Morten Hjorth-Jensen
5517 lines
892 KiB
Plaintext
5517 lines
892 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, September 23-27, 2024"
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]
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"source": [
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"## Lecture Monday September 23\n",
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"\n",
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"**Material for the lecture on Monday September 23.**\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 gradient methods\n",
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"\n",
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" * Stochastic Gradient descent with examples and automatic differentiation (theme also for next week).\n",
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"\n",
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" * [Video of lecture](https://youtu.be/ISGpTC28Vmk)\n",
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"\n",
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" * [Whiteboard notes](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2024/NotesSeptember23.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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" * Raschka et al, pages 53-76 on Logistic regression and pages 37-52 on gradient optimization \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)"
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]
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"source": [
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"## Lab sessions 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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" * A general guideline can be found at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/EvaluationGrading/EvaluationForm.md>."
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]
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"source": [
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"## Lecture Monday September 23, 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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]
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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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]
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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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]
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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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]
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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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"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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},
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"source": [
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"or in matrix form as"
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]
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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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]
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"cell_type": "markdown",
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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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"source": [
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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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"source": [
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"yielding"
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]
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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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]
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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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]
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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",
|
||
"interpretation, namely $x_{n+1}$ is the point where the tangent from\n",
|
||
"$(x_n,f(x_n))$ crosses the $x$-axis. Close to the solution,\n",
|
||
"Newton-Raphson converges fast to the desired result. However, if we\n",
|
||
"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",
|
||
"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",
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||
"guess near such a local extremum, so that the first derivative nearly\n",
|
||
"vanishes, then Newton-Raphson may fail totally"
|
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]
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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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"cell_type": "markdown",
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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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"source": [
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||
"$$\n",
|
||
"\\begin{array}{cc} 0=f_1(x_1+h_1,x_2+h_2)=&f_1(x_1,x_2)+h_1\n",
|
||
" \\partial f_1/\\partial x_1+h_2\n",
|
||
" \\partial f_1/\\partial x_2+\\dots\\\\\n",
|
||
" 0=f_2(x_1+h_1,x_2+h_2)=&f_2(x_1,x_2)+h_1\n",
|
||
" \\partial f_2/\\partial x_1+h_2\n",
|
||
" \\partial f_2/\\partial x_2+\\dots\n",
|
||
" \\end{array}.\n",
|
||
"$$"
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]
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},
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{
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"cell_type": "markdown",
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"id": "7e03330a",
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"metadata": {
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"editable": true
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},
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"source": [
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||
"Defining the Jacobian matrix ${\\bf \\boldsymbol{J}}$ we have"
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||
]
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},
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{
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"cell_type": "markdown",
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"id": "8b6bbcc0",
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"metadata": {
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"editable": true
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},
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"source": [
|
||
"$$\n",
|
||
"{\\bf \\boldsymbol{J}}=\\left( \\begin{array}{cc}\n",
|
||
" \\partial f_1/\\partial x_1 & \\partial f_1/\\partial x_2 \\\\\n",
|
||
" \\partial f_2/\\partial x_1 &\\partial f_2/\\partial x_2\n",
|
||
" \\end{array} \\right),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "942ef368",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"we can rephrase Newton's method as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8d383d9e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\left(\\begin{array}{c} x_1^{n+1} \\\\ x_2^{n+1} \\end{array} \\right)=\n",
|
||
"\\left(\\begin{array}{c} x_1^{n} \\\\ x_2^{n} \\end{array} \\right)+\n",
|
||
"\\left(\\begin{array}{c} h_1^{n} \\\\ h_2^{n} \\end{array} \\right),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f3cbe6ed",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where we have defined"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c4086d22",
|
||
"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": "e6317de3",
|
||
