution $\\boldsymbol{x}$ is also the unique minimizer of the quadratic form"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a8ab3c6e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"f(\\boldsymbol{x}) = \\frac{1}{2}\\boldsymbol{x}^T\\boldsymbol{A}\\boldsymbol{x} - \\boldsymbol{x}^T \\boldsymbol{x} , \\quad \\boldsymbol{x}\\in\\mathbf{R}^n.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e30ea38e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"This suggests taking the first basis vector $\\boldsymbol{p}_1$ \n",
|
||
"to be the gradient of $f$ at $\\boldsymbol{x}=\\boldsymbol{x}_0$, \n",
|
||
"which equals"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ede52cdd",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{A}\\boldsymbol{x}_0-\\boldsymbol{b},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "3cdf6ffd",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"and \n",
|
||
"$\\boldsymbol{x}_0=0$ it is equal $-\\boldsymbol{b}$.\n",
|
||
"The other vectors in the basis will be conjugate to the gradient, \n",
|
||
"hence the name conjugate gradient method."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d66ac756",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Conjugate gradient method\n",
|
||
"Let $\\boldsymbol{r}_k$ be the residual at the $k$-th step:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "59b7a9f5",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{r}_k=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "769980be",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Note that $\\boldsymbol{r}_k$ is the negative gradient of $f$ at \n",
|
||
"$\\boldsymbol{x}=\\boldsymbol{x}_k$, \n",
|
||
"so the gradient descent method would be to move in the direction $\\boldsymbol{r}_k$. \n",
|
||
"Here, we insist that the directions $\\boldsymbol{p}_k$ are conjugate to each other, \n",
|
||
"so we take the direction closest to the gradient $\\boldsymbol{r}_k$ \n",
|
||
"under the conjugacy constraint. \n",
|
||
"This gives the following expression"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "3ae7691f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{p}_{k+1}=\\boldsymbol{r}_k-\\frac{\\boldsymbol{p}_k^T \\boldsymbol{A}\\boldsymbol{r}_k}{\\boldsymbol{p}_k^T\\boldsymbol{A}\\boldsymbol{p}_k} \\boldsymbol{p}_k.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9cf530dc",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Conjugate gradient method\n",
|
||
"We can also compute the residual iteratively as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6398a5d7",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{r}_{k+1}=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_{k+1},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b64c8282",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which equals"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4b9bcf21",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{b}-\\boldsymbol{A}(\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{p}_k),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6d15e4b9",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"or"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "592ac2b7",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"(\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k)-\\alpha_k\\boldsymbol{A}\\boldsymbol{p}_k,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c54989ac",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which gives"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "87adadc2",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{r}_{k+1}=\\boldsymbol{r}_k-\\boldsymbol{A}\\boldsymbol{p}_{k},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "00250e67",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Revisiting our first homework\n",
|
||
"\n",
|
||
"We will use linear regression as a case study for the gradient descent\n",
|
||
"methods. Linear regression is a great test case for the gradient\n",
|
||
"descent methods discussed in the lectures since it has several\n",
|
||
"desirable properties such as:\n",
|
||
"\n",
|
||
"1. An analytical solution (recall homework set 1).\n",
|
||
"\n",
|
||
"2. The gradient can be computed analytically.\n",
|
||
"\n",
|
||
"3. The cost function is convex which guarantees that gradient descent converges for small enough learning rates\n",
|
||
"\n",
|
||
"We revisit an example similar to what we had in the first homework set. We had a function of the type"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 6,
|
||
"id": "47a98c7c",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"ename": "NameError",
|
||
"evalue": "name 'm' is not defined",
|
||
"output_type": "error",
|
||
"traceback": [
|
||
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
||
"\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)",
|
||
"Input \u001b[0;32mIn [6]\u001b[0m, in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0m x \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m2\u001b[39m\u001b[38;5;241m*\u001b[39mnp\u001b[38;5;241m.\u001b[39mrandom\u001b[38;5;241m.\u001b[39mrand(\u001b[43mm\u001b[49m,\u001b[38;5;241m1\u001b[39m)\n\u001b[1;32m 2\u001b[0m y \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m4\u001b[39m\u001b[38;5;241m+\u001b[39m\u001b[38;5;241m3\u001b[39m\u001b[38;5;241m*\u001b[39mx\u001b[38;5;241m+\u001b[39mnp\u001b[38;5;241m.\u001b[39mrandom\u001b[38;5;241m.\u001b[39mrandn(m,\u001b[38;5;241m1\u001b[39m)\n",
|
||
"\u001b[0;31mNameError\u001b[0m: name 'm' is not defined"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"x = 2*np.random.rand(m,1)\n",
|
||
"y = 4+3*x+np.random.randn(m,1)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e3007f3b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"with $x_i \\in [0,1] $ is chosen randomly using a uniform distribution. Additionally we have a stochastic noise chosen according to a normal distribution $\\cal {N}(0,1)$. \n",
|
||
"The linear regression model is given by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c5b7179d",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"h_\\beta(x) = \\boldsymbol{y} = \\beta_0 + \\beta_1 x,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8a4d63b4",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"such that"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "206c9402",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{y}_i = \\beta_0 + \\beta_1 x_i.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "939b3b78",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Gradient descent example\n",
|
||
"\n",
|
||
"Let $\\mathbf{y} = (y_1,\\cdots,y_n)^T$, $\\mathbf{\\boldsymbol{y}} = (\\boldsymbol{y}_1,\\cdots,\\boldsymbol{y}_n)^T$ and $\\beta = (\\beta_0, \\beta_1)^T$\n",
|
||
"\n",
|
||
"It is convenient to write $\\mathbf{\\boldsymbol{y}} = X\\beta$ where $X \\in \\mathbb{R}^{100 \\times 2} $ is the design matrix given by (we keep the intercept here)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b867af05",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"X \\equiv \\begin{bmatrix}\n",
|
||
"1 & x_1 \\\\\n",
|
||
"\\vdots & \\vdots \\\\\n",
|
||
"1 & x_{100} & \\\\\n",
|
||
"\\end{bmatrix}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "76738c60",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"The cost/loss/risk function is given by ("
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c01273f5",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"C(\\beta) = \\frac{1}{n}||X\\beta-\\mathbf{y}||_{2}^{2} = \\frac{1}{n}\\sum_{i=1}^{100}\\left[ (\\beta_0 + \\beta_1 x_i)^2 - 2 y_i (\\beta_0 + \\beta_1 x_i) + y_i^2\\right]\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "5d680787",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"and we want to find $\\beta$ such that $C(\\beta)$ is minimized."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "2ef9ff3b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## The derivative of the cost/loss function\n",
|
||
"\n",
|
||
"Computing $\\partial C(\\beta) / \\partial \\beta_0$ and $\\partial C(\\beta) / \\partial \\beta_1$ we can show that the gradient can be written as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e5a81fba",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\nabla_{\\beta} C(\\beta) = \\frac{2}{n}\\begin{bmatrix} \\sum_{i=1}^{100} \\left(\\beta_0+\\beta_1x_i-y_i\\right) \\\\\n",
|
||
"\\sum_{i=1}^{100}\\left( x_i (\\beta_0+\\beta_1x_i)-y_ix_i\\right) \\\\\n",
|
||
"\\end{bmatrix} = \\frac{2}{n}X^T(X\\beta - \\mathbf{y}),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b7298ace",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where $X$ is the design matrix defined above."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "64cfb75f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## The Hessian matrix\n",
|
||
"The Hessian matrix of $C(\\beta)$ is given by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "99503e16",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{H} \\equiv \\begin{bmatrix}\n",
|
||
"\\frac{\\partial^2 C(\\beta)}{\\partial \\beta_0^2} & \\frac{\\partial^2 C(\\beta)}{\\partial \\beta_0 \\partial \\beta_1} \\\\\n",
|
||
"\\frac{\\partial^2 C(\\beta)}{\\partial \\beta_0 \\partial \\beta_1} & \\frac{\\partial^2 C(\\beta)}{\\partial \\beta_1^2} & \\\\\n",
|
||
"\\end{bmatrix} = \\frac{2}{n}X^T X.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4a567780",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"This result implies that $C(\\beta)$ is a convex function since the matrix $X^T X$ always is positive semi-definite."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "22c576da",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Simple program\n",
|
||
"\n",
|
||
"We can now write a program that minimizes $C(\\beta)$ using the gradient descent method with a constant learning rate $\\gamma$ according to"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "44a99f62",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\beta_{k+1} = \\beta_k - \\gamma \\nabla_\\beta C(\\beta_k), \\ k=0,1,\\cdots\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7021c749",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"We can use the expression we computed for the gradient and let use a\n",
|
||
"$\\beta_0$ be chosen randomly and let $\\gamma = 0.001$. Stop iterating\n",
|
||
"when $||\\nabla_\\beta C(\\beta_k) || \\leq \\epsilon = 10^{-8}$. **Note that the code below does not include the latter stop criterion**.\n",
|
||
"\n",
|
||
"And finally we can compare our solution for $\\beta$ with the analytic result given by \n",
|
||
"$\\beta= (X^TX)^{-1} X^T \\mathbf{y}$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6044e7a8",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Gradient Descent Example\n",
|
||
"\n",
|
||
"Here our simple example"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 7,
|
||
"id": "72003ff9",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"\n",
|
||
"# Importing various packages\n",
|
||
"from random import random, seed\n",
|
||
"import numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from mpl_toolkits.mplot3d import Axes3D\n",
|
||
"from matplotlib import cm\n",
|
||
"from matplotlib.ticker import LinearLocator, FormatStrFormatter\n",
|
||
"import sys\n",
|
||
"\n",
|
||
"# the number of datapoints\n",
|
||
"n = 100\n",
|
||
"x = 2*np.random.rand(n,1)\n",
|
||
"y = 4+3*x+np.random.randn(n,1)\n",
|
||
"\n",
|
||
"X = np.c_[np.ones((n,1)), x]\n",
|
||
"# Hessian matrix\n",
|
||
"H = (2.0/n)* X.T @ X\n",
|
||
"# Get the eigenvalues\n",
|
||
"EigValues, EigVectors = np.linalg.eig(H)\n",
|
||
"print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
|
||
"\n",
|
||
"beta_linreg = np.linalg.inv(X.T @ X) @ X.T @ y\n",
|
||
"print(beta_linreg)\n",
|
||
"beta = np.random.randn(2,1)\n",
|
||
"\n",
|
||
"eta = 1.0/np.max(EigValues)\n",
|
||
"Niterations = 1000\n",
|
||
"\n",
|
||
"for iter in range(Niterations):\n",
|
||
" gradient = (2.0/n)*X.T @ (X @ beta-y)\n",
|
||
" beta -= eta*gradient\n",
|
||
"\n",
|
||
"print(beta)\n",
|
||
"xnew = np.array([[0],[2]])\n",
|
||
"xbnew = np.c_[np.ones((2,1)), xnew]\n",
|
||
"ypredict = xbnew.dot(beta)\n",
|
||
"ypredict2 = xbnew.dot(beta_linreg)\n",
|
||
"plt.plot(xnew, ypredict, \"r-\")\n",
|
||
"plt.plot(xnew, ypredict2, \"b-\")\n",
|
||
"plt.plot(x, y ,'ro')\n",
|
||
"plt.axis([0,2.0,0, 15.0])\n",
|
||
"plt.xlabel(r'$x$')\n",
|
||
"plt.ylabel(r'$y$')\n",
|
||
"plt.title(r'Gradient descent example')\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "01fdfcaf",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## And a corresponding example using **scikit-learn**"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 8,
|
||
"id": "d16ddbdc",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Importing various packages\n",
|
||
"from random import random, seed\n",
|
||
"import numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from sklearn.linear_model import SGDRegressor\n",
|
||
"\n",
|
||
"n = 100\n",
|
||
"x = 2*np.random.rand(n,1)\n",
|
||
"y = 4+3*x+np.random.randn(n,1)\n",
|
||
"\n",
|
||
"X = np.c_[np.ones((n,1)), x]\n",
|
||
"beta_linreg = np.linalg.inv(X.T @ X) @ (X.T @ y)\n",
|
||
"print(beta_linreg)\n",
|
||
"sgdreg = SGDRegressor(max_iter = 50, penalty=None, eta0=0.1)\n",
|
||
"sgdreg.fit(x,y.ravel())\n",
|
||
"print(sgdreg.intercept_, sgdreg.coef_)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "08aaf479",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Gradient descent and Ridge\n",
|
||
"\n",
|
||
"We have also discussed Ridge regression where the loss function contains a regularized term given by the $L_2$ norm of $\\beta$,"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0aa5045f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"C_{\\text{ridge}}(\\beta) = \\frac{1}{n}||X\\beta -\\mathbf{y}||^2 + \\lambda ||\\beta||^2, \\ \\lambda \\geq 0.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6474d14b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"In order to minimize $C_{\\text{ridge}}(\\beta)$ using GD we adjust the gradient as follows"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9335b39d",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\nabla_\\beta C_{\\text{ridge}}(\\beta) = \\frac{2}{n}\\begin{bmatrix} \\sum_{i=1}^{100} \\left(\\beta_0+\\beta_1x_i-y_i\\right) \\\\\n",
|
||
"\\sum_{i=1}^{100}\\left( x_i (\\beta_0+\\beta_1x_i)-y_ix_i\\right) \\\\\n",
|
||
"\\end{bmatrix} + 2\\lambda\\begin{bmatrix} \\beta_0 \\\\ \\beta_1\\end{bmatrix} = 2 (\\frac{1}{n}X^T(X\\beta - \\mathbf{y})+\\lambda \\beta).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0680a59f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"We can easily extend our program to minimize $C_{\\text{ridge}}(\\beta)$ using gradient descent and compare with the analytical solution given by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "de5afdeb",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\beta_{\\text{ridge}} = \\left(X^T X + n\\lambda I_{2 \\times 2} \\right)^{-1} X^T \\mathbf{y}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0042d7e6",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## The Hessian matrix for Ridge Regression\n",
|
||
"The Hessian matrix of Ridge Regression for our simple example is given by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "02cf311f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{H} \\equiv \\begin{bmatrix}\n",
|
||
"\\frac{\\partial^2 C(\\beta)}{\\partial \\beta_0^2} & \\frac{\\partial^2 C(\\beta)}{\\partial \\beta_0 \\partial \\beta_1} \\\\\n",
|
||
"\\frac{\\partial^2 C(\\beta)}{\\partial \\beta_0 \\partial \\beta_1} & \\frac{\\partial^2 C(\\beta)}{\\partial \\beta_1^2} & \\\\\n",
|
||
"\\end{bmatrix} = \\frac{2}{n}X^T X+2\\lambda\\boldsymbol{I}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "3dbc50e6",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"This implies that the Hessian matrix is positive definite, hence the stationary point is a\n",
|
||
"minimum.\n",
|
||
"Note that the Ridge cost function is convex being a sum of two convex\n",
|
||
"functions. Therefore, the stationary point is a global\n",
|
||
"minimum of this function."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "437e17bc",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Program example for gradient descent with Ridge Regression"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 9,
|
||
"id": "f11ee927",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"from random import random, seed\n",
|
||
"import numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from mpl_toolkits.mplot3d import Axes3D\n",
|
||
"from matplotlib import cm\n",
|
||
"from matplotlib.ticker import LinearLocator, FormatStrFormatter\n",
|
||
"import sys\n",
|
||
"\n",
|
||
"# the number of datapoints\n",
|
||
"n = 100\n",
|
||
"x = 2*np.random.rand(n,1)\n",
|
||
"y = 4+3*x+np.random.randn(n,1)\n",
|
||
"\n",
|
||
"X = np.c_[np.ones((n,1)), x]\n",
|
||
"XT_X = X.T @ X\n",
|
||
"\n",
|
||
"#Ridge parameter lambda\n",
|
||
"lmbda = 0.001\n",
|
||
"Id = n*lmbda* np.eye(XT_X.shape[0])\n",
|
||
"\n",
|
||
"# Hessian matrix\n",
|
||
"H = (2.0/n)* XT_X+2*lmbda* np.eye(XT_X.shape[0])\n",
|
||
"# Get the eigenvalues\n",
|
||
"EigValues, EigVectors = np.linalg.eig(H)\n",
|
||
"print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
|
||
"\n",
|
||
"\n",
|
||
"beta_linreg = np.linalg.inv(XT_X+Id) @ X.T @ y\n",
|
||
"print(beta_linreg)\n",
|
||
"# Start plain gradient descent\n",
|
||
"beta = np.random.randn(2,1)\n",
|
||
"\n",
|
||
"eta = 1.0/np.max(EigValues)\n",
|
||
"Niterations = 100\n",
|
||
"\n",
|
||
"for iter in range(Niterations):\n",
|
||
" gradients = 2.0/n*X.T @ (X @ (beta)-y)+2*lmbda*beta\n",
|
||
" beta -= eta*gradients\n",
|
||
"\n",
|
||
"print(beta)\n",
|
||
"ypredict = X @ beta\n",
|
||
"ypredict2 = X @ beta_linreg\n",
|
||
"plt.plot(x, ypredict, \"r-\")\n",
|
||
"plt.plot(x, ypredict2, \"b-\")\n",
|
||
"plt.plot(x, y ,'ro')\n",
|
||
"plt.axis([0,2.0,0, 15.0])\n",
|
||
"plt.xlabel(r'$x$')\n",
|
||
"plt.ylabel(r'$y$')\n",
|
||
"plt.title(r'Gradient descent example for Ridge')\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c06cf31f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Using gradient descent methods, limitations\n",
|
||
"\n",
|
||
"* **Gradient descent (GD) finds local minima of our function**. Since the GD algorithm is deterministic, if it converges, it will converge to a local minimum of our cost/loss/risk function. Because in ML we are often dealing with extremely rugged landscapes with many local minima, this can lead to poor performance.\n",
|
||
"\n",
|
||
"* **GD is sensitive to initial conditions**. One consequence of the local nature of GD is that initial conditions matter. Depending on where one starts, one will end up at a different local minima. Therefore, it is very important to think about how one initializes the training process. This is true for GD as well as more complicated variants of GD.\n",
|
||
"\n",
|
||
"* **Gradients are computationally expensive to calculate for large datasets**. In many cases in statistics and ML, the cost/loss/risk function is a sum of terms, with one term for each data point. For example, in linear regression, $E \\propto \\sum_{i=1}^n (y_i - \\mathbf{w}^T\\cdot\\mathbf{x}_i)^2$; for logistic regression, the square error is replaced by the cross entropy. To calculate the gradient we have to sum over *all* $n$ data points. Doing this at every GD step becomes extremely computationally expensive. An ingenious solution to this, is to calculate the gradients using small subsets of the data called \"mini batches\". This has the added benefit of introducing stochasticity into our algorithm.\n",
|
||
"\n",
|
||
"* **GD is very sensitive to choices of learning rates**. GD is extremely sensitive to the choice of learning rates. If the learning rate is very small, the training process take an extremely long time. For larger learning rates, GD can diverge and give poor results. Furthermore, depending on what the local landscape looks like, we have to modify the learning rates to ensure convergence. Ideally, we would *adaptively* choose the learning rates to match the landscape.\n",
|
||
"\n",
|
||
"* **GD treats all directions in parameter space uniformly.** Another major drawback of GD is that unlike Newton's method, the learning rate for GD is the same in all directions in parameter space. For this reason, the maximum learning rate is set by the behavior of the steepest direction and this can significantly slow down training. Ideally, we would like to take large steps in flat directions and small steps in steep directions. Since we are exploring rugged landscapes where curvatures change, this requires us to keep track of not only the gradient but second derivatives. The ideal scenario would be to calculate the Hessian but this proves to be too computationally expensive. \n",
|
||
"\n",
|
||
"* GD can take exponential time to escape saddle points, even with random initialization. As we mentioned, GD is extremely sensitive to initial condition since it determines the particular local minimum GD would eventually reach. However, even with a good initialization scheme, through the introduction of randomness, GD can still take exponential time to escape saddle points."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "870586cd",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Improving gradient descent with momentum\n",
|
||
"\n",
|
||
"We discuss here some simple examples where we introduce what is called 'memory'about previous steps, or what is normally called momentum gradient descent. The mathematics is explained below in connection with Stochastic gradient descent."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 10,
|
||
"id": "24517bb5",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"from numpy import asarray\n",
|
||
"from numpy import arange\n",
|
||
"from numpy.random import rand\n",
|
||
"from numpy.random import seed\n",
|
||
"from matplotlib import pyplot\n",
|
||
" \n",
|
||
"# objective function\n",
|
||
"def objective(x):\n",
|
||
"\treturn x**2.0\n",
|
||
" \n",
|
||
"# derivative of objective function\n",
|
||
"def derivative(x):\n",
|
||
"\treturn x * 2.0\n",
|
||
" \n",
|
||
"# gradient descent algorithm\n",
|
||
"def gradient_descent(objective, derivative, bounds, n_iter, step_size):\n",
|
||
"\t# track all solutions\n",
|
||
"\tsolutions, scores = list(), list()\n",
|
||
"\t# generate an initial point\n",
|
||
"\tsolution = bounds[:, 0] + rand(len(bounds)) * (bounds[:, 1] - bounds[:, 0])\n",
|
||
"\t# run the gradient descent\n",
|
||
"\tfor i in range(n_iter):\n",
|
||
"\t\t# calculate gradient\n",
|
||
"\t\tgradient = derivative(solution)\n",
|
||
"\t\t# take a step\n",
|
||
"\t\tsolution = solution - step_size * gradient\n",
|
||
"\t\t# evaluate candidate point\n",
|
||
"\t\tsolution_eval = objective(solution)\n",
|
||
"\t\t# store solution\n",
|
||
"\t\tsolutions.append(solution)\n",
|
||
"\t\tscores.append(solution_eval)\n",
|
||
"\t\t# report progress\n",
|
||
"\t\tprint('>%d f(%s) = %.5f' % (i, solution, solution_eval))\n",
|
||
"\treturn [solutions, scores]\n",
|
||
" \n",
|
||
"# seed the pseudo random number generator\n",
|
||
"seed(4)\n",
|
||
"# define range for input\n",
|
||
"bounds = asarray([[-1.0, 1.0]])\n",
|
||
"# define the total iterations\n",
|
||
"n_iter = 30\n",
|
||
"# define the step size\n",
|
||
"step_size = 0.1\n",
|
||
"# perform the gradient descent search\n",
|
||
"solutions, scores = gradient_descent(objective, derivative, bounds, n_iter, step_size)\n",
|
||
"# sample input range uniformly at 0.1 increments\n",
|
||
"inputs = arange(bounds[0,0], bounds[0,1]+0.1, 0.1)\n",
|
||
"# compute targets\n",
|
||
"results = objective(inputs)\n",
|
||
"# create a line plot of input vs result\n",
|
||
"pyplot.plot(inputs, results)\n",
|
||
"# plot the solutions found\n",
|
||
"pyplot.plot(solutions, scores, '.-', color='red')\n",
|
||
"# show the plot\n",
|
||
"pyplot.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "57647429",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Same code but now with momentum gradient descent"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 11,