"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": "edf2bfe8",
|
||
"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": "a7fb938f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathbf{x}_{k+1} = \\mathbf{x}_k - \\gamma_k \\nabla F(\\mathbf{x}_k),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d847b9be",
|
||
"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": "9b5b4acb",
|
||
"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": "ce9525ec",
|
||
"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": "54d2e571",
|
||
"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": "c35ee552",
|
||
"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": "2f025ad9",
|
||
"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": "80f3bd26",
|
||
"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": "199afe72",
|
||
"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": "26f4fb05",
|
||
"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": "ef861245",
|
||
"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": "989686b9",
|
||
"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": "8f0a01ed",
|
||
"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": "098985af",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{A}\\boldsymbol{x} = \\boldsymbol{b}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ca3b1849",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"In the iterative process we end up with a problem like"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a9026b79",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{r}= \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "dff64482",
|
||
"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": "502eba66",
|
||
"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": "fde7d2c9",
|
||
"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": "636a5eb2",
|
||
"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": "ce3be231",
|
||
"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": "f87ac8d2",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{x}_0=0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7961c3fc",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"or consider the system"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9ae1698c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{A}\\boldsymbol{z} = \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b5e2f728",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"instead."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f3d7aa36",
|
||
"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": "2acb11da",
|
||
"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": "ee51e96c",
|
||
"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": "921a7d11",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{A}\\boldsymbol{x}_0-\\boldsymbol{b},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "30f50187",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"and \n",
|
||
"$\\boldsymbol{x}_0=0$ it is equal $-\\boldsymbol{b}$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "268a19dd",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Final expressions\n",
|
||
"We can compute the residual iteratively as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "bc9ef63b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{r}_{k+1}=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_{k+1},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4b2a66e9",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which equals"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "cc10185f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{b}-\\boldsymbol{A}(\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{r}_k),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "bfea4d71",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"or"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0db69549",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"(\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k)-\\alpha_k\\boldsymbol{A}\\boldsymbol{r}_k,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e950ac57",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which gives"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0d0be156",
|
||
"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": "5a44b7f9",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"leading to the iterative scheme"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7fcb3188",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{x}_{k+1}=\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{r}_{k},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "59681f93",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Steepest descent example"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 1,
|
||
"id": "b27b7d36",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"<mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x13a82fc10>"
|
||
]
|
||
},
|
||
"execution_count": 1,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"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.add_subplot(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": "3cec05a7",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"And then as countor plot"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 2,
|
||
"id": "3f348ef8",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"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": "b4e35f32",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Find guesses"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 3,
|
||
"id": "41aa6226",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"x = guesses[-1]\n",
|
||
"s = -df(x)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "03977607",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Run it!"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 4,
|
||
"id": "318314e2",
|
||
"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": "a0261d67",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"What happened?"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 5,
|
||
"id": "43d274e3",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"[<matplotlib.lines.Line2D at 0x13c4215e0>]"
|
||
]
|
||
},
|
||
"execution_count": 5,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"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": "a38a2dab",
|
||
"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": "54215dfb",
|
||
"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": "b78458c4",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{s}^T\\boldsymbol{A}\\boldsymbol{t}= 0.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e4ff83c9",
|
||
"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": "8f583f25",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{x}_i^T\\boldsymbol{A}\\boldsymbol{x}_j= 0.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "cef5af3c",
|
||
"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": "121f7cf6",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Conjugate gradient method\n",
|
||
"An example is given by the eigenvectors of the matrix"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "bd6f31c1",
|
||
"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": "49e134c5",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which is zero unless $i=j$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "246cde51",
|
||
"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": "8f37039b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{x}_{i+1}=\\boldsymbol{x}_{i}+\\alpha_i\\boldsymbol{p}_{i}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "87526237",
|
||
"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": "3e9efa18",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{x} = \\sum^{n}_{i=1} \\alpha_i \\boldsymbol{p}_i.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "93a7fb4b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Conjugate gradient method\n",
|
||
"The coefficients are given by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8a737bc7",
|
||
"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": "383e3298",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Multiplying with $\\boldsymbol{p}_k^T$ from the left gives"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c25b2dfa",
|
||
"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": "4b3f5db3",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"and we can define the coefficients $\\alpha_k$ as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ebd88b2e",
|
||
"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": "baa81bcb",
|
||
"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": "46e17082",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{x}_0=0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ed1e6366",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"or consider the system"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "44dfe77f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{A}\\boldsymbol{z} = \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "51b93467",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"instead."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "659810a9",
|
||
"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": "62890f2c",
|
||
"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": "c0fe14af",
|
||
"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": "1e52026b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{A}\\boldsymbol{x}_0-\\boldsymbol{b},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "bcf59df7",
|
||
"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": "292e8dc5",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Conjugate gradient method\n",
|
||
"Let $\\boldsymbol{r}_k$ be the residual at the $k$-th step:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "093ad28a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{r}_k=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9ee5dacc",
|
||
"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": "68f99505",
|
||
"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": "bcac1586",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Conjugate gradient method\n",
|
||
"We can also compute the residual iteratively as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ce27b155",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{r}_{k+1}=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_{k+1},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "524bcfdb",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which equals"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1386c597",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{b}-\\boldsymbol{A}(\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{p}_k),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6f813648",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"or"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4c3248f2",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"(\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k)-\\alpha_k\\boldsymbol{A}\\boldsymbol{p}_k,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9bc69068",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which gives"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "14e706f1",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{r}_{k+1}=\\boldsymbol{r}_k-\\boldsymbol{A}\\boldsymbol{p}_{k},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8ff319c8",
|
||
"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": "7e7faa97",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"m = 100\n",
|
||
"x = 2*np.random.rand(m,1)\n",
|
||
"y = 4+3*x+np.random.randn(m,1)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7885df38",
|
||
"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": "20151eb1",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"h_\\beta(x) = \\boldsymbol{y} = \\beta_0 + \\beta_1 x,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "87c3b2cd",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"such that"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "493e2541",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{y}_i = \\beta_0 + \\beta_1 x_i.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8a082762",
|
||
"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": "5c54bcb6",
|
||
"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": "23d09807",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"The cost/loss/risk function is given by ("
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e4d67729",
|
||
"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": "2eef4f99",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"and we want to find $\\beta$ such that $C(\\beta)$ is minimized."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "56f73ade",
|
||
"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": "8deab8b6",
|
||
"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": "fd240c75",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where $X$ is the design matrix defined above."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "fdf6f2dd",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## The Hessian matrix\n",
|
||
"The Hessian matrix of $C(\\beta)$ is given by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f930ee8a",
|
||
"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": "898e06cb",
|
||
"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": "81725bf9",
|
||
"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": "4ef5633f",
|
||
"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": "142ffc92",
|
||
"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": "28051170",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Gradient Descent Example\n",
|
||
"\n",
|
||
"Here our simple example"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 7,
|
||
"id": "481d02c8",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Eigenvalues of Hessian Matrix:[0.27540816 4.20676564]\n",
|
||
"[[4.42946675]\n",
|
||
" [2.77225311]]\n",
|
||
"[[4.42946675]\n",
|
||
" [2.77225311]]\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"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": "35b0af87",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## And a corresponding example using **scikit-learn**"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 8,
|
||
"id": "d0822e39",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[[4.01958347]\n",
|
||
" [2.99622289]]\n",
|
||
"[3.9423229] [2.93628788]\n"
|
||
]
|
||
}
|
||
],
|
||
"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": "af7ac4d0",
|
||
"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": "9e04fb04",
|
||
"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": "740b9955",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"In order to minimize $C_{\\text{ridge}}(\\beta)$ using GD we adjust the gradient as follows"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c3ffbc6f",
|
||
"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": "20eb1fff",
|
||
"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": "e995e244",
|
||
"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": "1c300f84",
|
||
"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": "7d165637",
|
||
"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": "08f0c5d1",
|
||
"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": "7d06856d",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Program example for gradient descent with Ridge Regression"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 9,
|
||
"id": "e439d732",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Eigenvalues of Hessian Matrix:[0.2407804 4.6388827]\n",
|
||
"[[4.2170777 ]\n",
|
||
" [2.80552961]]\n",