|
||
"id": "b8365c93",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"from numpy import asarray\n",
|
||
"from numpy import arange\n",
|
||
"from numpy.random import rand\n",
|
||
"from numpy.random import seed\n",
|
||
"from matplotlib import pyplot\n",
|
||
" \n",
|
||
"# objective function\n",
|
||
"def objective(x):\n",
|
||
"\treturn x**2.0\n",
|
||
" \n",
|
||
"# derivative of objective function\n",
|
||
"def derivative(x):\n",
|
||
"\treturn x * 2.0\n",
|
||
" \n",
|
||
"# gradient descent algorithm\n",
|
||
"def gradient_descent(objective, derivative, bounds, n_iter, step_size, momentum):\n",
|
||
"\t# track all solutions\n",
|
||
"\tsolutions, scores = list(), list()\n",
|
||
"\t# generate an initial point\n",
|
||
"\tsolution = bounds[:, 0] + rand(len(bounds)) * (bounds[:, 1] - bounds[:, 0])\n",
|
||
"\t# keep track of the change\n",
|
||
"\tchange = 0.0\n",
|
||
"\t# run the gradient descent\n",
|
||
"\tfor i in range(n_iter):\n",
|
||
"\t\t# calculate gradient\n",
|
||
"\t\tgradient = derivative(solution)\n",
|
||
"\t\t# calculate update\n",
|
||
"\t\tnew_change = step_size * gradient + momentum * change\n",
|
||
"\t\t# take a step\n",
|
||
"\t\tsolution = solution - new_change\n",
|
||
"\t\t# save the change\n",
|
||
"\t\tchange = new_change\n",
|
||
"\t\t# evaluate candidate point\n",
|
||
"\t\tsolution_eval = objective(solution)\n",
|
||
"\t\t# store solution\n",
|
||
"\t\tsolutions.append(solution)\n",
|
||
"\t\tscores.append(solution_eval)\n",
|
||
"\t\t# report progress\n",
|
||
"\t\tprint('>%d f(%s) = %.5f' % (i, solution, solution_eval))\n",
|
||
"\treturn [solutions, scores]\n",
|
||
" \n",
|
||
"# seed the pseudo random number generator\n",
|
||
"seed(4)\n",
|
||
"# define range for input\n",
|
||
"bounds = asarray([[-1.0, 1.0]])\n",
|
||
"# define the total iterations\n",
|
||
"n_iter = 30\n",
|
||
"# define the step size\n",
|
||
"step_size = 0.1\n",
|
||
"# define momentum\n",
|
||
"momentum = 0.3\n",
|
||
"# perform the gradient descent search with momentum\n",
|
||
"solutions, scores = gradient_descent(objective, derivative, bounds, n_iter, step_size, momentum)\n",
|
||
"# sample input range uniformly at 0.1 increments\n",
|
||
"inputs = arange(bounds[0,0], bounds[0,1]+0.1, 0.1)\n",
|
||
"# compute targets\n",
|
||
"results = objective(inputs)\n",
|
||
"# create a line plot of input vs result\n",
|
||
"pyplot.plot(inputs, results)\n",
|
||
"# plot the solutions found\n",
|
||
"pyplot.plot(solutions, scores, '.-', color='red')\n",
|
||
"# show the plot\n",
|
||
"pyplot.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "3c5b105d",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Overview video on Stochastic Gradient Descent\n",
|
||
"\n",
|
||
"[What is Stochastic Gradient Descent](https://www.youtube.com/watch?v=vMh0zPT0tLI&ab_channel=StatQuestwithJoshStarmer)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e78e4fcf",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Batches and mini-batches\n",
|
||
"\n",
|
||
"In gradient descent we compute the cost function and its gradient for all data points we have.\n",
|
||
"\n",
|
||
"In large-scale applications such as the [ILSVRC challenge](https://www.image-net.org/challenges/LSVRC/), the\n",
|
||
"training data can have on order of millions of examples. Hence, it\n",
|
||
"seems wasteful to compute the full cost function over the entire\n",
|
||
"training set in order to perform only a single parameter update. A\n",
|
||
"very common approach to addressing this challenge is to compute the\n",
|
||
"gradient over batches of the training data. For example, a typical batch could contain some thousand examples from\n",
|
||
"an entire training set of several millions. This batch is then used to\n",
|
||
"perform a parameter update."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9e856c0b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Stochastic Gradient Descent (SGD)\n",
|
||
"\n",
|
||
"In stochastic gradient descent, the extreme case is the case where we\n",
|
||
"have only one batch, that is we include the whole data set.\n",
|
||
"\n",
|
||
"This process is called Stochastic Gradient\n",
|
||
"Descent (SGD) (or also sometimes on-line gradient descent). This is\n",
|
||
"relatively less common to see because in practice due to vectorized\n",
|
||
"code optimizations it can be computationally much more efficient to\n",
|
||
"evaluate the gradient for 100 examples, than the gradient for one\n",
|
||
"example 100 times. Even though SGD technically refers to using a\n",
|
||
"single example at a time to evaluate the gradient, you will hear\n",
|
||
"people use the term SGD even when referring to mini-batch gradient\n",
|
||
"descent (i.e. mentions of MGD for “Minibatch Gradient Descent”, or BGD\n",
|
||
"for “Batch gradient descent” are rare to see), where it is usually\n",
|
||
"assumed that mini-batches are used. The size of the mini-batch is a\n",
|
||
"hyperparameter but it is not very common to cross-validate or bootstrap it. It is\n",
|
||
"usually based on memory constraints (if any), or set to some value,\n",
|
||
"e.g. 32, 64 or 128. We use powers of 2 in practice because many\n",
|
||
"vectorized operation implementations work faster when their inputs are\n",
|
||
"sized in powers of 2.\n",
|
||
"\n",
|
||
"In our notes with SGD we mean stochastic gradient descent with mini-batches."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8400c2e5",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Stochastic Gradient Descent\n",
|
||
"\n",
|
||
"Stochastic gradient descent (SGD) and variants thereof address some of\n",
|
||
"the shortcomings of the Gradient descent method discussed above.\n",
|
||
"\n",
|
||
"The underlying idea of SGD comes from the observation that the cost\n",
|
||
"function, which we want to minimize, can almost always be written as a\n",
|
||
"sum over $n$ data points $\\{\\mathbf{x}_i\\}_{i=1}^n$,"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d0ceff52",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"C(\\mathbf{\\beta}) = \\sum_{i=1}^n c_i(\\mathbf{x}_i,\n",
|
||
"\\mathbf{\\beta}).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "562ca1d7",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Computation of gradients\n",
|
||
"\n",
|
||
"This in turn means that the gradient can be\n",
|
||
"computed as a sum over $i$-gradients"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ffea7df9",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\nabla_\\beta C(\\mathbf{\\beta}) = \\sum_i^n \\nabla_\\beta c_i(\\mathbf{x}_i,\n",
|
||
"\\mathbf{\\beta}).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "20f1bd07",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Stochasticity/randomness is introduced by only taking the\n",
|
||
"gradient on a subset of the data called minibatches. If there are $n$\n",
|
||
"data points and the size of each minibatch is $M$, there will be $n/M$\n",
|
||
"minibatches. We denote these minibatches by $B_k$ where\n",
|
||
"$k=1,\\cdots,n/M$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4589bb1b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## SGD example\n",
|
||
"As an example, suppose we have $10$ data points $(\\mathbf{x}_1,\\cdots, \\mathbf{x}_{10})$ \n",
|
||
"and we choose to have $M=5$ minibathces,\n",
|
||
"then each minibatch contains two data points. In particular we have\n",
|
||
"$B_1 = (\\mathbf{x}_1,\\mathbf{x}_2), \\cdots, B_5 =\n",
|
||
"(\\mathbf{x}_9,\\mathbf{x}_{10})$. Note that if you choose $M=1$ you\n",
|
||
"have only a single batch with all data points and on the other extreme,\n",
|
||
"you may choose $M=n$ resulting in a minibatch for each datapoint, i.e\n",
|
||
"$B_k = \\mathbf{x}_k$.\n",
|
||
"\n",
|
||
"The idea is now to approximate the gradient by replacing the sum over\n",
|
||
"all data points with a sum over the data points in one the minibatches\n",
|
||
"picked at random in each gradient descent step"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0df2146b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\nabla_{\\beta}\n",
|
||
"C(\\mathbf{\\beta}) = \\sum_{i=1}^n \\nabla_\\beta c_i(\\mathbf{x}_i,\n",
|
||
"\\mathbf{\\beta}) \\rightarrow \\sum_{i \\in B_k}^n \\nabla_\\beta\n",
|
||
"c_i(\\mathbf{x}_i, \\mathbf{\\beta}).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "890e6746",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## The gradient step\n",
|
||
"\n",
|
||
"Thus a gradient descent step now looks like"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b6e42059",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\beta_{j+1} = \\beta_j - \\gamma_j \\sum_{i \\in B_k}^n \\nabla_\\beta c_i(\\mathbf{x}_i,\n",
|
||
"\\mathbf{\\beta})\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9dd3abbf",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where $k$ is picked at random with equal\n",
|
||
"probability from $[1,n/M]$. An iteration over the number of\n",
|
||
"minibathces (n/M) is commonly referred to as an epoch. Thus it is\n",
|
||
"typical to choose a number of epochs and for each epoch iterate over\n",
|
||
"the number of minibatches, as exemplified in the code below."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "97279f92",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Simple example code"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 12,
|
||
"id": "cb0c6322",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"import numpy as np \n",
|
||
"\n",
|
||
"n = 100 #100 datapoints \n",
|
||
"M = 5 #size of each minibatch\n",
|
||
"m = int(n/M) #number of minibatches\n",
|
||
"n_epochs = 10 #number of epochs\n",
|
||
"\n",
|
||
"j = 0\n",
|
||
"for epoch in range(1,n_epochs+1):\n",
|
||
" for i in range(m):\n",
|
||
" k = np.random.randint(m) #Pick the k-th minibatch at random\n",
|
||
" #Compute the gradient using the data in minibatch Bk\n",
|
||
" #Compute new suggestion for \n",
|
||
" j += 1"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c0868aae",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Taking the gradient only on a subset of the data has two important\n",
|
||
"benefits. First, it introduces randomness which decreases the chance\n",
|
||
"that our opmization scheme gets stuck in a local minima. Second, if\n",
|
||
"the size of the minibatches are small relative to the number of\n",
|
||
"datapoints ($M < n$), the computation of the gradient is much\n",
|
||
"cheaper since we sum over the datapoints in the $k-th$ minibatch and not\n",
|
||
"all $n$ datapoints."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1e17bb0f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## When do we stop?\n",
|
||
"\n",
|
||
"A natural question is when do we stop the search for a new minimum?\n",
|
||
"One possibility is to compute the full gradient after a given number\n",
|
||
"of epochs and check if the norm of the gradient is smaller than some\n",
|
||
"threshold and stop if true. However, the condition that the gradient\n",
|
||
"is zero is valid also for local minima, so this would only tell us\n",
|
||
"that we are close to a local/global minimum. However, we could also\n",
|
||
"evaluate the cost function at this point, store the result and\n",
|
||
"continue the search. If the test kicks in at a later stage we can\n",
|
||
"compare the values of the cost function and keep the $\\beta$ that\n",
|
||
"gave the lowest value."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f050ca70",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Slightly different approach\n",
|
||
"\n",
|
||
"Another approach is to let the step length $\\gamma_j$ depend on the\n",
|
||
"number of epochs in such a way that it becomes very small after a\n",
|
||
"reasonable time such that we do not move at all. Such approaches are\n",
|
||
"also called scaling. There are many such ways to [scale the learning\n",
|
||
"rate](https://towardsdatascience.com/gradient-descent-the-learning-rate-and-the-importance-of-feature-scaling-6c0b416596e1)\n",
|
||