|
||
"[[4.21180334]\n",
|
||
" [2.80984014]]\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"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": "aa6db5fd",
|
||
"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": "4cf99d2c",
|
||
"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": "3eaa6001",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
">0 f([0.74724774]) = 0.55838\n",
|
||
">1 f([0.59779819]) = 0.35736\n",
|
||
">2 f([0.47823856]) = 0.22871\n",
|
||
">3 f([0.38259084]) = 0.14638\n",
|
||
">4 f([0.30607268]) = 0.09368\n",
|
||
">5 f([0.24485814]) = 0.05996\n",
|
||
">6 f([0.19588651]) = 0.03837\n",
|
||
">7 f([0.15670921]) = 0.02456\n",
|
||
">8 f([0.12536737]) = 0.01572\n",
|
||
">9 f([0.10029389]) = 0.01006\n",
|
||
">10 f([0.08023512]) = 0.00644\n",
|
||
">11 f([0.06418809]) = 0.00412\n",
|
||
">12 f([0.05135047]) = 0.00264\n",
|
||
">13 f([0.04108038]) = 0.00169\n",
|
||
">14 f([0.0328643]) = 0.00108\n",
|
||
">15 f([0.02629144]) = 0.00069\n",
|
||
">16 f([0.02103315]) = 0.00044\n",
|
||
">17 f([0.01682652]) = 0.00028\n",
|
||
">18 f([0.01346122]) = 0.00018\n",
|
||
">19 f([0.01076897]) = 0.00012\n",
|
||
">20 f([0.00861518]) = 0.00007\n",
|
||
">21 f([0.00689214]) = 0.00005\n",
|
||
">22 f([0.00551372]) = 0.00003\n",
|
||
">23 f([0.00441097]) = 0.00002\n",
|
||
">24 f([0.00352878]) = 0.00001\n",
|
||
">25 f([0.00282302]) = 0.00001\n",
|
||
">26 f([0.00225842]) = 0.00001\n",
|
||
">27 f([0.00180673]) = 0.00000\n",
|
||
">28 f([0.00144539]) = 0.00000\n",
|
||
">29 f([0.00115631]) = 0.00000\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_11683/394505933.py:33: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n",
|
||
" print('>%d f(%s) = %.5f' % (i, solution, solution_eval))\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"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": "a94bcdd8",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Same code but now with momentum gradient descent"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 11,
|
||
"id": "a83da0e4",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
">0 f([0.74724774]) = 0.55838\n",
|
||
">1 f([0.54175461]) = 0.29350\n",
|
||
">2 f([0.37175575]) = 0.13820\n",
|
||
">3 f([0.24640494]) = 0.06072\n",
|
||
">4 f([0.15951871]) = 0.02545\n",
|
||
">5 f([0.1015491]) = 0.01031\n",
|
||
">6 f([0.0638484]) = 0.00408\n",
|
||
">7 f([0.03976851]) = 0.00158\n",
|
||
">8 f([0.02459084]) = 0.00060\n",
|
||
">9 f([0.01511937]) = 0.00023\n",
|
||
">10 f([0.00925406]) = 0.00009\n",
|
||
">11 f([0.00564365]) = 0.00003\n",
|
||
">12 f([0.0034318]) = 0.00001\n",
|
||
">13 f([0.00208188]) = 0.00000\n",
|
||
">14 f([0.00126053]) = 0.00000\n",
|
||
">15 f([0.00076202]) = 0.00000\n",
|
||
">16 f([0.00046006]) = 0.00000\n",
|
||
">17 f([0.00027746]) = 0.00000\n",
|
||
">18 f([0.00016719]) = 0.00000\n",
|
||
">19 f([0.00010067]) = 0.00000\n",
|
||
">20 f([6.05804744e-05]) = 0.00000\n",
|
||
">21 f([3.64373635e-05]) = 0.00000\n",
|
||
">22 f([2.19069576e-05]) = 0.00000\n",
|
||
">23 f([1.31664443e-05]) = 0.00000\n",
|
||
">24 f([7.91100141e-06]) = 0.00000\n",
|
||
">25 f([4.75216828e-06]) = 0.00000\n",
|
||
">26 f([2.85408468e-06]) = 0.00000\n",
|
||
">27 f([1.71384267e-06]) = 0.00000\n",
|
||
">28 f([1.02900153e-06]) = 0.00000\n",
|
||
">29 f([6.17748881e-07]) = 0.00000\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_11683/476849792.py:39: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n",
|
||
" print('>%d f(%s) = %.5f' % (i, solution, solution_eval))\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"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": "3ac55f04",
|
||
"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": "2a8579fd",
|
||
"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": "d07dbbb0",
|
||
"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": "f7050d91",
|
||
"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": "53a1eb81",
|
||
"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": "e4d86364",
|
||
"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": "0fb47ea3",
|
||
"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": "61242d66",
|
||
"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": "242ed688",
|
||
"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": "9888d0c0",
|
||
"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": "00908421",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## The gradient step\n",
|
||
"\n",
|
||
"Thus a gradient descent step now looks like"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4dfe9a45",
|
||
"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": "d91957f8",
|
||
"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": "2bf38592",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Simple example code"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 12,
|
||
"id": "43232599",
|
||
"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": "b6d1acf5",
|
||
"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": "a14ce3ad",
|
||
"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": "5d674391",
|
||
"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": "b01f74c8",
|
||
"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": "81c42935",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"gamma_j after 500 epochs: 9.97108e-05\n"
|
||
]
|
||
}
|
||
],
|
||
"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": "5a28593f",
|
||
"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": "94ca81fd",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Own inversion\n",
|
||
"[[4.08687303]\n",
|
||
" [3.00141727]]\n",
|
||
"Eigenvalues of Hessian Matrix:[0.29653038 4.0474753 ]\n",
|
||
"theta from own gd\n",
|
||
"[[4.08687303]\n",
|
||
" [3.00141727]]\n",
|
||
"theta from own sdg\n",
|
||
"[[4.014934 ]\n",
|
||
" [3.0042992]]\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"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": "603b60cd",
|
||
"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": "19b9dcdb",
|
||
"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": "a22a038a",
|
||
"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": "787585ab",
|
||
"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": "96ff0afc",
|
||
"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": "61791f14",
|
||
"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": "f823f328",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where we have defined $\\Delta \\boldsymbol{\\theta}_{t}= \\boldsymbol{\\theta}_t-\\boldsymbol{\\theta}_{t-1}$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c4d9d496",
|
||
"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": "391417ce",
|
||
"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": "4f023c4e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"We can discretize this equation in the usual way to get"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "69270617",
|
||
"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": "2a4e6d30",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Rearranging this equation, we can rewrite this as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "359bd99b",
|
||
"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": "7ea6f847",
|
||
"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": "691c8355",
|
||
"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": "36be1849",
|
||
"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": "2b7f8487",
|
||
"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": "d8a09725",
|
||
"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": "2d94a01d",
|
||
"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": "65d01e36",
|
||
"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": "8da72974",
|
||
"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": "c58d0f20",
|
||
"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": "e5dc0738",