"and [discussions here](https://www.jmlr.org/papers/volume23/20-1258/20-1258.pdf). See\n",
|
||
"also\n",
|
||
"<https://towardsdatascience.com/learning-rate-schedules-and-adaptive-learning-rate-methods-for-deep-learning-2c8f433990d1>\n",
|
||
"for a discussion of different scaling functions for the learning rate."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6a900f78",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Time decay rate\n",
|
||
"\n",
|
||
"As an example, let $e = 0,1,2,3,\\cdots$ denote the current epoch and let $t_0, t_1 > 0$ be two fixed numbers. Furthermore, let $t = e \\cdot m + i$ where $m$ is the number of minibatches and $i=0,\\cdots,m-1$. Then the function $$\\gamma_j(t; t_0, t_1) = \\frac{t_0}{t+t_1} $$ goes to zero as the number of epochs gets large. I.e. we start with a step length $\\gamma_j (0; t_0, t_1) = t_0/t_1$ which decays in *time* $t$.\n",
|
||
"\n",
|
||
"In this way we can fix the number of epochs, compute $\\beta$ and\n",
|
||
"evaluate the cost function at the end. Repeating the computation will\n",
|
||
"give a different result since the scheme is random by design. Then we\n",
|
||
"pick the final $\\beta$ that gives the lowest value of the cost\n",
|
||
"function."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 13,
|
||
"id": "1324db42",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"import numpy as np \n",
|
||
"\n",
|
||
"def step_length(t,t0,t1):\n",
|
||
" return t0/(t+t1)\n",
|
||
"\n",
|
||
"n = 100 #100 datapoints \n",
|
||
"M = 5 #size of each minibatch\n",
|
||
"m = int(n/M) #number of minibatches\n",
|
||
"n_epochs = 500 #number of epochs\n",
|
||
"t0 = 1.0\n",
|
||
"t1 = 10\n",
|
||
"\n",
|
||
"gamma_j = t0/t1\n",
|
||
"j = 0\n",
|
||
"for epoch in range(1,n_epochs+1):\n",
|
||
" for i in range(m):\n",
|
||
" k = np.random.randint(m) #Pick the k-th minibatch at random\n",
|
||
" #Compute the gradient using the data in minibatch Bk\n",
|
||
" #Compute new suggestion for beta\n",
|
||
" t = epoch*m+i\n",
|
||
" gamma_j = step_length(t,t0,t1)\n",
|
||
" j += 1\n",
|
||
"\n",
|
||
"print(\"gamma_j after %d epochs: %g\" % (n_epochs,gamma_j))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0c365408",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Code with a Number of Minibatches which varies\n",
|
||
"\n",
|
||
"In the code here we vary the number of mini-batches."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 14,
|
||
"id": "79417e81",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Importing various packages\n",
|
||
"from math import exp, sqrt\n",
|
||
"from random import random, seed\n",
|
||
"import numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"\n",
|
||
"n = 100\n",
|
||
"x = 2*np.random.rand(n,1)\n",
|
||
"y = 4+3*x+np.random.randn(n,1)\n",
|
||
"\n",
|
||
"X = np.c_[np.ones((n,1)), x]\n",
|
||
"XT_X = X.T @ X\n",
|
||
"theta_linreg = np.linalg.inv(X.T @ X) @ (X.T @ y)\n",
|
||
"print(\"Own inversion\")\n",
|
||
"print(theta_linreg)\n",
|
||
"# Hessian matrix\n",
|
||
"H = (2.0/n)* XT_X\n",
|
||
"EigValues, EigVectors = np.linalg.eig(H)\n",
|
||
"print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
|
||
"\n",
|
||
"theta = np.random.randn(2,1)\n",
|
||
"eta = 1.0/np.max(EigValues)\n",
|
||
"Niterations = 1000\n",
|
||
"\n",
|
||
"\n",
|
||
"for iter in range(Niterations):\n",
|
||
" gradients = 2.0/n*X.T @ ((X @ theta)-y)\n",
|
||
" theta -= eta*gradients\n",
|
||
"print(\"theta from own gd\")\n",
|
||
"print(theta)\n",
|
||
"\n",
|
||
"xnew = np.array([[0],[2]])\n",
|
||
"Xnew = np.c_[np.ones((2,1)), xnew]\n",
|
||
"ypredict = Xnew.dot(theta)\n",
|
||
"ypredict2 = Xnew.dot(theta_linreg)\n",
|
||
"\n",
|
||
"n_epochs = 50\n",
|
||
"M = 5 #size of each minibatch\n",
|
||
"m = int(n/M) #number of minibatches\n",
|
||
"t0, t1 = 5, 50\n",
|
||
"\n",
|
||
"def learning_schedule(t):\n",
|
||
" return t0/(t+t1)\n",
|
||
"\n",
|
||
"theta = np.random.randn(2,1)\n",
|
||
"\n",
|
||
"for epoch in range(n_epochs):\n",
|
||
"# Can you figure out a better way of setting up the contributions to each batch?\n",
|
||
" for i in range(m):\n",
|
||
" random_index = M*np.random.randint(m)\n",
|
||
" xi = X[random_index:random_index+M]\n",
|
||
" yi = y[random_index:random_index+M]\n",
|
||
" gradients = (2.0/M)* xi.T @ ((xi @ theta)-yi)\n",
|
||
" eta = learning_schedule(epoch*m+i)\n",
|
||
" theta = theta - eta*gradients\n",
|
||
"print(\"theta from own sdg\")\n",
|
||
"print(theta)\n",
|
||
"\n",
|
||
"plt.plot(xnew, ypredict, \"r-\")\n",
|
||
"plt.plot(xnew, ypredict2, \"b-\")\n",
|
||
"plt.plot(x, y ,'ro')\n",
|
||
"plt.axis([0,2.0,0, 15.0])\n",
|
||
"plt.xlabel(r'$x$')\n",
|
||
"plt.ylabel(r'$y$')\n",
|
||
"plt.title(r'Random numbers ')\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "dd16fd67",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Replace or not\n",
|
||
"\n",
|
||
"In the above code, we have use replacement in setting up the\n",
|
||
"mini-batches. The discussion\n",
|
||
"[here](https://sebastianraschka.com/faq/docs/sgd-methods.html) may be\n",
|
||
"useful."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "2bbf7fbd",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Momentum based GD\n",
|
||
"\n",
|
||
"The stochastic gradient descent (SGD) is almost always used with a\n",
|
||
"*momentum* or inertia term that serves as a memory of the direction we\n",
|
||
"are moving in parameter space. This is typically implemented as\n",
|
||
"follows"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d4aa4448",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathbf{v}_{t}=\\gamma \\mathbf{v}_{t-1}+\\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t) \\nonumber\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "fdcd258f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto1\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation} \n",
|
||
"\\boldsymbol{\\theta}_{t+1}= \\boldsymbol{\\theta}_t -\\mathbf{v}_{t},\n",
|
||
"\\label{_auto1} \\tag{2}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "52ec5bfb",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where we have introduced a momentum parameter $\\gamma$, with\n",
|
||
"$0\\le\\gamma\\le 1$, and for brevity we dropped the explicit notation to\n",
|
||
"indicate the gradient is to be taken over a different mini-batch at\n",
|
||
"each step. We call this algorithm gradient descent with momentum\n",
|
||
"(GDM). From these equations, it is clear that $\\mathbf{v}_t$ is a\n",
|
||
"running average of recently encountered gradients and\n",
|
||
"$(1-\\gamma)^{-1}$ sets the characteristic time scale for the memory\n",
|
||
"used in the averaging procedure. Consistent with this, when\n",
|
||
"$\\gamma=0$, this just reduces down to ordinary SGD as discussed\n",
|
||
"earlier. An equivalent way of writing the updates is"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "38004062",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\Delta \\boldsymbol{\\theta}_{t+1} = \\gamma \\Delta \\boldsymbol{\\theta}_t -\\ \\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9d07c567",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where we have defined $\\Delta \\boldsymbol{\\theta}_{t}= \\boldsymbol{\\theta}_t-\\boldsymbol{\\theta}_{t-1}$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4dbba8bc",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## More on momentum based approaches\n",
|
||
"\n",
|
||
"Let us try to get more intuition from these equations. It is helpful\n",
|
||
"to consider a simple physical analogy with a particle of mass $m$\n",
|
||
"moving in a viscous medium with drag coefficient $\\mu$ and potential\n",
|
||
"$E(\\mathbf{w})$. If we denote the particle's position by $\\mathbf{w}$,\n",
|
||
"then its motion is described by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "dab76529",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"m {d^2 \\mathbf{w} \\over dt^2} + \\mu {d \\mathbf{w} \\over dt }= -\\nabla_w E(\\mathbf{w}).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6e049d15",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"We can discretize this equation in the usual way to get"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "5079f465",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"m { \\mathbf{w}_{t+\\Delta t}-2 \\mathbf{w}_{t} +\\mathbf{w}_{t-\\Delta t} \\over (\\Delta t)^2}+\\mu {\\mathbf{w}_{t+\\Delta t}- \\mathbf{w}_{t} \\over \\Delta t} = -\\nabla_w E(\\mathbf{w}).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "51c2ed45",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Rearranging this equation, we can rewrite this as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7e8f7b16",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\Delta \\mathbf{w}_{t +\\Delta t}= - { (\\Delta t)^2 \\over m +\\mu \\Delta t} \\nabla_w E(\\mathbf{w})+ {m \\over m +\\mu \\Delta t} \\Delta \\mathbf{w}_t.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ae0505aa",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Momentum parameter\n",
|
||
"\n",
|
||
"Notice that this equation is identical to previous one if we identify\n",
|
||
"the position of the particle, $\\mathbf{w}$, with the parameters\n",
|
||
"$\\boldsymbol{\\theta}$. This allows us to identify the momentum\n",
|
||
"parameter and learning rate with the mass of the particle and the\n",
|
||
"viscous drag as:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9e7f520b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\gamma= {m \\over m +\\mu \\Delta t }, \\qquad \\eta = {(\\Delta t)^2 \\over m +\\mu \\Delta t}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "5c0aa1f6",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Thus, as the name suggests, the momentum parameter is proportional to\n",
|
||
"the mass of the particle and effectively provides inertia.\n",
|
||
"Furthermore, in the large viscosity/small learning rate limit, our\n",
|
||
"memory time scales as $(1-\\gamma)^{-1} \\approx m/(\\mu \\Delta t)$.\n",
|
||
"\n",
|
||
"Why is momentum useful? SGD momentum helps the gradient descent\n",
|
||
"algorithm gain speed in directions with persistent but small gradients\n",
|
||
"even in the presence of stochasticity, while suppressing oscillations\n",
|
||
"in high-curvature directions. This becomes especially important in\n",
|
||
"situations where the landscape is shallow and flat in some directions\n",
|
||
"and narrow and steep in others. It has been argued that first-order\n",
|
||
"methods (with appropriate initial conditions) can perform comparable\n",
|
||
"to more expensive second order methods, especially in the context of\n",
|
||
"complex deep learning models.\n",
|
||
"\n",
|
||
"These beneficial properties of momentum can sometimes become even more\n",
|
||
"pronounced by using a slight modification of the classical momentum\n",
|
||
"algorithm called Nesterov Accelerated Gradient (NAG).\n",
|
||
"\n",
|
||
"In the NAG algorithm, rather than calculating the gradient at the\n",
|
||
"current parameters, $\\nabla_\\theta E(\\boldsymbol{\\theta}_t)$, one\n",
|
||
"calculates the gradient at the expected value of the parameters given\n",
|
||
"our current momentum, $\\nabla_\\theta E(\\boldsymbol{\\theta}_t +\\gamma\n",
|
||
"\\mathbf{v}_{t-1})$. This yields the NAG update rule"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "991c2c15",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathbf{v}_{t}=\\gamma \\mathbf{v}_{t-1}+\\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t +\\gamma \\mathbf{v}_{t-1}) \\nonumber\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c643afb5",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto2\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation} \n",
|
||
"\\boldsymbol{\\theta}_{t+1}= \\boldsymbol{\\theta}_t -\\mathbf{v}_{t}.\n",
|
||
"\\label{_auto2} \\tag{3}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ac4a060d",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"One of the major advantages of NAG is that it allows for the use of a larger learning rate than GDM for the same choice of $\\gamma$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "37584d4d",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Second moment of the gradient\n",
|
||
"\n",
|
||
"In stochastic gradient descent, with and without momentum, we still\n",
|
||
"have to specify a schedule for tuning the learning rates $\\eta_t$\n",
|
||
"as a function of time. As discussed in the context of Newton's\n",
|
||
"method, this presents a number of dilemmas. The learning rate is\n",
|
||
"limited by the steepest direction which can change depending on the\n",
|
||
"current position in the landscape. To circumvent this problem, ideally\n",
|
||
"our algorithm would keep track of curvature and take large steps in\n",
|
||
"shallow, flat directions and small steps in steep, narrow directions.\n",
|
||
"Second-order methods accomplish this by calculating or approximating\n",
|
||
"the Hessian and normalizing the learning rate by the\n",
|
||
"curvature. However, this is very computationally expensive for\n",
|
||
"extremely large models. Ideally, we would like to be able to\n",
|
||
"adaptively change the step size to match the landscape without paying\n",
|
||
"the steep computational price of calculating or approximating\n",
|
||
"Hessians.\n",
|
||
"\n",
|
||
"Recently, a number of methods have been introduced that accomplish\n",
|
||
"this by tracking not only the gradient, but also the second moment of\n",
|
||
"the gradient. These methods include AdaGrad, AdaDelta, Root Mean Squared Propagation (RMS-Prop), and\n",
|
||
"[ADAM](https://arxiv.org/abs/1412.6980)."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0e9c907f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## RMS prop\n",
|
||
"\n",
|
||
"In RMS prop, in addition to keeping a running average of the first\n",
|
||
"moment of the gradient, we also keep track of the second moment\n",
|
||
"denoted by $\\mathbf{s}_t=\\mathbb{E}[\\mathbf{g}_t^2]$. The update rule\n",
|
||
"for RMS prop is given by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "cb4567f1",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto3\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
"\\mathbf{g}_t = \\nabla_\\theta E(\\boldsymbol{\\theta}) \n",
|
||
"\\label{_auto3} \\tag{4}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "71805d3d",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathbf{s}_t =\\beta \\mathbf{s}_{t-1} +(1-\\beta)\\mathbf{g}_t^2 \\nonumber\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "09794996",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{\\theta}_{t+1}=\\boldsymbol{\\theta}_t - \\eta_t { \\mathbf{g}_t \\over \\sqrt{\\mathbf{s}_t +\\epsilon}}, \\nonumber\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "aeb48f66",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where $\\beta$ controls the averaging time of the second moment and is\n",
|
||
"typically taken to be about $\\beta=0.9$, $\\eta_t$ is a learning rate\n",
|
||
"typically chosen to be $10^{-3}$, and $\\epsilon\\sim 10^{-8} $ is a\n",
|
||
"small regularization constant to prevent divergences. Multiplication\n",
|
||
"and division by vectors is understood as an element-wise operation. It\n",
|
||
"is clear from this formula that the learning rate is reduced in\n",
|
||
"directions where the norm of the gradient is consistently large. This\n",
|
||
"greatly speeds up the convergence by allowing us to use a larger\n",
|
||
"learning rate for flat directions."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "68e08134",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## [ADAM optimizer](https://arxiv.org/abs/1412.6980)\n",
|
||
"\n",
|
||
"A related algorithm is the ADAM optimizer. In\n",
|
||
"[ADAM](https://arxiv.org/abs/1412.6980), we keep a running average of\n",
|
||
"both the first and second moment of the gradient and use this\n",
|
||
"information to adaptively change the learning rate for different\n",
|
||
"parameters. The method isefficient when working with large\n",
|
||
"problems involving lots data and/or parameters. It is a combination of the\n",
|
||
"gradient descent with momentum algorithm and the RMSprop algorithm\n",
|
||
"discussed above.\n",
|
||
"\n",
|
||
"In addition to keeping a running average of the first and\n",
|
||
"second moments of the gradient\n",
|
||
"(i.e. $\\mathbf{m}_t=\\mathbb{E}[\\mathbf{g}_t]$ and\n",
|
||
"$\\mathbf{s}_t=\\mathbb{E}[\\mathbf{g}^2_t]$, respectively), ADAM\n",
|
||
"performs an additional bias correction to account for the fact that we\n",
|
||
"are estimating the first two moments of the gradient using a running\n",
|
||
"average (denoted by the hats in the update rule below). The update\n",
|
||
"rule for ADAM is given by (where multiplication and division are once\n",
|
||
"again understood to be element-wise operations below)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "69308397",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto4\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
"\\mathbf{g}_t = \\nabla_\\theta E(\\boldsymbol{\\theta}) \n",
|
||
"\\label{_auto4} \\tag{5}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d23ab794",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathbf{m}_t = \\beta_1 \\mathbf{m}_{t-1} + (1-\\beta_1) \\mathbf{g}_t \\nonumber\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c4cef70b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathbf{s}_t =\\beta_2 \\mathbf{s}_{t-1} +(1-\\beta_2)\\mathbf{g}_t^2 \\nonumber\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6aebd1b5",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{\\mathbf{m}}_t={\\mathbf{m}_t \\over 1-\\beta_1^t} \\nonumber\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c43fe267",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{\\mathbf{s}}_t ={\\mathbf{s}_t \\over1-\\beta_2^t} \\nonumber\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9ae56692",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{\\theta}_{t+1}=\\boldsymbol{\\theta}_t - \\eta_t { \\boldsymbol{\\mathbf{m}}_t \\over \\sqrt{\\boldsymbol{\\mathbf{s}}_t} +\\epsilon}, \\nonumber\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "784ba00e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto5\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation} \n",
|
||
"\\label{_auto5} \\tag{6}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a187dfb2",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where $\\beta_1$ and $\\beta_2$ set the memory lifetime of the first and\n",
|
||
"second moment and are typically taken to be $0.9$ and $0.99$\n",
|
||
"respectively, and $\\eta$ and $\\epsilon$ are identical to RMSprop.\n",
|
||
"\n",
|
||
"Like in RMSprop, the effective step size of a parameter depends on the\n",
|
||
"magnitude of its gradient squared. To understand this better, let us\n",
|
||
"rewrite this expression in terms of the variance\n",
|
||
"$\\boldsymbol{\\sigma}_t^2 = \\boldsymbol{\\mathbf{s}}_t -\n",
|
||
"(\\boldsymbol{\\mathbf{m}}_t)^2$. Consider a single parameter $\\theta_t$. The\n",
|
||
"update rule for this parameter is given by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "832cc99c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\Delta \\theta_{t+1}= -\\eta_t { \\boldsymbol{m}_t \\over \\sqrt{\\sigma_t^2 + m_t^2 }+\\epsilon}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b1a24342",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Algorithms and codes for Adagrad, RMSprop and Adam\n",
|
||
"\n",
|
||
"The algorithms we have implemented are well described in the text by [Goodfellow, Bengio and Courville, chapter 8](https://www.deeplearningbook.org/contents/optimization.html).\n",
|
||
"\n",
|
||
"The codes which implement these algorithms are discussed after our presentation of automatic differentiation."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8a97509f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Practical tips\n",
|
||
"\n",
|
||
"* **Randomize the data when making mini-batches**. It is always important to randomly shuffle the data when forming mini-batches. Otherwise, the gradient descent method can fit spurious correlations resulting from the order in which data is presented.\n",
|
||
"\n",
|
||
"* **Transform your inputs**. Learning becomes difficult when our landscape has a mixture of steep and flat directions. One simple trick for minimizing these situations is to standardize the data by subtracting the mean and normalizing the variance of input variables. Whenever possible, also decorrelate the inputs. To understand why this is helpful, consider the case of linear regression. It is easy to show that for the squared error cost function, the Hessian of the cost function is just the correlation matrix between the inputs. Thus, by standardizing the inputs, we are ensuring that the landscape looks homogeneous in all directions in parameter space. Since most deep networks can be viewed as linear transformations followed by a non-linearity at each layer, we expect this intuition to hold beyond the linear case.\n",
|
||
"\n",
|
||
"* **Monitor the out-of-sample performance.** Always monitor the performance of your model on a validation set (a small portion of the training data that is held out of the training process to serve as a proxy for the test set. If the validation error starts increasing, then the model is beginning to overfit. Terminate the learning process. This *early stopping* significantly improves performance in many settings.\n",
|
||
"\n",
|
||
"* **Adaptive optimization methods don't always have good generalization.** Recent studies have shown that adaptive methods such as ADAM, RMSPorp, and AdaGrad tend to have poor generalization compared to SGD or SGD with momentum, particularly in the high-dimensional limit (i.e. the number of parameters exceeds the number of data points). Although it is not clear at this stage why these methods perform so well in training deep neural networks, simpler procedures like properly-tuned SGD may work as well or better in these applications.\n",
|
||
"\n",
|
||
"Geron's text, see chapter 11, has several interesting discussions."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "631a2aa8",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Automatic differentiation\n",
|
||
"\n",
|
||
"[Automatic differentiation (AD)](https://en.wikipedia.org/wiki/Automatic_differentiation), \n",
|
||
"also called algorithmic\n",
|
||
"differentiation or computational differentiation,is a set of\n",
|
||
"techniques to numerically evaluate the derivative of a function\n",
|
||
"specified by a computer program. AD exploits the fact that every\n",
|
||
"computer program, no matter how complicated, executes a sequence of\n",
|
||
"elementary arithmetic operations (addition, subtraction,\n",
|
||
"multiplication, division, etc.) and elementary functions (exp, log,\n",
|
||
"sin, cos, etc.). By applying the chain rule repeatedly to these\n",
|
||
"operations, derivatives of arbitrary order can be computed\n",
|
||
"automatically, accurately to working precision, and using at most a\n",
|
||
"small constant factor more arithmetic operations than the original\n",
|
||
"program.\n",
|
||
"\n",
|
||
"Automatic differentiation is neither:\n",
|
||
"\n",
|
||
"* Symbolic differentiation, nor\n",
|
||
"\n",
|
||
"* Numerical differentiation (the method of finite differences).\n",
|
||
"\n",
|
||
"Symbolic differentiation can lead to inefficient code and faces the\n",
|
||
"difficulty of converting a computer program into a single expression,\n",
|
||
"while numerical differentiation can introduce round-off errors in the\n",
|
||
"discretization process and cancellation\n",
|
||
"\n",
|
||
"Python has tools for so-called **automatic differentiation**.\n",
|
||
"Consider the following example"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "472b23f2",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"f(x) = \\sin\\left(2\\pi x + x^2\\right)\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1c91c90f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which has the following derivative"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a85c6aab",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"f'(x) = \\cos\\left(2\\pi x + x^2\\right)\\left(2\\pi + 2x\\right)\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "89a0bdbb",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Using **autograd** we have"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 15,