|
||
"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": "fbd6fdd8",
|
||
"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": "626dc040",
|
||
"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": "6fcf9b87",
|
||
"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": "88bbaad2",
|
||
"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": "b4349ab6",
|
||
"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": "b2215a9e",
|
||
"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": "4d2452fb",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{\\mathbf{m}}_t={\\mathbf{m}_t \\over 1-\\beta_1^t} \\nonumber\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "2af543bd",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{\\mathbf{s}}_t ={\\mathbf{s}_t \\over1-\\beta_2^t} \\nonumber\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "67134da9",
|
||
"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": "59683156",
|
||
"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": "56b23d7b",
|
||
"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": "ef6b130f",
|
||
"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": "55d1d0ff",
|
||
"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": "5b0fb743",
|
||
"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": "ea05bbe2",
|
||
"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": "b4cf1ace",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"f(x) = \\sin\\left(2\\pi x + x^2\\right)\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "862002bf",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which has the following derivative"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "be897152",
|
||
"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": "13e4ae3a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Using **autograd** we have"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 15,
|
||
"id": "d4a79e0d",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"The max absolute difference is: 1.77636e-15\n"
|
||
]
|
||
}
|
||
],
|
||
"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": "4d3694c5",
|
||
"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": "a9719490",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"The gradient of f1 evaluated at a = 1 using autograd is: 3\n",
|
||
"The gradient of f1 evaluated at a = 1 by finding the analytic expression is: 3\n"
|
||
]
|
||
}
|
||
],
|
||
"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": "b2259ecd",
|
||
"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": "5b154fa9",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Evaluating at x1 = 1, x2 = 3\n",
|
||
"------------------------------\n",
|
||
"The derivative of f2 w.r.t x1: 12\n",
|
||
"The analytical derivative of f2 w.r.t x1: 12\n",
|
||
"\n",
|
||
"The derivative of f2 w.r.t x2: -4\n",
|
||
"The analytical derivative of f2 w.r.t x2: -4\n"
|
||
]
|
||
}
|
||
],
|
||
"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": "733bbca1",
|
||
"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": "d817341e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## More complicated functions using the elements of their arguments directly"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 18,
|
||
"id": "1289ab58",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"The computed gradient of f3 is: [ 2. 3. 5. 7. 88.]\n",
|
||
"The analytical gradient of f3 is: [ 2. 3. 5. 7. 88.]\n"
|
||
]
|
||
}
|
||
],
|
||
"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": "7d4fed1d",
|
||
"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": "5ad8360a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Functions using mathematical functions from Numpy"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 19,
|
||
"id": "0cf2c306",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"The computed derivative of f4 at x = 2.7 is: 13.8759\n",
|
||
"The analytical gradient of f4 at x = 2.7 is: 13.8759\n"
|
||
]
|
||
}
|
||
],
|
||
"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": "70050aa3",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## More autograd"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 20,
|
||
"id": "7eee1b5e",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"The computed derivative of f5 at x = 2.7 is: 5.4\n"
|
||
]
|
||
}
|
||
],
|
||
"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": "352a0503",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## And with loops"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 21,
|
||
"id": "943cc42b",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"The computed derivative of f6_for at x = 0.5 is: 3.95703\n",
|
||
"The computed derivative of f6_while at x = 0.5 is: 3.95703\n"
|
||
]
|
||
}
|
||
],
|
||
"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": "e8664459",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"The analytical derivative of f6 at x = 0.5 is: 3.95703\n"
|
||
]
|
||
}
|
||
],
|
||
"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": "6ddce8f0",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Using recursion"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 23,
|
||
"id": "96a3253f",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"The computed derivative of f7 at n = 2 is: 1\n",
|
||
"The analytical derivative of f7 at n = 2 is: 1\n"
|
||
]
|
||
}
|
||
],
|
||
"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": "8b25fa4c",
|
||
"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": "e225412f",
|
||
"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": "89af0ad7",
|
||
"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": "87db5510",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Here, running this code, 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": "21d8ac43",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## The syntax a.dot(b) when finding the dot product"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 25,
|
||
"id": "5411f897",
|
||
"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": "f6b40ee1",
|
||
"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": "9590986c",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"The gradient of f9 is: [1. 2.]\n"
|
||
]
|
||
}
|
||
],
|
||
"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": "2085a755",
|
||
"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": 27,
|
||
"id": "8108ae0a",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Own inversion\n",
|
||
"[[3.94499279]\n",
|
||
" [3.03306538]]\n",
|
||
"Eigenvalues of Hessian Matrix:[0.31248425 4.44418124]\n",
|
||
"theta from own gd\n",
|
||
"[[3.94499279]\n",
|
||
" [3.03306538]]\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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TGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0zwehjZv3gydTofIyEhIkoRly5ZZ9t28eROvvvoqmjVrhuDgYERGRuLxxx/H6dOnPVdgIiIi8ioeD0MFBQVo0aIFZs2aVWLftWvXsGvXLrzxxhvYtWsX0tLScPDgQfTp08cDJSUiIiJvJAkhhKcLYSZJEpYuXYp+/frZPWbnzp1o27YtTpw4gTp16jh03ry8PISGhiI3NxchISEylZaIiIhcyV2f334uO7OL5ObmQpIkVK1a1e4xRUVFKCoqsvycl5fnhpIRERGRGnm8mcwZhYWFePXVVzF06NBSE2JqaipCQ0MtXzExMW4sJREREamJasLQzZs3MXjwYAgh8Omnn5Z67IQJE5Cbm2v5ysrKclMpiYiISG1U0UxmDkInTpzAxo0by2w3DAgIQEBAgJtKR0RERGqm+DBkDkKHDx9Geno6atSo4ekiERERkRfxeBi6evUqjhw5Yvk5MzMTu3fvRvXq1REREYGBAwdi165dWLlyJQwGA3JycgAA1atXh7+/v6eKTURERF7C40PrMzIy0KVLlxLbhw8fjkmTJiE2Ntbm49LT05GUlOTQc3BoPRERkfpoZmh9UlISSstjCpoGiYiIiLyQx8MQERERqZTBAGzZApw5A0REAImJgK+vp0vlNIYhIiIicl5aGjB2LHDq1K1t0dHAzJlA//6eK1c5qGaeISIiIlKItDRg4EDrIAQA2dmm7WlpnilXOTEMERERKYXBAGRkAAsWmL4bDJ4uUUkGg6lGyFafXvO2lBRllt0OhiEiIiIlSEsD6tUDunQBHnnE9L1ePeXVsmzZUrJG6HZCAFlZpuNUgmGIiIjI09TU7HTmjLzHKQDDEBERkSeprdkpIkLe4xSAYYiIiMiT1NbslJhoGjUmSbb3SxIQE2M6TiUYhoiIiDxJbc1Ovr6m4fNAyUBk/nnGDFXNN8QwRERE5ElqbHbq3x9YvBiIirLeHh1t2q6yeYY8vjaZO3BtMiIiUiyDwTRqLDvbdr8hSTKFjMxM5dW2uHgGas2sTUZERKRp5mangQNNwef2QKT