|
||
"id": "6fe48a50",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"import autograd.numpy as np\n",
|
||
"\n",
|
||
"# To do elementwise differentiation:\n",
|
||
"from autograd import elementwise_grad as egrad \n",
|
||
"\n",
|
||
"# To plot:\n",
|
||
"import matplotlib.pyplot as plt \n",
|
||
"\n",
|
||
"\n",
|
||
"def f(x):\n",
|
||
" return np.sin(2*np.pi*x + x**2)\n",
|
||
"\n",
|
||
"def f_grad_analytic(x):\n",
|
||
" return np.cos(2*np.pi*x + x**2)*(2*np.pi + 2*x)\n",
|
||
"\n",
|
||
"# Do the comparison:\n",
|
||
"x = np.linspace(0,1,1000)\n",
|
||
"\n",
|
||
"f_grad = egrad(f)\n",
|
||
"\n",
|
||
"computed = f_grad(x)\n",
|
||
"analytic = f_grad_analytic(x)\n",
|
||
"\n",
|
||
"plt.title('Derivative computed from Autograd compared with the analytical derivative')\n",
|
||
"plt.plot(x,computed,label='autograd')\n",
|
||
"plt.plot(x,analytic,label='analytic')\n",
|
||
"\n",
|
||
"plt.xlabel('x')\n",
|
||
"plt.ylabel('y')\n",
|
||
"plt.legend()\n",
|
||
"\n",
|
||
"plt.show()\n",
|
||
"\n",
|
||
"print(\"The max absolute difference is: %g\"%(np.max(np.abs(computed - analytic))))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "cab7d753",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Using autograd\n",
|
||
"\n",
|
||
"Here we\n",
|
||
"experiment with what kind of functions Autograd is capable\n",
|
||
"of finding the gradient of. The following Python functions are just\n",
|
||
"meant to illustrate what Autograd can do, but please feel free to\n",
|
||
"experiment with other, possibly more complicated, functions as well."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 16,
|
||
"id": "ca4d6b32",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"import autograd.numpy as np\n",
|
||
"from autograd import grad\n",
|
||
"\n",
|
||
"def f1(x):\n",
|
||
" return x**3 + 1\n",
|
||
"\n",
|
||
"f1_grad = grad(f1)\n",
|
||
"\n",
|
||
"# Remember to send in float as argument to the computed gradient from Autograd!\n",
|
||
"a = 1.0\n",
|
||
"\n",
|
||
"# See the evaluated gradient at a using autograd:\n",
|
||
"print(\"The gradient of f1 evaluated at a = %g using autograd is: %g\"%(a,f1_grad(a)))\n",
|
||
"\n",
|
||
"# Compare with the analytical derivative, that is f1'(x) = 3*x**2 \n",
|
||
"grad_analytical = 3*a**2\n",
|
||
"print(\"The gradient of f1 evaluated at a = %g by finding the analytic expression is: %g\"%(a,grad_analytical))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4a748513",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Autograd with more complicated functions\n",
|
||
"\n",
|
||
"To differentiate with respect to two (or more) arguments of a Python\n",
|
||
"function, Autograd need to know at which variable the function if\n",
|
||
"being differentiated with respect to."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 17,
|
||
"id": "f235cd43",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"import autograd.numpy as np\n",
|
||
"from autograd import grad\n",
|
||
"def f2(x1,x2):\n",
|
||
" return 3*x1**3 + x2*(x1 - 5) + 1\n",
|
||
"\n",
|
||
"# By sending the argument 0, Autograd will compute the derivative w.r.t the first variable, in this case x1\n",
|
||
"f2_grad_x1 = grad(f2,0)\n",
|
||
"\n",
|
||
"# ... and differentiate w.r.t x2 by sending 1 as an additional arugment to grad\n",
|
||
"f2_grad_x2 = grad(f2,1)\n",
|
||
"\n",
|
||
"x1 = 1.0\n",
|
||
"x2 = 3.0 \n",
|
||
"\n",
|
||
"print(\"Evaluating at x1 = %g, x2 = %g\"%(x1,x2))\n",
|
||
"print(\"-\"*30)\n",
|
||
"\n",
|
||
"# Compare with the analytical derivatives:\n",
|
||
"\n",
|
||
"# Derivative of f2 w.r.t x1 is: 9*x1**2 + x2:\n",
|
||
"f2_grad_x1_analytical = 9*x1**2 + x2\n",
|
||
"\n",
|
||
"# Derivative of f2 w.r.t x2 is: x1 - 5:\n",
|
||
"f2_grad_x2_analytical = x1 - 5\n",
|
||
"\n",
|
||
"# See the evaluated derivations:\n",
|
||
"print(\"The derivative of f2 w.r.t x1: %g\"%( f2_grad_x1(x1,x2) ))\n",
|
||
"print(\"The analytical derivative of f2 w.r.t x1: %g\"%( f2_grad_x1(x1,x2) ))\n",
|
||
"\n",
|
||
"print()\n",
|
||
"\n",
|
||
"print(\"The derivative of f2 w.r.t x2: %g\"%( f2_grad_x2(x1,x2) ))\n",
|
||
"print(\"The analytical derivative of f2 w.r.t x2: %g\"%( f2_grad_x2(x1,x2) ))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "5d8df033",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Note that the grad function will not produce the true gradient of the function. The true gradient of a function with two or more variables will produce a vector, where each element is the function differentiated w.r.t a variable."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "2f7de144",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## More complicated functions using the elements of their arguments directly"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 18,
|
||
"id": "a2ed8fd6",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"import autograd.numpy as np\n",
|
||
"from autograd import grad\n",
|
||
"def f3(x): # Assumes x is an array of length 5 or higher\n",
|
||
" return 2*x[0] + 3*x[1] + 5*x[2] + 7*x[3] + 11*x[4]**2\n",
|
||
"\n",
|
||
"f3_grad = grad(f3)\n",
|
||
"\n",
|
||
"x = np.linspace(0,4,5)\n",
|
||
"\n",
|
||
"# Print the computed gradient:\n",
|
||
"print(\"The computed gradient of f3 is: \", f3_grad(x))\n",
|
||
"\n",
|
||
"# The analytical gradient is: (2, 3, 5, 7, 22*x[4])\n",
|
||
"f3_grad_analytical = np.array([2, 3, 5, 7, 22*x[4]])\n",
|
||
"\n",
|
||
"# Print the analytical gradient:\n",
|
||
"print(\"The analytical gradient of f3 is: \", f3_grad_analytical)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1f633736",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Note that in this case, when sending an array as input argument, the\n",
|
||
"output from Autograd is another array. This is the true gradient of\n",
|
||
"the function, as opposed to the function in the previous example. By\n",
|
||
"using arrays to represent the variables, the output from Autograd\n",
|
||
"might be easier to work with, as the output is closer to what one\n",
|
||
"could expect form a gradient-evaluting function."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a73225d4",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Functions using mathematical functions from Numpy"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 19,
|
||
"id": "39059d20",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"import autograd.numpy as np\n",
|
||
"from autograd import grad\n",
|
||
"def f4(x):\n",
|
||
" return np.sqrt(1+x**2) + np.exp(x) + np.sin(2*np.pi*x)\n",
|
||
"\n",
|
||
"f4_grad = grad(f4)\n",
|
||
"\n",
|
||
"x = 2.7\n",
|
||
"\n",
|
||
"# Print the computed derivative:\n",
|
||
"print(\"The computed derivative of f4 at x = %g is: %g\"%(x,f4_grad(x)))\n",
|
||
"\n",
|
||
"# The analytical derivative is: x/sqrt(1 + x**2) + exp(x) + cos(2*pi*x)*2*pi\n",
|
||
"f4_grad_analytical = x/np.sqrt(1 + x**2) + np.exp(x) + np.cos(2*np.pi*x)*2*np.pi\n",
|
||
"\n",
|
||
"# Print the analytical gradient:\n",
|
||
"print(\"The analytical gradient of f4 at x = %g is: %g\"%(x,f4_grad_analytical))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d147b69e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## More autograd"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 20,
|
||
"id": "90a2d143",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"import autograd.numpy as np\n",
|
||
"from autograd import grad\n",
|
||
"def f5(x):\n",
|
||
" if x >= 0:\n",
|
||
" return x**2\n",
|
||
" else:\n",
|
||
" return -3*x + 1\n",
|
||
"\n",
|
||
"f5_grad = grad(f5)\n",
|
||
"\n",
|
||
"x = 2.7\n",
|
||
"\n",
|
||
"# Print the computed derivative:\n",
|
||
"print(\"The computed derivative of f5 at x = %g is: %g\"%(x,f5_grad(x)))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6655faec",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## And with loops"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 21,
|
||
"id": "639ea2a9",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"import autograd.numpy as np\n",
|
||
"from autograd import grad\n",
|
||
"def f6_for(x):\n",
|
||
" val = 0\n",
|
||
" for i in range(10):\n",
|
||
" val = val + x**i\n",
|
||
" return val\n",
|
||
"\n",
|
||
"def f6_while(x):\n",
|
||
" val = 0\n",
|
||
" i = 0\n",
|
||
" while i < 10:\n",
|
||
" val = val + x**i\n",
|
||
" i = i + 1\n",
|
||
" return val\n",
|
||
"\n",
|
||
"f6_for_grad = grad(f6_for)\n",
|
||
"f6_while_grad = grad(f6_while)\n",
|
||
"\n",
|
||
"x = 0.5\n",
|
||
"\n",
|
||
"# Print the computed derivaties of f6_for and f6_while\n",
|
||
"print(\"The computed derivative of f6_for at x = %g is: %g\"%(x,f6_for_grad(x)))\n",
|
||
"print(\"The computed derivative of f6_while at x = %g is: %g\"%(x,f6_while_grad(x)))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 22,
|
||
"id": "a53c5633",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"import autograd.numpy as np\n",
|
||
"from autograd import grad\n",
|
||
"# Both of the functions are implementation of the sum: sum(x**i) for i = 0, ..., 9\n",
|
||
"# The analytical derivative is: sum(i*x**(i-1)) \n",
|
||
"f6_grad_analytical = 0\n",
|
||
"for i in range(10):\n",
|
||
" f6_grad_analytical += i*x**(i-1)\n",
|
||
"\n",
|
||
"print(\"The analytical derivative of f6 at x = %g is: %g\"%(x,f6_grad_analytical))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "be5e41d4",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Using recursion"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 23,
|
||
"id": "786e19d0",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"import autograd.numpy as np\n",
|
||
"from autograd import grad\n",
|
||
"\n",
|
||
"def f7(n): # Assume that n is an integer\n",
|
||
" if n == 1 or n == 0:\n",
|
||
" return 1\n",
|
||
" else:\n",
|
||
" return n*f7(n-1)\n",
|
||
"\n",
|
||
"f7_grad = grad(f7)\n",
|
||
"\n",
|
||
"n = 2.0\n",
|
||
"\n",
|
||
"print(\"The computed derivative of f7 at n = %d is: %g\"%(n,f7_grad(n)))\n",
|
||
"\n",
|
||
"# The function f7 is an implementation of the factorial of n.\n",
|
||
"# By using the product rule, one can find that the derivative is:\n",
|
||
"\n",
|
||
"f7_grad_analytical = 0\n",
|
||
"for i in range(int(n)-1):\n",
|
||
" tmp = 1\n",
|
||
" for k in range(int(n)-1):\n",
|
||
" if k != i:\n",
|
||
" tmp *= (n - k)\n",
|
||
" f7_grad_analytical += tmp\n",
|
||
"\n",
|
||
"print(\"The analytical derivative of f7 at n = %d is: %g\"%(n,f7_grad_analytical))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "114e7e25",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Note that if n is equal to zero or one, Autograd will give an error message. This message appears when the output is independent on input."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "24c8ffa6",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Unsupported functions\n",
|
||
"Autograd supports many features. However, there are some functions that is not supported (yet) by Autograd.\n",
|
||
"\n",
|
||
"Assigning a value to the variable being differentiated with respect to"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 24,
|
||
"id": "59f521ac",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"import autograd.numpy as np\n",
|
||
"from autograd import grad\n",
|
||
"def f8(x): # Assume x is an array\n",
|
||
" x[2] = 3\n",
|
||
" return x*2\n",
|
||
"\n",
|
||
"f8_grad = grad(f8)\n",
|
||
"\n",
|
||
"x = 8.4\n",
|
||
"\n",
|
||
"print(\"The derivative of f8 is:\",f8_grad(x))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "686c34bb",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Here, Autograd tells us that an 'ArrayBox' does not support item assignment. The item assignment is done when the program tries to assign x[2] to the value 3. However, Autograd has implemented the computation of the derivative such that this assignment is not possible."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9b4cc4f3",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## The syntax a.dot(b) when finding the dot product"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 25,
|
||
"id": "dea954af",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"import autograd.numpy as np\n",
|
||
"from autograd import grad\n",
|
||
"def f9(a): # Assume a is an array with 2 elements\n",
|
||
" b = np.array([1.0,2.0])\n",
|
||
" return a.dot(b)\n",
|
||
"\n",
|
||
"f9_grad = grad(f9)\n",
|
||
"\n",
|
||
"x = np.array([1.0,0.0])\n",
|
||
"\n",
|
||
"print(\"The derivative of f9 is:\",f9_grad(x))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9732d039",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Here we are told that the 'dot' function does not belong to Autograd's\n",
|
||
"version of a Numpy array. To overcome this, an alternative syntax\n",
|
||
"which also computed the dot product can be used:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 26,
|
||
"id": "f580c6a1",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"import autograd.numpy as np\n",
|
||
"from autograd import grad\n",
|
||
"def f9_alternative(x): # Assume a is an array with 2 elements\n",
|
||
" b = np.array([1.0,2.0])\n",
|
||
" return np.dot(x,b) # The same as x_1*b_1 + x_2*b_2\n",
|
||
"\n",
|
||
"f9_alternative_grad = grad(f9_alternative)\n",
|
||
"\n",
|
||
"x = np.array([3.0,0.0])\n",
|
||
"\n",
|
||
"print(\"The gradient of f9 is:\",f9_alternative_grad(x))\n",
|
||
"\n",
|
||
"# The analytical gradient of the dot product of vectors x and b with two elements (x_1,x_2) and (b_1, b_2) respectively\n",
|
||
"# w.r.t x is (b_1, b_2)."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d8714004",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Recommended to avoid\n",
|
||
"The documentation recommends to avoid inplace operations such as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 27,
|
||
"id": "e56cbb47",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"a += b\n",
|
||
"a -= b\n",
|
||
"a*= b\n",
|
||
"a /=b"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "fac1a7da",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Using Autograd with OLS\n",
|
||
"\n",
|
||
"We conclude the part on optmization by showing how we can make codes\n",
|
||
"for linear regression and logistic regression using **autograd**. The\n",
|
||
"first example shows results with ordinary leats squares."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 28,
|
||
"id": "c4c5b9c0",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Using Autograd to calculate gradients for OLS\n",
|
||
"from random import random, seed\n",
|
||
"import numpy as np\n",
|
||
"import autograd.numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from autograd import grad\n",
|
||
"\n",
|
||
"def CostOLS(beta):\n",
|
||
" return (1.0/n)*np.sum((y-X @ beta)**2)\n",
|
||
"\n",
|
||
"n = 100\n",
|
||
"x = 2*np.random.rand(n,1)\n",
|
||
"y = 4+3*x+np.random.randn(n,1)\n",
|
||
"\n",
|
||
"X = np.c_[np.ones((n,1)), x]\n",
|
||
"XT_X = X.T @ X\n",
|
||
"theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
|
||
"print(\"Own inversion\")\n",
|
||
"print(theta_linreg)\n",
|
||
"# Hessian matrix\n",
|
||
"H = (2.0/n)* XT_X\n",
|
||
"EigValues, EigVectors = np.linalg.eig(H)\n",
|
||
"print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
|
||
"\n",
|
||
"theta = np.random.randn(2,1)\n",
|
||
"eta = 1.0/np.max(EigValues)\n",
|
||
"Niterations = 1000\n",
|
||
"# define the gradient\n",
|
||
"training_gradient = grad(CostOLS)\n",
|
||
"\n",
|
||
"for iter in range(Niterations):\n",
|
||
" gradients = training_gradient(theta)\n",
|
||
" theta -= eta*gradients\n",
|
||
"print(\"theta from own gd\")\n",
|
||
"print(theta)\n",
|
||
"\n",
|
||
"xnew = np.array([[0],[2]])\n",
|
||
"Xnew = np.c_[np.ones((2,1)), xnew]\n",
|
||
"ypredict = Xnew.dot(theta)\n",
|
||
"ypredict2 = Xnew.dot(theta_linreg)\n",
|
||
"\n",
|
||
"plt.plot(xnew, ypredict, \"r-\")\n",
|
||
"plt.plot(xnew, ypredict2, \"b-\")\n",
|
||
"plt.plot(x, y ,'ro')\n",
|
||
"plt.axis([0,2.0,0, 15.0])\n",
|
||
"plt.xlabel(r'$x$')\n",
|
||
"plt.ylabel(r'$y$')\n",
|
||
"plt.title(r'Random numbers ')\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b16d7700",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Same code but now with momentum gradient descent"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 29,
|
||
"id": "7453efe5",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Using Autograd to calculate gradients for OLS\n",
|
||
"from random import random, seed\n",
|
||
"import numpy as np\n",
|
||
"import autograd.numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from autograd import grad\n",
|
||
"\n",
|
||
"def CostOLS(beta):\n",
|
||
" return (1.0/n)*np.sum((y-X @ beta)**2)\n",
|
||
"\n",
|
||
"n = 100\n",
|
||
"x = 2*np.random.rand(n,1)\n",
|
||
"y = 4+3*x#+np.random.randn(n,1)\n",
|
||
"\n",
|
||
"X = np.c_[np.ones((n,1)), x]\n",
|
||
"XT_X = X.T @ X\n",
|
||
"theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
|
||
"print(\"Own inversion\")\n",
|
||
"print(theta_linreg)\n",
|
||
"# Hessian matrix\n",
|
||
"H = (2.0/n)* XT_X\n",
|
||
"EigValues, EigVectors = np.linalg.eig(H)\n",
|
||
"print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
|
||
"\n",
|
||
"theta = np.random.randn(2,1)\n",
|
||
"eta = 1.0/np.max(EigValues)\n",
|
||
"Niterations = 30\n",
|
||
"\n",
|
||
"# define the gradient\n",
|
||
"training_gradient = grad(CostOLS)\n",
|
||
"\n",
|
||
"for iter in range(Niterations):\n",
|
||
" gradients = training_gradient(theta)\n",
|
||
" theta -= eta*gradients\n",
|
||
" print(iter,gradients[0],gradients[1])\n",
|
||
"print(\"theta from own gd\")\n",
|
||
"print(theta)\n",
|
||
"\n",
|
||
"# Now improve with momentum gradient descent\n",
|
||
"change = 0.0\n",
|
||
"delta_momentum = 0.3\n",
|
||
"for iter in range(Niterations):\n",
|
||
" # calculate gradient\n",
|
||
" gradients = training_gradient(theta)\n",
|
||
" # calculate update\n",
|
||
" new_change = eta*gradients+delta_momentum*change\n",
|
||
" # take a step\n",
|
||
" theta -= new_change\n",
|
||
" # save the change\n",
|
||
" change = new_change\n",
|
||
" print(iter,gradients[0],gradients[1])\n",
|
||
"print(\"theta from own gd wth momentum\")\n",
|
||
"print(theta)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0a417277",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## But noen of these can compete with Newton's method"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 30,
|
||
"id": "1a541fef",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Using Newton's method\n",
|
||
"from random import random, seed\n",
|
||
"import numpy as np\n",
|
||
"import autograd.numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from autograd import grad\n",
|
||
"\n",
|
||
"def CostOLS(beta):\n",
|
||
" return (1.0/n)*np.sum((y-X @ beta)**2)\n",
|
||
"\n",
|
||
"n = 100\n",
|
||
"x = 2*np.random.rand(n,1)\n",
|
||
"y = 4+3*x+np.random.randn(n,1)\n",
|
||
"\n",
|
||
"X = np.c_[np.ones((n,1)), x]\n",
|
||
"XT_X = X.T @ X\n",
|
||
"beta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
|
||
"print(\"Own inversion\")\n",
|
||
"print(beta_linreg)\n",
|
||
"# Hessian matrix\n",
|
||
"H = (2.0/n)* XT_X\n",
|
||
"# Note that here the Hessian does not depend on the parameters beta\n",
|
||
"invH = np.linalg.pinv(H)\n",
|
||
"EigValues, EigVectors = np.linalg.eig(H)\n",
|
||
"print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
|
||
"\n",
|
||
"beta = np.random.randn(2,1)\n",
|
||
"Niterations = 5\n",
|
||
"\n",
|
||
"# define the gradient\n",
|
||
"training_gradient = grad(CostOLS)\n",
|
||
"\n",
|
||
"for iter in range(Niterations):\n",
|
||
" gradients = training_gradient(beta)\n",
|
||
" beta -= invH @ gradients\n",
|
||
" print(iter,gradients[0],gradients[1])\n",
|
||
"print(\"beta from own Newton code\")\n",
|
||
"print(beta)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9e937e4f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Including Stochastic Gradient Descent with Autograd\n",
|
||
"In this code we include the stochastic gradient descent approach discussed above. Note here that we specify which argument we are taking the derivative with respect to when using **autograd**."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 31,
|
||
"id": "9afef100",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Using Autograd to calculate gradients using SGD\n",
|
||
"# OLS example\n",
|
||
"from random import random, seed\n",
|
||
"import numpy as np\n",
|
||
"import autograd.numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from autograd import grad\n",
|
||
"\n",
|
||
"# Note change from previous example\n",
|
||
"def CostOLS(y,X,theta):\n",
|
||
" return np.sum((y-X @ theta)**2)\n",
|
||
"\n",
|
||
"n = 100\n",
|
||
"x = 2*np.random.rand(n,1)\n",
|
||
"y = 4+3*x+np.random.randn(n,1)\n",
|
||
"\n",
|
||
"X = np.c_[np.ones((n,1)), x]\n",
|
||
"XT_X = X.T @ X\n",
|
||
"theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
|
||
"print(\"Own inversion\")\n",
|
||
"print(theta_linreg)\n",
|
||
"# Hessian matrix\n",
|
||
"H = (2.0/n)* XT_X\n",
|
||
"EigValues, EigVectors = np.linalg.eig(H)\n",
|
||
"print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
|
||
"\n",
|
||
"theta = np.random.randn(2,1)\n",
|
||
"eta = 1.0/np.max(EigValues)\n",
|
||
"Niterations = 1000\n",
|
||
"\n",
|
||
"# Note that we request the derivative wrt third argument (theta, 2 here)\n",
|
||
"training_gradient = grad(CostOLS,2)\n",
|
||
"\n",
|
||
"for iter in range(Niterations):\n",
|
||
" gradients = (1.0/n)*training_gradient(y, X, theta)\n",
|
||
" theta -= eta*gradients\n",
|
||
"print(\"theta from own gd\")\n",
|
||
"print(theta)\n",
|
||
"\n",
|
||
"xnew = np.array([[0],[2]])\n",
|
||
"Xnew = np.c_[np.ones((2,1)), xnew]\n",
|
||
"ypredict = Xnew.dot(theta)\n",
|
||
"ypredict2 = Xnew.dot(theta_linreg)\n",
|
||
"\n",
|
||
"plt.plot(xnew, ypredict, \"r-\")\n",
|
||
"plt.plot(xnew, ypredict2, \"b-\")\n",
|
||
"plt.plot(x, y ,'ro')\n",
|
||
"plt.axis([0,2.0,0, 15.0])\n",
|
||
"plt.xlabel(r'$x$')\n",
|
||
"plt.ylabel(r'$y$')\n",
|
||
"plt.title(r'Random numbers ')\n",
|
||
"plt.show()\n",
|
||
"\n",
|
||
"n_epochs = 50\n",
|
||
"M = 5 #size of each minibatch\n",
|
||
"m = int(n/M) #number of minibatches\n",
|
||
"t0, t1 = 5, 50\n",
|
||
"def learning_schedule(t):\n",
|
||
" return t0/(t+t1)\n",
|
||
"\n",
|
||
"theta = np.random.randn(2,1)\n",
|
||
"\n",
|
||
"for epoch in range(n_epochs):\n",
|
||
"# Can you figure out a better way of setting up the contributions to each batch?\n",
|
||
" for i in range(m):\n",
|
||
" random_index = M*np.random.randint(m)\n",
|
||
" xi = X[random_index:random_index+M]\n",
|
||
" yi = y[random_index:random_index+M]\n",
|
||
" gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
|
||
" eta = learning_schedule(epoch*m+i)\n",
|
||
" theta = theta - eta*gradients\n",
|
||
"print(\"theta from own sdg\")\n",
|
||
"print(theta)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "2a7e982c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Same code but now with momentum gradient descent"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 32,
|
||
"id": "91311a17",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Using Autograd to calculate gradients using SGD\n",
|
||
"# OLS example\n",
|
||
"from random import random, seed\n",
|
||
"import numpy as np\n",
|
||
"import autograd.numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from autograd import grad\n",
|
||
"\n",
|
||
"# Note change from previous example\n",
|
||
"def CostOLS(y,X,theta):\n",
|
||
" return np.sum((y-X @ theta)**2)\n",
|
||
"\n",
|
||
"n = 100\n",
|
||
"x = 2*np.random.rand(n,1)\n",
|
||
"y = 4+3*x+np.random.randn(n,1)\n",
|
||
"\n",
|
||
"X = np.c_[np.ones((n,1)), x]\n",
|
||
"XT_X = X.T @ X\n",
|
||
"theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
|
||
"print(\"Own inversion\")\n",
|
||
"print(theta_linreg)\n",
|
||
"# Hessian matrix\n",
|
||
"H = (2.0/n)* XT_X\n",
|
||
"EigValues, EigVectors = np.linalg.eig(H)\n",
|
||
"print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
|
||
"\n",
|
||
"theta = np.random.randn(2,1)\n",
|
||
"eta = 1.0/np.max(EigValues)\n",
|
||
"Niterations = 100\n",
|
||
"\n",
|
||
"# Note that we request the derivative wrt third argument (theta, 2 here)\n",
|
||
"training_gradient = grad(CostOLS,2)\n",
|
||
"\n",
|
||
"for iter in range(Niterations):\n",
|
||
" gradients = (1.0/n)*training_gradient(y, X, theta)\n",
|
||
" theta -= eta*gradients\n",
|
||
"print(\"theta from own gd\")\n",
|
||
"print(theta)\n",
|
||
"\n",
|
||
"\n",
|
||
"n_epochs = 50\n",
|
||
"M = 5 #size of each minibatch\n",
|
||
"m = int(n/M) #number of minibatches\n",
|
||
"t0, t1 = 5, 50\n",
|
||
"def learning_schedule(t):\n",
|
||
" return t0/(t+t1)\n",
|
||
"\n",
|
||
"theta = np.random.randn(2,1)\n",
|
||
"\n",
|
||
"change = 0.0\n",
|
||
"delta_momentum = 0.3\n",
|
||
"\n",
|
||
"for epoch in range(n_epochs):\n",
|
||
" for i in range(m):\n",
|
||
" random_index = M*np.random.randint(m)\n",
|
||
" xi = X[random_index:random_index+M]\n",
|
||
" yi = y[random_index:random_index+M]\n",
|
||
" gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
|
||
" eta = learning_schedule(epoch*m+i)\n",
|
||
" # calculate update\n",
|
||
" new_change = eta*gradients+delta_momentum*change\n",
|
||
" # take a step\n",
|
||
" theta -= new_change\n",
|
||
" # save the change\n",
|
||
" change = new_change\n",
|
||
"print(\"theta from own sdg with momentum\")\n",
|
||
"print(theta)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "516999d8",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Similar (second order function now) problem but now with AdaGrad"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 33,
|
||
"id": "e8292719",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Using Autograd to calculate gradients using AdaGrad and Stochastic Gradient descent\n",
|
||
"# OLS example\n",
|
||
"from random import random, seed\n",
|
||
"import numpy as np\n",
|
||
"import autograd.numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from autograd import grad\n",
|
||
"\n",
|
||
"# Note change from previous example\n",
|
||
"def CostOLS(y,X,theta):\n",
|
||
" return np.sum((y-X @ theta)**2)\n",
|
||
"\n",
|
||
"n = 1000\n",
|
||
"x = np.random.rand(n,1)\n",
|
||
"y = 2.0+3*x +4*x*x\n",
|
||
"\n",
|
||
"X = np.c_[np.ones((n,1)), x, x*x]\n",
|
||
"XT_X = X.T @ X\n",
|
||
"theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
|
||
"print(\"Own inversion\")\n",
|
||
"print(theta_linreg)\n",
|
||
"\n",
|
||
"\n",
|
||
"# Note that we request the derivative wrt third argument (theta, 2 here)\n",
|
||
"training_gradient = grad(CostOLS,2)\n",
|
||
"# Define parameters for Stochastic Gradient Descent\n",
|
||
"n_epochs = 50\n",
|
||
"M = 5 #size of each minibatch\n",
|
||
"m = int(n/M) #number of minibatches\n",
|
||
"# Guess for unknown parameters theta\n",
|
||
"theta = np.random.randn(3,1)\n",
|
||
"\n",
|
||
"# Value for learning rate\n",
|
||
"eta = 0.01\n",
|
||
"# Including AdaGrad parameter to avoid possible division by zero\n",
|
||
"delta = 1e-8\n",
|
||
"for epoch in range(n_epochs):\n",
|
||
" Giter = 0.0\n",
|
||
" for i in range(m):\n",
|
||
" random_index = M*np.random.randint(m)\n",
|
||
" xi = X[random_index:random_index+M]\n",
|
||
" yi = y[random_index:random_index+M]\n",
|
||
" gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
|
||
" Giter += gradients*gradients\n",
|
||
" update = gradients*eta/(delta+np.sqrt(Giter))\n",
|
||
" theta -= update\n",
|
||
"print(\"theta from own AdaGrad\")\n",
|
||
"print(theta)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "bd67f5cb",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Running this code we note an almost perfect agreement with the results from matrix inversion."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "eb0d5fd0",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## RMSprop for adaptive learning rate with Stochastic Gradient Descent"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 34,
|
||
"id": "d2eb93d1",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Using Autograd to calculate gradients using RMSprop and Stochastic Gradient descent\n",
|
||
"# OLS example\n",
|
||
"from random import random, seed\n",
|
||
"import numpy as np\n",
|
||
"import autograd.numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from autograd import grad\n",
|
||
"\n",
|
||
"# Note change from previous example\n",
|
||
"def CostOLS(y,X,theta):\n",
|
||
" return np.sum((y-X @ theta)**2)\n",
|
||
"\n",
|
||
"n = 1000\n",
|
||
"x = np.random.rand(n,1)\n",
|
||
"y = 2.0+3*x +4*x*x# +np.random.randn(n,1)\n",
|
||
"\n",
|
||
"X = np.c_[np.ones((n,1)), x, x*x]\n",
|
||
"XT_X = X.T @ X\n",
|
||
"theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
|
||
"print(\"Own inversion\")\n",
|
||
"print(theta_linreg)\n",
|
||
"\n",
|
||
"\n",
|
||
"# Note that we request the derivative wrt third argument (theta, 2 here)\n",
|
||
"training_gradient = grad(CostOLS,2)\n",
|
||
"# Define parameters for Stochastic Gradient Descent\n",
|
||
"n_epochs = 50\n",
|
||
"M = 5 #size of each minibatch\n",
|
||
"m = int(n/M) #number of minibatches\n",
|
||
"# Guess for unknown parameters theta\n",
|
||
"theta = np.random.randn(3,1)\n",
|
||
"\n",
|
||
"# Value for learning rate\n",
|
||
"eta = 0.01\n",
|
||
"# Value for parameter rho\n",
|
||
"rho = 0.99\n",
|
||
"# Including AdaGrad parameter to avoid possible division by zero\n",
|
||
"delta = 1e-8\n",
|
||
"for epoch in range(n_epochs):\n",
|
||
" Giter = 0.0\n",
|
||
" for i in range(m):\n",
|
||
" random_index = M*np.random.randint(m)\n",
|
||
" xi = X[random_index:random_index+M]\n",
|
||
" yi = y[random_index:random_index+M]\n",
|
||
" gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
|
||
"\t# Accumulated gradient\n",
|
||
"\t# Scaling with rho the new and the previous results\n",
|
||
" Giter = (rho*Giter+(1-rho)*gradients*gradients)\n",
|
||
"\t# Taking the diagonal only and inverting\n",
|
||
" update = gradients*eta/(delta+np.sqrt(Giter))\n",
|
||
"\t# Hadamard product\n",
|
||
" theta -= update\n",
|
||
"print(\"theta from own RMSprop\")\n",
|
||
"print(theta)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "669b56c2",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## And finally [ADAM](https://arxiv.org/pdf/1412.6980.pdf)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 35,
|
||
"id": "bb3f553d",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Using Autograd to calculate gradients using RMSprop and Stochastic Gradient descent\n",
|
||
"# OLS example\n",
|
||
"from random import random, seed\n",
|
||
"import numpy as np\n",
|
||
"import autograd.numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from autograd import grad\n",
|
||
"\n",
|
||
"# Note change from previous example\n",
|
||
"def CostOLS(y,X,theta):\n",
|
||
" return np.sum((y-X @ theta)**2)\n",
|
||
"\n",
|
||
"n = 1000\n",
|
||
"x = np.random.rand(n,1)\n",
|
||
"y = 2.0+3*x +4*x*x# +np.random.randn(n,1)\n",
|
||
"\n",
|
||
"X = np.c_[np.ones((n,1)), x, x*x]\n",
|
||
"XT_X = X.T @ X\n",
|
||
"theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
|
||
"print(\"Own inversion\")\n",
|
||
"print(theta_linreg)\n",
|
||
"\n",
|
||
"\n",
|
||
"# Note that we request the derivative wrt third argument (theta, 2 here)\n",
|
||
"training_gradient = grad(CostOLS,2)\n",
|
||
"# Define parameters for Stochastic Gradient Descent\n",
|
||
"n_epochs = 50\n",
|
||
"M = 5 #size of each minibatch\n",
|
||
"m = int(n/M) #number of minibatches\n",
|
||
"# Guess for unknown parameters theta\n",
|
||
"theta = np.random.randn(3,1)\n",
|
||
"\n",
|
||
"# Value for learning rate\n",
|
||
"eta = 0.01\n",
|
||
"# Value for parameters beta1 and beta2, see https://arxiv.org/abs/1412.6980\n",
|
||
"beta1 = 0.9\n",
|
||
"beta2 = 0.999\n",
|
||
"# Including AdaGrad parameter to avoid possible division by zero\n",
|
||
"delta = 1e-7\n",
|
||
"iter = 0\n",
|
||
"for epoch in range(n_epochs):\n",
|
||
" first_moment = 0.0\n",
|
||
" second_moment = 0.0\n",
|
||
" iter += 1\n",
|
||
" for i in range(m):\n",
|
||
" random_index = M*np.random.randint(m)\n",
|
||
" xi = X[random_index:random_index+M]\n",
|
||
" yi = y[random_index:random_index+M]\n",
|
||
" gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
|
||
" # Computing moments first\n",
|
||
" first_moment = beta1*first_moment + (1-beta1)*gradients\n",
|
||
" second_moment = beta2*second_moment+(1-beta2)*gradients*gradients\n",
|
||
" first_term = first_moment/(1.0-beta1**iter)\n",
|
||
" second_term = second_moment/(1.0-beta2**iter)\n",
|
||
"\t# Scaling with rho the new and the previous results\n",
|
||
" update = eta*first_term/(np.sqrt(second_term)+delta)\n",
|
||
" theta -= update\n",
|
||
"print(\"theta from own ADAM\")\n",
|
||
"print(theta)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4e5c58ea",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## And Logistic Regression"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 36,
|
||
"id": "1fec659e",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"import autograd.numpy as np\n",
|
||
"from autograd import grad\n",
|
||
"\n",
|
||
"def sigmoid(x):\n",
|
||
" return 0.5 * (np.tanh(x / 2.) + 1)\n",
|
||
"\n",
|
||
"def logistic_predictions(weights, inputs):\n",
|
||
" # Outputs probability of a label being true according to logistic model.\n",
|
||
" return sigmoid(np.dot(inputs, weights))\n",
|
||
"\n",
|
||
"def training_loss(weights):\n",
|
||
" # Training loss is the negative log-likelihood of the training labels.\n",
|
||
" preds = logistic_predictions(weights, inputs)\n",
|
||
" label_probabilities = preds * targets + (1 - preds) * (1 - targets)\n",
|
||
" return -np.sum(np.log(label_probabilities))\n",
|
||
"\n",
|
||
"# Build a toy dataset.\n",
|
||
"inputs = np.array([[0.52, 1.12, 0.77],\n",
|
||
" [0.88, -1.08, 0.15],\n",
|
||
" [0.52, 0.06, -1.30],\n",
|
||
" [0.74, -2.49, 1.39]])\n",
|
||
"targets = np.array([True, True, False, True])\n",
|
||
"\n",
|
||
"# Define a function that returns gradients of training loss using Autograd.\n",
|
||
"training_gradient_fun = grad(training_loss)\n",
|
||
"\n",
|
||
"# Optimize weights using gradient descent.\n",
|
||
"weights = np.array([0.0, 0.0, 0.0])\n",
|
||
"print(\"Initial loss:\", training_loss(weights))\n",
|
||
"for i in range(100):\n",
|
||
" weights -= training_gradient_fun(weights) * 0.01\n",
|
||
"\n",
|
||
"print(\"Trained loss:\", training_loss(weights))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ac14943c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Introducing [JAX](https://jax.readthedocs.io/en/latest/)\n",
|
||
"\n",
|
||
"Presently, instead of using **autograd**, we recommend using [JAX](https://jax.readthedocs.io/en/latest/)\n",
|
||
"\n",
|
||
"**JAX** is Autograd and [XLA (Accelerated Linear Algebra))](https://www.tensorflow.org/xla),\n",
|
||
"brought together for high-performance numerical computing and machine learning research.\n",
|
||
"It provides composable transformations of Python+NumPy programs: differentiate, vectorize, parallelize, Just-In-Time compile to GPU/TPU, and more.\n",
|
||
"\n",
|
||
"Here's a simple example on how you can use **JAX** to compute the derivate of the logistic function."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 37,
|
||
"id": "57b4e540",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"import jax.numpy as jnp\n",
|
||
"from jax import grad, jit, vmap\n",
|
||
"\n",
|
||
"def sum_logistic(x):\n",
|
||
" return jnp.sum(1.0 / (1.0 + jnp.exp(-x)))\n",
|
||
"\n",
|
||
"x_small = jnp.arange(3.)\n",
|
||
"derivative_fn = grad(sum_logistic)\n",
|
||
"print(derivative_fn(x_small))"
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"language_info": {
|
||
"codemirror_mode": {
|
||
"name": "ipython",
|
||
"version": 3
|
||
},
|
||
"file_extension": ".py",
|
||
"mimetype": "text/x-python",
|
||
"name": "python",
|
||
"nbconvert_exporter": "python",
|
||
"pygments_lexer": "ipython3",
|
||
"version": "3.9.10"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 5
|
||
} |