0ZidfX8DBRdOVjM1kREREnuZlzU5qw5ohIiIiJejfH+jb1ysWPlUbhiEiIiKl8JJmJ7VhMxkRERFpGsMQERERaRrDEBEREWkawxARERFpGsMQERERaRrDEBEREWkah9YTERF5IxcvleFNGIaIiIi8TVoaMHYscOrUrW3R0aZlPzibdQlsJiMiIvImaWmmdc5uD0KAaSHYgQNN+8kKwxAREZGZwQBkZAALFpi+GwyeLpFzDAZTjdDti72ambelpKjvulyMYYiIiAgw1ZjUqwd06QI88ojpe7166qpJ2bKlZI3Q7YQAsrJMx7mCSsMkwxAREZG3NC2dOSPvcc5QcZhkGCIiIm3zpqaliAh5j3OUysMkwxAREWmbp5uW5JSYaBo1Jkm290sSEBNjOk4uXhAmGYaIiEjbPNm0JDdfX9PweaBkIDL/PGOGvPMNeUGYZBgiIiJt81TTkqv07w8sXgxERVlvj442bZd7niEvCJOcdJGIiLTN3LSUnW27qUeSTPvlbFpytb59gdBQ04guAEhKMn3JPQO1wQCcPevYsQoOkwxDRESkbeampYEDTcHn9kDkqqYlVzEYgHfeMV3PpUu3ts+dK//s07Zmubbl9jCp0CVC2ExGRETk7qYlV0hLA8LCgIkTrYMQIP+oLnujx+50e5hcvlyxQ+8lIWzVCXqXvLw8hIaGIjc3FyEhIZ4uDhERKZVCay7KZA4npX2km2toMjMrdk0GgynElBWEANPItRkzTP+2VT5zWLITON31+c0wREREpGbOhBMASE839R8qr4wMU61OWaZPB154wfTv0spXSkhz1+c3m8mIiEi9VLr8g6zKGtp+p4qO6nL08WFhpnCjgqH37EBNRETqZKsDb3S0/B2Flc7ZcFPRUV3OTkWggqH3Hq8Z2rx5M3Q6HSIjIyFJEpYtW2a1XwiBN998ExEREQgKCkJycjIOHz7smcISEZEyqHz5B1k5E27kmH3a2VmuVTCPk8fDUEFBAVq0aIFZs2bZ3P/uu+/iww8/xGeffYYdO3YgODgY3bt3R2FhoZtLSkREiuAFyz/Iqqxwcjs5pghwdpZrR8on9xIhTvJ4GOrZsyfefvttPPTQQyX2CSEwY8YMvP766+jbty+aN2+Ob775BqdPny5Rg0RERBqhgj4oblVaODGrUQNYskS+5kNnpiK4vXz2PPywzZBmuOGeQOvxMFSazMxM5OTkIDk52bItNDQU7dq1w7Zt2+w+rqioCHl5eVZfRETkJVTQB8Xt7IWTGjWAyZNNs0SXNwjZ66Tevz9w/LhpdNr8+abvmZm2n6d/f+Cf/7T/HNOmWZo2r+ZcRdor2zGy0RY0qnW5fGV2kqI7UOfk5AAAwsLCrLaHhYVZ9tmSmpqKyZMnu7RsRETkISrog+IR/fubluGQc56ksjqp+/o6NkzfYDCFKTuEAK4+9iyGBEVhw6WWuIH7/t7jnsoMRdcMldeECROQm5tr+crKyvJ0kYiISC7OduDVEnM4GTq04muRydlJvYymTQkCVa6fw7VL13EDAWjgdwIp92zCirf/V87CO0fRYSg8PBwAcPaOReDOnj1r2WdLQEAAQkJCrL6IiMhLONuBl5wndyd1B5ssx7fYgP36ozhcVAfTd3VG5xdaOHb+ClJ0GIqNjUV4eDg2bNhg2ZaXl4cdO3agffv2HiwZERF5lDesJaZkMnVSz/7tDGY/uhkTnrvi0NPqZnRF094NIPk4MDJORh7vM3T16lUcOXLE8nNmZiZ2796N6tWro06dOkhJScHbb7+NRo0aITY2Fm+88QYiIyPRr18/zxWaiIg8zxV9ZMiknJ3UhVFg1/wD0H95Fvpfw7DrelMAEfBBRzyH/0MUsuEDG7VNt69s7wEeD0O//fYbuty2xsm4ceMAAMOHD8fcuXPxyiuvoKCgAE899RSuXLmCTp06YfXq1QgMDPRUkYmISCkc7cBLznGik/r1S9ex8cO90C+8Dv3BRjhtbAqgKQBAghHt7tqHPh0uQrR8FdJ7LwKQrJvfFNC0yYVaiYiItMhgsF+rZl78NTvbZr8hIUkoCKqFYVWWYs3ZlriOypZ9wbiKByL2QtfjJnqNb4La8bVuPdDW6DTzyvZctd61GIaIiIhu48i6bubRZIBVIDLCVJMzEIuxFP3hAwP6+yxFz8g/kfBAFJq/+xgCawTbf+7SQtgdGIZkxDBERET0N3PIufPj39xc9XcH9KK8Iux/eibqLZ6GasXnLYedRAxSMAOnghvj5dgl6Hv6U/hfum3uPxkXy2UYkhHDEBERaUJZtS7m5i87I8WEJKGgci2MqJKG1TktUIC74AMDErEFdXEcUdWuoUGvODw4vikijm11KFRVhLs+vz3egZqIiIhk4EjTV1mTHwqBuwrO4ULBTRTgLkT6nEHvuw9DN6gyuqYMQVD1INOBBgOgK2UeIkkyzUPUt2/JMKbA0X8MQ0RERGpnr+nLPFu0uZbGwSHzY5puwPv/CkOrR5pA8rExssyZeYjMo/0cCWsewjBERKQlCv3LXFHU9hqVNVu0JMEw5kUsWF0DR5ZewiQHTjnwk65AUlP7Bzg7D5GjYc1DFD0DNRERySgtzdRfpEsX4JFHTN/r1XNujSlvp8bXyIFaGt8z2fjyC4G3LjyDLERbRoSV4Oi6bs4sliv30h4uwDBERKQFci666a3U+ho5WEvTrtLvmNBxC64/O97Ux7ki67o5s1iuTEt7uBLDEBGRt1PBX+Yep9LX6HLmFWxYeNGhY6eubY23f07C3Z+kQKroum7OLJZbzqU93IlhiIjI26ngL3OPU9FrdHjdcXzQNwNdqv2BWvXvwgPLnnW+6at/f+D4cSA9HZg/3/Q9M9O5fjuOLpbrTJOah7ADNRGRt1PBX+Yep+DXqLiwGL98sQ/6by5D/2cdHLxRH0A9y/74gMPYVHc0Hj00CUKSIDm67pcc67o5sliuuUnNztIenl6kFWAYIiLyfir4y9zjFPYa5Z7MxZrp+6BfbsSq43G4JFpY9vnhJjpX2wNdUj50L8aiflIjAG8CaQm2h67bWfdLNmWFKnOT2sCBpuCjsEVaAc5ATUTk/cpYdNPyl3lmprKHkLuSu18jG8P3j23Jhv7DTOgzqmDT5WYoRiXL4dWky+hVbx90fX3Q/aV4hNYJdfi8irmnTi7SCnA5DlkxDBGR5tlZdFPOpRNUz12vkY1QkINwPIdZWIpb52/sfwy65iehe7waOoyOh1+gFzTmOBnWGIZkxDBERIRy/WWuOS5+ja5/+R0CRz8GAFbdnc2dnydVfhdVk9tAN6YeGnWrV+HnUzuGIRkxDBER/U3JzShKIfNrdHJbNvTTj+DHDYH4/NIARCLb5lBuIUmQtN5ceQcu1EpERPKTYwSRt6vga2QsNmLnvP3Qz7kA/e8R+LOwMYAodEYGopFt93GSrfW8yC0YhoiIiCqo4FwB1s/YC/2SG1h5pDHOGhMs+3xgQIeQvRgfuwH4nwMnszV8nzV6LsUwREREVA6ndp7ByumHoV8fhA3nm6EI7Sz7qiAPPaL3QdfLgJ4vNUXNxi2AjMtAl7fLPvGdw/cVvNq7t2CfISIiUi4F1YgIo8Cu+Qeg//Is9L+GYdd161Xd6/llQRd3DLqhd6HzmGbwv8vf+gTlGb5vb7V3jYwCZAdqGTEMERGpkAJqRK5fuo4NM/ZAv6gQKw81wmnjrVobCUbcd9c+6DpchO6ZKMT3bQjJx86SGGbODN83hyd7y4RoYH4ohiEZMQwREamMB2tEzuw+ix+nH4J+rT/W5TTDdVS27AvGVTwQsRe6HjfRa3wT1I6v5fwTODp8PyMD6NKl7POlp3tth2uOJiMiIm0qawV5STKtIN+3ryw1IsIo8L9Fh6D//Az0O2phZ0E8gDDL/hjfbOiaHoFuSDCSxiQgsOp9FXtCR9bzAhS9Xpq3YRgiIiJlcWYF+XLWiBReKUTGx3uh/6EA+r8aIsvQGEBjy/57g/dB1+48dE9FoMWguyH5RNk/WXk4MnxfYeuleTOGISIiUhYX1Yic23ceP75/APrVlbD2TAIK0MayLwjX0C18D3QP3ECvl+5GRMt4p87tEipY7d1bMAwREZGyyFQjIowC+5Yfgf6zbKz4pQZ2XI2HwK3gEC2dQkr0EnRpk4f4EW0R0CtZWR2RVbDau7dgB2oiIlKWCqwgf+PqDWz6eA/0C65Cv78+jhfHWO1vFfQXdG3PYliLP1E/7T1IZY1UU8LQfg2vKcfRZDJiGCIir6WED2tXcGII+sXDl7Dq/f1YsdIXa7LjkY9bv+cDUIiutfZAl3wdvV9qhOh7IxwfqaaAof0W3nqfy8AwJCOGISLySkr6sHYFOzUi4oPpOBDYEvpPsqDfWg2/5CXAiFvBIMznHHo3PAjdAH8kpyQguHbwrcc7OnfPBx8AgwdrdrJDpWAYkhHDEBF5Ha3MTPx3jUjx8Szs+bUQ/93WACv2NsDR4rpWhzUPPAhd6zPo82QttBnWFD5+ttaFh+Nz99SqBZw/b3ufBiY7VArOM0RERLa5eR4eT7mceQU/TdsH/Up//HSyD3IRatnnjyJ0qbEHun8UoPfYBqjb0XpovF2OjkCzF4QAWYb2k7IwDBERqY0b5uHxlMPrjkP/8XGs2FQVP+cmwICOln01pQvoVf8A+vT3Q7eUeFSJbFPKmeyQc04eTnboNRiGiIjUxotmJi4uLMYvX+zDynkXkPO/s7hZLOEMIrAFzWCEL+IDDkN3TzZ0I2qg3cg4+Pp3qtgTOjJ3T82apdcMmXGyQ6/BMEREpDYqn5k492Qu1kzfhxXLBH460RSdxVHMxFjE4FZtV35QLRS89hbC33waQCP5ntyRuXtmzQLGjeNkhxrCMEREpDYqnJn4WMZJ6D/MhD6jCjZdboZidAAAPIQ0LMZASLC+jiqFF1Bl0rNAQi35O4L372/qYG5rJJ557h5fX052qCEcTUZEpEZOzMPjCYYbBuyYsx8r5lyEfnc09hc1tNrf2P8Y+jbPxH+OPAr/K2ch2TqJq0dtlTV3j4YnO1QKDq2XEcMQEXklhX1Y55/Ox9rpe6FfasCPx5rggqhp2eeLYiRW3QPd/bnQjamHRt3qOT7MPT3dcx3BNTrZoVJwaD0REZWuf3/T8HkPflif2HoK+hlHoU8PRsbFZriB9pZ9ochFzzr70KcP0GNcHKrF3mP9YDV0BHdkdXlSPcWHIYPBgEmTJuHbb79FTk4OIiMjMWLECLz++uuQJJsVq0RE2uHmD2tjsRE75+2Hfs4F6H+PwJ+FjQFEwwcGJGIL7vH9Ew3rGxH3VCd0eq4FKlXuYP9kKu8ITt5D8WFo6tSp+PTTTzFv3jzEx8fjt99+w8iRIxEaGooXX3zR08UjIndjs4XbFZwrwLrpe6FfcgM/Hm2Ms8YEyz4fGPBa0Ey8KqYgpPA8YABwGMDMaKB+GcuCmDuClzZnEuDYMHeiClB8n6HevXsjLCwMX331lWXbgAEDEBQUhG+//dahc7DPEJGXUOtaXCoMcKd2nsHK6YehXx+EDeeboQiBln1VkIce0fug62VAv4SjqPLiyPIvC7J4MTBoUOmFiYnxzqUvVPi+cDe3fX4LhXvnnXdE3bp1xcGDB4UQQuzevVvUrl1bfPvttw6fIzc3VwAQubm5riomEbnakiVCSJIQpo/dW1+SZPpassTTJbRtyRIhoqOtyxwdrbjyGm4axM55+8Sb96eLe4L2l3iZ6/mdFC+2yBDrpv4uivKLTA8qLi55bXfem5gY03H2pKfbf/ztX+npbngV3Egl7wtPc9fnt+KbyV577TXk5eWhSZMm8PX1hcFgwDvvvINHH33U7mOKiopQVFRk+TkvL88dRSUiV1HrWlz2FlPNzjZt9/Dw9+uXrmPDjD3QLyrEykONcNoYByAOACDBiPvu2gddh4vQPROF+L4NIfnEWJ9AjmVB1NCJWm4Kf19okeLD0MKFC/Hdd99h/vz5iI+Px+7du5GSkoLIyEgMHz7c5mNSU1MxefJkN5eUiFxGjWtxKTHAGQy4OGc5/jdvN9bvC8eHl4ehAG0tu4NxFd0j90LXsxgPvtQYteOblX4+OYKMt3aiNhhMUwdkZJh+Tkq69d5U2vuClN9MFh0dLT7++GOrbW+99ZZo3Lix3ccUFhaK3Nxcy1dWVhabyYjUbP58x5pS5s/3dElNiouFmD5dEc0/RoNR/PH9AbEwYbLIkcKsnvskosVon8/FcwkZ4qe3dorrl687d3I5mrjMTW22mkAdbWpTmiVLhKhRo+S11KghxOTJinhfqAWbyf527do1+Pj4WG3z9fWF0Wi0+5iAgAAEBAS4umhE3k8pHTzVVHtgq5N3aVzQ/FN4pRDpH+6BfuF1rDzQAG0M+7AYk4A7lryIRjZmi6chTV4M9O/s/BOdP296PxgMtvc7siyII2uFObv0hSfft2lpwIABtvddvAhMnOjYebypWVANXBq1ZDB8+HARFRUlVq5cKTIzM0VaWpqoWbOmeOWVVxw+BztQE5WDHB08i4tNf+HOn2/6Xt6/7tVSe2Cvk7cbagDO7j0nvh65WTwUsU0EI99yeh8UiyxECWNFOjmX91qd6dhu6/0WE+N8h2JPdkwuLhYiKsq5+8+aoVK56/Nb8WEoLy9PjB07VtSpU0cEBgaK+vXri3//+9+iqKjI4XMwDBE5SY6RW3J/KJnLdGe5lDKarKyRVTIHOKPBKP5cfFC80y1d3HfXn0KCwer0kT6nxdNNN4lfhn8q/4evI9fq6yvEokXOXVRFw7OnRxw62mzowveFt2EYkhHDEJET5Bgu7aoPJblqD1zBmQ/Ccr4ORflFYm3qb+KF5hmint/JEqdtFbRfTOycLn77735hNBhND5K7v5WC+kOVKFdF37cV5ehrfXuZlBjsFYR9hojIMyo6csuVo6gUsBaXXc708YiOdngx1QsHL2LV+39Bv8oXa7LjkY/Wln2BuI6utfdAl1yI3i81QlSbpgCaWp9Azv5WCugPZVd537dy9i9yps/a5MnAF1+UnEDUQ4vsah3DEJHayd1ZtKLDpV09DF6pC2c6+kE4fTrwwgt275EwChxYdQz6T7Kw4ufq2JYfDyM6WfaH+ZxD74YHoRvgj+SUBATXbmvzPBbmJS+ys20HVEc6OQP258Ypjas6tNt6z5fnfSv3jOaJiUBUlOm1Lk10NPDvf5u+lBjstciZaqSTJ0+6qobKpdhMRl7LFZ1FKzpcWm3D4OVSgU7eNwpuiA3TdomUezJEA7/jJR7aIvCAeL1Tutjx9V5huGlwvmwV7W/l5v5QZV6Lrfe8s0PWXdmUW1YZ2AzmMEX2GapcubJ44403REFBgavK4xIMQ+SVXPXLvKIjt7S6vIIQToWOS8cui++e+1k8XGerCMUVq8P9USi619gpPh6UIY7/nCXPqLyK9LdyQ38oh6/B3nseMM3j48j71tX9i0qbZ4hByCmKDENbt24Vbdu2FZGRkWLOnDkuKpL8GIbI67jjl3l5axI8NQxermH8FWUrdNSqJcTCheLg6mNiWu900Tn0D+GLm1aH1JTOixENN4slL28Tedl5pZ/PVu2fI9df3tfImY7BrurQ7sh73hyGynrfuiOwFxcLsX69EK+/bvpav54jxMpBkWHIbN68eSI6Olq0atVKbN68We4yyY5hiLyOO36ZV6Qmwd3D4JW26OWiRaYAdFt5TiNcPIQlVkWMDzgkXrsvXWz97E9RXGTjg9LR2j+5r//O0LR+vWPvt+nTXRdyX3/dsTJMnlz2+1aNTblKCftupugwJIQQBQUF4o033hDBwcFiwIAB4tixY3KWS1YMQ+R13PXLvCK/gN01DN7Tc8vc4epn3wgjUGKSQwMkYYAkJt31rpjZP0McTT9R+okcrf1buFDe67cXrBxtgpKTrbI48p4v632rtqZcpYV9N1JFGNqyZYsYO3as8PHxEYGBgeLll18W+fn5cpZPFgxDpEql/UJXyy9zV/81q4S5ZYQQR9NPiBkPZYjkqr+Kk4gSBjvlMTpTHkfvcc2aFbv+2++RvU7It4cgd9b2OTubt6PvebXMaC6E4sK+uykyDH366afiiSeeEM2aNRN+fn7C399ftGrVSjz33HNi9uzZokuXLiImJkbs3LnTVeUtF4YhUp2y/hIs65c5YGqmcWKmdlXyUCgsLioWP3/yP/Fqu3QRF3DY8jSdIWN5nJ3ArzzP50zNi7lPzp3LTbiits/Z0WvlCTBKn9FcCMWEfU9SZBiKjo4WAwYMEO+9957YsmWLuHbtWolj3nnnHREfHy9bAeXAMERuV9HmJUf7idj6ZW4vQHkjN/b9yMvOE4v/+Yt4vP4WUVM6b3V6X9wUSVV3iZWtHOzX4kh55FjaobTnK2/Ny/r1ru+74uy1y9kkqJQZzYVQTw2wCykyDDkiJydH+Pj4yH3aCmEYIreqSPu+s38JlvWXfUX+ylVDh01nPizKcT3Hf84SHw3MEA/U2Cn8UWh1ylBcEUPr/izmj9kqLh277Hx5yuJIU84dnbQdfr7y1Lw4E+QqytlasYoEGCW/z9XY0Vtmqg1DRqNRZGRkyH3aCmEYIrepaPt+eT5Mi4oq3m/E1nWoocOmo30/Fi1y6HoMNw1i+5d7xL86pItmgQdLnK5hpUzxUqt0sfH9XeJGwY3yl0euphzzdTn7fBWpdXJHLYSj5Xv9deUFGDmxZki9YUiJGIbILeRo3y/PX4Jy/8JUUodNR/5qLyswvPxyqddz/evvxNLXtosnGm0WYT5nrQ7xQbFIDNkt3n0wXfz149Fbi5+WRu6+KGU15ZTn+crTH8md/VPU1MHZlfg6MAzJiWGI3EKOUFKec8hZla6kDpvO1E7ZCwwLF5Z6PQZAnES08EGxZXMV5IpB0b+Ib57eIi4cuihf2V3ZlOPs87mrT05FqKGDszto/HVgGJIRwxC5hRyhpDx/CcpZM6SUavny1E7ZCgwOXs/DPt+LF1tkiHVTfxdF+TKNwHN3XxRnns+R0YhyBbmKUHoHZ3fR8Ovgrs9vrlpPJBdHV+gu7ThfX9OK2QMHmlYTF+LWPkkyfZ8xw3pla7lWJQcqvmK9HAwG00ritq5FCNP1pKQAfftavw53rGZ/7cI1/DVzC1o78JTzvzFAerRzRUtu7Y7ylJutFdptrWzuzPM58j6bNAlo1Mizq6n372+6z1pf2Z2vg+u5NGopBGuGyC3kbN939i9BuarSlVAzVIEynP4jR3w+bJPQhW0XQSiQd94fT3B1R3YN1ziQOrjr81sSwtafX94lLy8PoaGhyM3NRUhIiKeLQ94sLc301zZg+6/txYtNf+U5wtEagdufe+xY4NSpW9tiYkw1Sc48Z716ZdcyZWa67q/SBQuARx4p+7j58yGGPIzdPxyE/osc6HfUxm/X4qwOqetzEn/4tEHV4vOQbJ3DHddTXub30p33oTzvpdI4+z4jciN3fX4zDBHJTY5QUl5yfLDJGejKIyMD6NKlzMOm15uB6VkDkWWIstreNngvdPddgO6pCDQfeDekZUs9ez3lYQ6lt7+HbqfkEEckI4YhGTEMkdup/a9tTwe6UmqnjJBwCtGIRSaM8EUQrqFb+B7oHriBXi/djYiWYSXP6cnrKQ8HAyHS0+Xpl0SkUAxDMmIYIioHDwY6sXgJMGgQAGHVvGX8+6enpC/g16QRdIOD8I8XExBUPajskxoMppCRkWH6OSnJ9KXEkOpEUyGGDnV9eYg8xF2f3xxNRkS2yTUaykFFeUXYNGsv9AuuYuVfbXEPFmMmxiIGt2pz8gNq4sLTr+OL6U9A8rHZC8i+5cuta4feftvU1DRzpvJqh+QYmUhEDmPNEBF5zIWDF7Hq/b+gX+WLNdnxyMet/5+BuI5utXZjVPNf0alLJVTvGFf+2il3dUaWixI6shMpAJvJZMQwRKQMwijw18qj0H96Cvqt1bEtPx5G3PowD/M5h94ND0I3wB/JKQkIrh1c8SdVa2dkT3dkJ1IANpMRkVe4ee0mtny6F/rv8qDfUw9HixsCaGjZ3yLwIHRtzkD3RC20GdYUPn615S3Ali32gxBgChpZWabjlNQZuX9/U+C5s+N3dLRyO34TqRTDEFFFqH3UmItcOnoZP72/H/qVElZnxSMX91j2+aMIXWrsge4fBeg9tgHqdmwMoLHrCqOEWbXLizMPE7kFwxC5nrcGBlvDtZXaIdcNDq3JhP7jE9BvqYqfcxNgQEfLvlrSefRqcAC6hyqhW0o8qkS2cV/B1N4Z2c0d2Ym0SNt9hrz1Q1pJvDUwqK1DrgsUFxZj6+y90P/3CvR/1sWhm7FW++MDDkN3Tzb6jKyBtiPi4Ovvof9b7IxMpFrsQC0jmy+mt35IK4m3Bga1dsiVQe7JXKx+fx/0KwRWnYjDZVHNsq8SbqBz9T3QJV2Fbmx9xN4f48GS3oGdkYlUiWFIRiVeTG/9kFYSbw4MGpsd+OjGE9B/dBz6TVWw+XIzFKOSZV916RIerLcfffr54oGUOITWCfVgScugtlmoiYijyVzGYDD9QrSVAYUwfUinpJg6LartQ1pJ1DqCxxFq7pDrAMMNA7Z/tQ/6eZew4o8Y/HWjAYC6lv1N/I9C1yILuserof2oePgFdvJcYZ3BzshEZIf2wpA3f0griTcHBrV3yLUh/3Q+1ry/F/plBqzKbIILorllny+KkVh1D/p0zoXuhVg07NoAQAPPFbYi2BmZiGzQXhjy5g9pJVFbYHCmM31ioqmJr6wOuYmJri1zBZ3Yegr6GUexYuNdyLjUDDfR3rKvqnQFPevsg04noce4OFSLvaeUMxERqZv2wpDaPqTVSk2BwdnO9L6+pn0DB5quw1aH3BkzFNf8Yiw24te5+6GfcwH6XZHYU3g3gGjL/oaVjkPX7Dj6DKuKjk/Fo1LljvZPRkTkRbTXgTo4mMNs3UUNI3gq0pneUx1ynajFKjhXgHXT92LFkhv48UgTnBO1LPt8YEDHkL3QdboM3fN10LhHrPOLnxIRuRBHk8nI7mgyQLkf0t7C3YHBmeYuOUa8uXuuKgdqsU7tPAP9B4eh3xCEjeeboQiBlkOrIA89ovehT28jeo5rihqNqruurEREFcQwJCOH5xniMFt5mYNCdjZw/jxQqxYQFeW6wOBsc5fahsjbqcUSkgQI4Pumk/Du8cHYfb2J1f5Yv5PQxWdC90gV3P9cAvzv8ndnqYmIyo1D612Nw2xdq7Rg4qogZKu5KzvbtN1WbZ+aOtOXMiWEJASMkNDxry/xJ/4NCUbcd9c+9Ol4EbpnoxGnawDJp45rysT/P0TkBbQbhgAOs3WV8gSTiijv3FFq6kxfxpQQPhCogyz8+OAnaPXuw6gd38y15eEM7kTkRXw8XQBHZGdn47HHHkONGjUQFBSEZs2a4bfffvN0sciWsoIJYAomBoN8z+nM3FG3M494k+x0GpYkU9Oph0a8CaPAHwsO4D//yMC/u+906DE9HquJ2vG1yj6wIsxh987X3Bx209Jc+/xERDJTfM3Q5cuX0bFjR3Tp0gU//fQTatWqhcOHD6NatWplP5jczxOTWpa3ucsTQ+TLaFoqvFKIjTP3QL/wOlYebIhThiYAmqCzo+d3dS0WZ3AnIi+k+DA0depUxMTEYM6cOZZtsbGxpTyCPMoT/XAq0tzVv7+p2c5Wk4/cnentNC1dGf8fpP2vIfRrKmHdmQQU4F74wIBEbME/sBYx1a6hwYONYVgfAd9zOZ6dt4kzuBORF1J8GFqxYgW6d++OQYMGYdOmTYiKisJzzz2H0aNH231MUVERioqKLD/n5eW5o6gEeKYfTkUneHRHZ3o7/aiMp7IR8tKTWInFWAZT8HpS+grv+k5A9eLzpoMuA9gUDTz+GDBtmmcnelRTp3MiIgcpvs/QsWPH8Omnn6JRo0ZYs2YNnn32Wbz44ouYN2+e3cekpqYiNDTU8hUTE+PGEmucJ/rhmJu7zOe/8/mAsoOCuTP90KGm7zI3jYkXXoStWSx8YNr2ifQ8JnfegKNjP8QXGH0rCJllZ5uC0D//aZqe4HbVqgFvvgmEhgILFpimDJCzT9bt1NTpnIjIQYqfZ8jf3x9t2rTBL7/8Ytn24osvYufOndi2bZvNx9iqGYqJiXH5PAX0N09NaqmwuaPO/3UBqz44gGPL/ofJF8aU/YD164ERI8qeBPLIEWDKFFMAvHTJ9rGuGtllnqiSM7gTkRu4a54hxdcMRUREIC4uzmpb06ZNcfLkSbuPCQgIQEhIiNUXuZG5H86dNRjR0a6d3bt/f+D4cdMkifPnm75nZrotCAmjwP4VRzC1ZwY6hfyJ8LhqGPFlJxy64OAszxkZjvXHmTIFmDTJfhACXDeyS45aOCIihVF8n6GOHTvi4MGDVtsOHTqEunXreqhE5BBPTWrp6rmj7hgNdrP1fdj82X7o5+dDv7cejhU3BNDQcniLwINIbngW2CtjGWbOtF0rcztXjuxyZ6dzIiI3UHwz2c6dO9GhQwdMnjwZgwcPxq+//orRo0fj888/x6OPPurQOdxVzeYVOKuwfTaa4bIRiRfwEZb+3fnZH0X4R80/oet6Db3HNkSd9lGONy3NmQMkJ8tf7unTgbAw+e8n3ytE5GJu+/wWKqDX60VCQoIICAgQTZo0EZ9//rlTj8/NzRUARG5urotK6CWWLBEiOloI00e26Ss62rRd4079+xNhBITh9tcGEAZIwgBJfBT+lljy8jaRl51n+wRLlgghSaav289h/jklRYj160u+/nJ/8X4SkYq46/Nb8TVDcmDNkAPsLaHh6k7PClVcWIyts/dC/98r+PF/0Vhb3AVROGWzk52QJEiOdBq21cHb19d65FeNGsDFi7JdRwkavZ9EpE5ctV5GDENlMDfjlDWKyctHCF05kYvV7++DfoXATyfjcFmYZjnvjAxkQKbV7c1NS8uXm/rXeIJG7icRqR9XrdciT/XB0PCswkc3noD+o+PQb6qCzZeboRgdLPtqSBfxYOxfeK7xJuAnB07myESDvr6m+zpsWPkLXVFefD+JiMqDYUgpPLkKuIZmFTbcMGDbl/ugn3cJ+t0x+OtGAwC3RiY28T8KXYss6B6vhvaj4uEX2AnIKHYsDDk60WBZ4dNdvOB+EhHJgWFICez11zHPFePq/h1ePqtw3qk8rJ2+D/plBvyY2RQXRXPLPl8U4/6qe6DrnAvdC7Fo2LUBgAbWJ6joch93kjOEmEeK1a5t+vncOeDsWeCll8p+rErvJxGR3NhnyNOU0F/HC2cVPv7zKehnHIU+/S5kXGqGm/C37KsqXUHPOvug00noMS4O1WKrln1COWfVzsgAujjQB6k0pd0TL7yfRKRNnIFaK5zpr+MqXjCrsLHYiO1f7sW/O2agedAhxCZG48UlnbHuUmvchD8aVcrEuNYZSJ++G+euBmP+8Y4Y+lEHx4IQIO+s2o6s31ajBlDdzszVZd0TL7ifRETuxDDkaUrpr+OpJTQq4GrOVSx9dTueuHsLIvwvov3oBPzfL0nYU3g3fGBAYsj/8O6DGTiw6hgO3YjF+78lISmlJSpVrlS+J5RruQ9Hwsrnn5uavCZPLhmKHLknKryfRESewmYyVytrhJijTSaODNuWg8JnFc7acRorZxyBfkMQNp5vhiIEWvaFIBc9YvZB10ug57imqNHIwTXBPMXRhWUrck8Ufj+JiErDeYZk5LEw5MgIMU/171DJh6Sx2IjfvzsA/VfnoP8tHLuvN7HaH+t3Err4TPR5tAoSn02A/13+ds6kUCq5D0REnsAwJCOPhCFnZnSWs3Ouo2Xz1DB+B1y7cA0bZu7FikWF+PHw3ThjDLfsk2BE+yp7oetwCbpnoxGnawDJx07fGyIiUjWGIRm5PQyVZ4SYo00mFaXQZTdO78rByg8OQb8uEOvPNUMhgiz77kI+Hojchz4PFuPBcU1Qq2lNt5ePiIjcj2FIRm4PQ+XtB+TqJhMlDOP/mzAK7P7hIFZ8ngP9r7Xx+7U4q/11fE9BF3cUuiHBSHqhGQJCAlxaHiIiUh4ux6Fm5R0h5uvr2k7S77zj+DD+xETZg1nhlUJsnLkH+oXXsfJgQ5wyNAFwqw9Q2+C90N13AX2eiUSz/o0g+URX6PmIiIgcwTDkCkqc0TktDZg40bFjly83rZ0lQ5+is3vPY+W0A9Cv8ce6nARcw72WfZVRgG7he6HrfgO9xjVGePMEp85NREQkBzaTuYLSZgAuq3nMEQ72KRJGgT1ph6GffRr6bTXxa0EcxG3TWUX5nEHvxofRZ0gQuryQgKDqQXbPRURE2sZmMjUzT6o3cKApRNgaIebOGYDlWBhUCFPZU1KAvn2tyl6UV4SMj/ZA/0MBVu5vgBOGuwHcbdnfuvJ+6Nqeg25UGO4Z2gSSD9fEIiIi5WAYchXzDMC2hrDLPUKsLHLNXn1bn6LzYQlY9cEB6H/yxZrsBFxFG8thgbiOrrX3oE+3QvRKaYSoNnEA4uyfV+04VxARkaoxDLlS//6mWhRPf1DK3DdpYs8deKvwfgh0smwL9zmL3o0OQjcgAMkvNUPlmm1lfU7FUvicTUREVDb2GdKCsvowOSkJ6diEJLQIPIg+956B7snaaP1oE/j4aWypO3tzNpktXAgMGuTeMhEReRH2GSL5lNaHyQnmR73WfhO+eb8R6rRvDKCxbMVUFYPBVCNU2ms5dKjp9TbPLk5ERIqksT/lVcRgME3euGCB6bvBULHz2VvF3AnS3189Tn2FOm3DyzrcuznSKd1gMNUMpaW5p0xERFQuDENKlJZmatbq0gV45BHT93r1Kv6h2r8/cPw4DGvWY/+w/8Onjd7HGYTDCCfX9jJPzKhlznRKT0mpeJglIiKXYTOZ0tjrh5KdbdpezrXDrpzIxer390G/QuCnk61wWXQFAKxDPSzGQBjhZDIu7wg1bxl55UyndHN4dOXs4kREVG4MQ0pSWj+UUub5sefIhhPQf5QJ/aZQbLmSgGJ0sOyrIV3Eg7F/Qdc3AoVNv0Hl/0xwbi6i8oxQ86aRV4mJprI7+prJNb0BERHJjqPJlKS8C7z+zXDDgG1f7oN+3iXod8fgrxsNrPY38T+KPi2zoBteHe1HxcPX/7ZAZa6xyc42Ba4LF2w/d3lnz7ZX4+XgzNaKlJYGDBjg2LHme+YtNWNERG7A0WRaVI4FXvNO5WHNB/ugX27AqsymuCiaW/b5ohj3V90DXedc6F6IRcOuDQA0sHFCWC8SGxR0awSUHLNny1zjpRj9+5uGzw8dar9PkDk8JiZ6V80YEZEXYRhSEgebnnIu+GHRwE3Qp9+FjEvNcBPtLfuqSlfwYJ190PWR0GN8PKrWvcf5csg9e3ZZI69um9ladf1qBg0yBR5b8wndHh6XL3dJXzAiIqo4NpM5yh3NG2VMjigA5CAC0ciCEbeeu1GlTOian4Dusaro+FQ8KlWuJF955LjmBQtMo+LKMn++qZZFjWzV+sTEmIJQ376lL5Tr7oV7iYhUgs1kSuKu5o3bJkcUkgTptkBkHv7+PD4GACSG/A+6TpfRZ0wdNO5ZH0CsfOW4vTxy1NQ42tla5mVDLNwRZEtbeiUjw3trxoiIvADDUFlcNNTdlqwdp6FfWAMX75qCkfkfIhrZln2nEYkfajyH/oPC8MW4XNRo1EKW53QL88gre8uB3N6vRm7u7KdjLzyWoy8YERG5D5vJSmNutnJR84ax2IjfvzsA/VfnoP8tHLuvN7Hs84EBg30Wo0f0PiT0jEazqcPgHxrk9HMohjlUArY7Zbuiz4xSRrBVcJQgEZFWuauZjGGoNC74ELt24RrWT98D/ZIirDzcGDnGMMs+CUa0r7IXug6XoHs2GnG6BpB8nJwdWslK61cjdyhxcZAtV1nKqhljnyEiIivsM6QEMjVvnN6Vg5UfHIJ+XSDWn2uGQrSz7LsL+Xggch/6PFiMB8c1Qa2mzUs5k8qV1q9GbkoawVbaQrnlna6AiIhkwzBUmnJ2/BVGgT8WHID+y7PQ/1obv1+LA3BrYdM6vqegizsK3ZBgJL3QDAEh98lYaIWTq1N2WZTWT0fu6QqIiEg22g5DZY0ycqLjb+GVQmycuQf6hdehP9AI2camAJpaDm0bvBd92l+A7ulINOvfCJJPtOuvT8s8PYLNFnfWjBERkcO01Wdo5UqE9Ohh+vBxdJRRKR1/BYANnf+Djw90w7qcBFxDsGV3ZRSgW/he6LrfQK9xjRHevLZrL5KssZ8OEZHqsQO1jCwvJoCQ6GjTxH7Tpjk+yshGcMqRwvGcmIWluHVclM8Z6Jochm5wELq8kICg6ioe/eUNPDGCjYiIZMMwJCOrMFTWwXfUGBTlFSHjoz1Y+X0ezu2/CB9jMc4gAluQCCN80bryfujanoNuVBjuGdrEu0Z/eQN3jmAjIiJZMQzZMWXKFEyYMAFjx47FjBkzHHqMU2Hob6sf/BBf/q8N1mQn4CqqWLYH4jqSa++BrlsheqU0QlQbN/Y5ofLhSvFERKrEofU27Ny5E7Nnz0bz5q4ffj5vVU0s+XsB1HCfs+jd6CB0AwKQ/FIzVK7Z1uXPTzJy1wg2IiJSJdWEoatXr+LRRx/FF198gbffftvlzxfsfxNvtMuA7snaaP1oE/j4hZX9ICIiIlId1YSh559/Hr169UJycnKZYaioqAhFRUWWn/Py8hx+HgEAPj74Mv9hwN+/nKVVITYlERGRRqkiDH3//ffYtWsXdu7c6dDxqampmDx5crmeSwIAoxH45RftNK04u5gpgxMREXkRH08XoCxZWVkYO3YsvvvuOwQGBjr0mAkTJiA3N9fylZWVZdlndPSJ5ZqZ2GAwrXG2YIHpu8Egz3krylyul14CBgwouXRFdrZpWHpamvX2tDTT/D1dugCPPGL6Xq9eyeOIiIhUQvGjyZYtW4aHHnoIvrfVPBgMBkiSBB8fHxQVFVnts8VqNFmtWsD582U/sRwriDtb4+Iutsply50TEyplFXgiItIEDq3/W35+Pk6cOGG1beTIkWjSpAleffVVJCQklHkOqxmou3UDGjRw/czESg0O9spVmvR0U1OYUlaBJyIiTXBXGFJ8M1mVKlWQkJBg9RUcHIwaNWo4FISsJCaaOkXPnGn6WbpjgkS5VhA3GEw1L7YCh3lbSor7m8xKK1dpzpxxbhV4IiIiFVF8GHIJ8wriUVHW26Oj5amxUWpwKKtc9kREuG4VeKX2qbJHbeUlIqIyqWI02Z0yMjIqfhJXriDuquBQUc4+n7npKzHR8eDmzCrwSu1TZY/ayktERA5RZRiSjatmJnY0EDgTHOTgzPPd2WSYmGj64C+rr1ViomPnt9d3yTyKrbw1dK4a9u+q8hIRkcdps5nM1czB4c4+SWaSZFos1NHg4K5y3e7OJkNfX/n6WrmqT5Wrhv0rtQ8YERHJgmHIFeQMDnJypFwpKabRY5mZJWs65Opr5Yo+VeaaG0fnS3KGUvuAERGRLBiGXMXVnbRdUa4lS4Dp001Nh/aCWv/+wPHjpsA0f7794FQauftUubrmRql9wIiISBba7jPkaq7spO3JclW0r5XcfaqcqbkpT7mV2geMiIhkwTDkaq7qpF1RniyX3J2xXV1zI3d5iYhIUdhMRu4nd58qV9fcKLUPGBERyYJhiDxDzj5V7hi9p9Q+YEREVGGKX5tMDu5a24TKQa55gcyjyQDrpiy514Jz1TxGRERUAhdqlRHDkEbYmiE6JsbUhMWaGyIi1XHX5zc7UJP3UOroPSIiUjSGIfIuSh29R0REisUO1ERERKRpDENERESkaQxDREREpGkMQ0RERKRpDENERESkaQxDREREpGkMQ0RERKRpDENERESkaQxDREREpGkMQ0RERKRpDENERESkaQxDREREpGkMQ0RERKRpDENERESkaQxDREREpGkMQ0RERKRpDENERESkaQxDREREpGkMQ0RERKRpDENERESkaQxDREREpGkMQ0RERKRpDENERESkaQxDREREpGkMQ0RERKRpDENERESkaYoPQ6mpqbj33ntRpUoV1K5dG/369cPBgwc9XSwiIiLyEooPQ5s2bcLzzz+P7du3Y926dbh58yYeeOABFBQUeLpoRERE5AUkIYTwdCGccf78edSuXRubNm3C/fff79Bj8vLyEBoaitzcXISEhLi4hERERCQHd31++7nszC6Sm5sLAKhevbrdY4qKilBUVGT5OS8vz+XlIiIiInVSfDPZ7YxGI1JSUtCxY0ckJCTYPS41NRWhoaGWr5iYGDeWkoiIiNREVc1kzz77LH766Sf8/PPPiI6OtnucrZqhmJgYNpMRERGpCJvJ7jBmzBisXLkSmzdvLjUIAUBAQAACAgLcVDIiIiJSM8WHISEEXnjhBSxduhQZGRmIjY31dJGIiIjIiyg+DD3//POYP38+li9fjipVqiAnJwcAEBoaiqCgIA+XjoiIiNRO8X2GJEmyuX3OnDkYMWKEQ+fg0HoiIiL1YZ+hvyk8qxEREZHKqWpoPREREZHcGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI01QThmbNmoV69eohMDAQ7dq1w6+//urpIhEREZEXUEUY+uGHHzBu3DhMnDgRu3btQosWLdC9e3ecO3fO00UjIiIilVNFGPrggw8wevRojBw5EnFxcfjss89QuXJlfP31154uGhEREamc4sPQjRs38PvvvyM5OdmyzcfHB8nJydi2bZsHS0ZERETewM/TBSjLhQsXYDAYEBYWZrU9LCwMBw4csPmYoqIiFBUVWX7Ozc0FAOTl5bmuoERERCQr8+e2EMKlz6P4MFQeqampmDx5contMTExHigNERERVcTFixcRGhrqsvMrPgzVrFkTvr6+OHv2rNX2s2fPIjw83OZjJkyYgHHjxll+vnLlCurWrYuTJ0+69MVUmry8PMTExCArKwshISGeLo7b8Lp53VrA6+Z1a0Fubi7q1KmD6tWru/R5FB+G/P390bp1a2zYsAH9+vUDABiNRmzYsAFjxoyx+ZiAgAAEBASU2B4aGqqpN5FZSEgIr1tDeN3awuvWFq1et4+Pa7s4Kz4MAcC4ceMwfPhwtGnTBm3btsWMGTNQUFCAkSNHerpoREREpHKqCENDhgzB+fPn8eabbyInJwctW7bE6tWrS3SqJiIiInKWKsIQAIwZM8Zus1hZAgICMHHiRJtNZ96M183r1gJeN69bC3jdrr1uSbh6vBoRERGRgil+0kUiIiIiV2IYIiIiIk1jGCIiIiJNYxgiIiIiTVNlGJo1axbq1auHwMBAtGvXDr/++mupxy9atAhNmjRBYGAgmjVrhlWrVlntF0LgzTffREREBIKCgpCcnIzDhw+78hLKxZnr/uKLL5CYmIhq1aqhWrVqSE5OLnH8iBEjIEmS1VePHj1cfRlOc+a6586dW+KaAgMDrY7xxvudlJRU4rolSUKvXr0sx6jhfm/evBk6nQ6RkZGQJAnLli0r8zEZGRlo1aoVAgIC0LBhQ8ydO7fEMc7+znA3Z687LS0N3bp1Q61atRASEoL27dtjzZo1VsdMmjSpxP1u0qSJC6/Cec5ed0ZGhs33eU5OjtVx3na/bf3flSQJ8fHxlmPUcL9TU1Nx7733okqVKqhduzb69euHgwcPlvk4d3yGqy4M/fDDDxg3bhwmTpyIXbt2oUWLFujevTvOnTtn8/hffvkFQ4cOxZNPPok//vgD/fr1Q79+/bB3717LMe+++y4+/PBDfPbZZ9ixYweCg4PRvXt3FBYWuuuyyuTsdWdkZGDo0KFIT0/Htm3bEBMTgwceeADZ2dlWx/Xo0QNnzpyxfC1YsMAdl+MwZ68bMM3Qevs1nThxwmq/N97vtLQ0q2veu3cvfH19MWjQIKvjlH6/CwoK0KJFC8yaNcuh4zMzM9GrVy906dIFu3fvRkpKCkaNGmUVDMrzHnI3Z6978+bN6NatG1atWoXff/8dXbp0gU6nwx9//GF1XHx8vNX9/vnnn11R/HJz9rrNDh48aHVdtWvXtuzzxvs9c+ZMq+vNyspC9erVS/z/Vvr93rRpE55//nls374d69atw82bN/HAAw+goKDA7mPc9hkuVKZt27bi+eeft/xsMBhEZGSkSE1NtXn84MGDRa9evay2tWvXTjz99NNCCCGMRqMIDw8X7733nmX/lStXREBAgFiwYIELrqB8nL3uOxUXF4sqVaqIefPmWbYNHz5c9O3bV+6iysrZ654zZ44IDQ21ez6t3O/p06eLKlWqiKtXr1q2qeF+3w6AWLp0aanHvPLKKyI+Pt5q25AhQ0T37t0tP1f0tXQ3R67blri4ODF58mTLzxMnThQtWrSQr2Au5sh1p6enCwDi8uXLdo/Rwv1eunSpkCRJHD9+3LJNbfdbCCHOnTsnAIhNmzbZPcZdn+Gqqhm6ceMGfv/9dyQnJ1u2+fj4IDk5Gdu2bbP5mG3btlkdDwDdu3e3HJ+ZmYmcnByrY0JDQ9GuXTu753S38lz3na5du4abN2+WWOwuIyMDtWvXRuPGjfHss8/i4sWLspa9Isp73VevXkXdunURExODvn37Yt++fZZ9WrnfX331FR5++GEEBwdbbVfy/S6Psv5/y/FaqoHRaER+fn6J/9+HDx9GZGQk6tevj0cffRQnT570UAnl1bJlS0RERKBbt27YunWrZbtW7vdXX32F5ORk1K1b12q72u53bm4uAJS6CKu7PsNVFYYuXLgAg8FQYhmOsLCwEm3GZjk5OaUeb/7uzDndrTzXfadXX30VkZGRVm+YHj164JtvvsGGDRswdepUbNq0CT179oTBYJC1/OVVnutu3Lgxvv76ayxfvhzffvstjEYjOnTogFOnTgHQxv3+9ddfsXfvXowaNcpqu9Lvd3nY+/+dl5eH69evy/J/Rw2mTZuGq1evYvDgwZZt7dq1w9y5c7F69Wp8+umnyMzMRGJiIvLz8z1Y0oqJiIjAZ599hiVLlmDJkiWIiYlBUlISdu3aBUCe35VKd/r0afz0008l/n+r7X4bjUakpKSgY8eOSEhIsHucuz7DVbMcB5XflClT8P333yMjI8OqM/HDDz9s+XezZs3QvHlzNGjQABkZGejatasnilph7du3R/v27S0/d+jQAU2bNsXs2bPx1ltvebBk7vPVV1+hWbNmaNu2rdV2b7zfBMyfPx+TJ0/G8uXLrfrO9OzZ0/Lv5s2bo127dqhbty4WLlyIJ5980hNFrbDGjRujcePGlp87dOiAo0ePYvr06fjvf//rwZK5z7x581C1alX069fParva7vfzzz+PvXv3KqZfk6pqhmrWrAlfX1+cPXvWavvZs2cRHh5u8zHh4eGlHm/+7sw53a081202bdo0TJkyBWvXrkXz5s1LPbZ+/fqoWbMmjhw5UuEyy6Ei121WqVIl3HPPPZZr8vb7XVBQgO+//96hX35Ku9/lYe//d0hICIKCgmR5DynZ999/j1GjRmHhwoUlmhLuVLVqVdx9992qvt+2tG3b1nJN3n6/hRD4+uuvMWzYMPj7+5d6rJLv95gxY7By5Uqkp6cjOjq61GPd9RmuqjDk7++P1q1bY8OGDZZtRqMRGzZssKoNuF379u2tjgeAdevWWY6PjY1FeHi41TF5eXnYsWOH3XO6W3muGzD1sH/rrbewevVqtGnTpsznOXXqFC5evIiIiAhZyl1R5b3u2xkMBuzZs8dyTd58vwHTENSioiI89thjZT6P0u53eZT1/1uO95BSLViwACNHjsSCBQusplCw5+rVqzh69Kiq77ctu3fvtlyTN99vwDQa68iRIw79saPE+y2EwJgxY7B06VJs3LgRsbGxZT7GbZ/hTnX9VoDvv/9eBAQEiLlz54r9+/eLp556SlStWlXk5OQIIYQYNmyYeO211yzHb926Vfj5+Ylp06aJv/76S0ycOFFUqlRJ7Nmzx3LMlClTRNWqVcXy5cvFn3/+Kfr27StiY2PF9evX3X599jh73VOmTBH+/v5i8eLF4syZM5av/Px8IYQQ+fn54p///KfYtm2byMzMFOvXrxetWrUSjRo1EoWFhR65Rlucve7JkyeLNWvWiKNHj4rff/9dPPzwwyIwMFDs27fPcow33m+zTp06iSFDhpTYrpb7nZ+fL/744w/xxx9/CADigw8+EH/88Yc4ceKEEEKI1157TQwbNsxy/LFjx0TlypXFyy+/LP766y8xa9Ys4evrK1avXm05pqzXUgmcve7vvvtO+Pn5iVmzZln9/75y5YrlmPHjx4uMjAyRmZkptm7dKpKTk0XNmjXFuXPn3H599jh73dOnTxfLli0Thw8fFnv27BFjx44VPj4+Yv369ZZjvPF+mz322GOiXbt2Ns+phvv97LPPitDQUJGRkWH1vr127ZrlGE99hqsuDAkhxEcffSTq1Kkj/P39Rdu2bcX27dst+zp37iyGDx9udfzChQvF3XffLfz9/UV8fLz48ccfrfYbjUbxxhtviLCwMBEQECC6du0qDh486I5LcYoz1123bl0BoMTXxIkThRBCXLt2TTzwwAOiVq1aolKlSqJu3bpi9OjRivqFYebMdaekpFiODQsLEw8++KDYtWuX1fm88X4LIcSBAwcEALF27doS51LL/TYPnb7zy3ytw4cPF507dy7xmJYtWwp/f39Rv359MWfOnBLnLe21VAJnr7tz586lHi+EaYqBiIgI4e/vL6KiosSQIUPEkSNH3HthZXD2uqdOnSoaNGggAgMDRfXq1UVSUpLYuHFjifN62/0WwjRcPCgoSHz++ec2z6mG+23rmgFY/Z/11Ge49HcBiYiIiDRJVX2GiIiIiOTGMERERESaxjBEREREmsYwRERERJrGMERERESaxjBEREREmsYwRERERJrGMERERESaxjBEREREmsYwRERERJrGMEREqrRgwQIEBQXhzJkzlm0jR45E8+bNkZub68GSEZHacG0yIlIlIQRatmyJ+++/Hx999BEmTpyIr7/+Gtu3b0dUVJSni0dEKuLn6QIQEZWHJEl45513MHDgQISHh+Ojjz7Cli1bGISIyGmsGSIiVWvVqhX27duHtWvXonPnzp4uDhGpEPsMEZFqrV69GgcOHIDBYEBYWJini0NEKsWaISJSpV27diEpKQmzZ8/G3LlzERISgkWLFnm6WESkQuwzRESqc/z4cfTq1Qv/+te/MHToUNSvXx/t27fHrl270KpVK08Xj4hUhjVDRKQqly5dQocOHZCUlITPPvvMsr1Xr14wGAxYvXq1B0tHRGrEMERERESaxg7UREREpGkMQ0RERKRpDENERESkaQxDREREpGkMQ0RERKRpDENERESkaQxDREREpGkMQ0RERKRpDENERESkaQxDREREpGkMQ0RERKRpDENERESkaf8P4w9FNnYrxycAAAAASUVORK5CYII=",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"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": "b11794c2",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Same code but now with momentum gradient descent"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 28,
|
||
"id": "d0d357c7",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Own inversion\n",
|
||
"[[4.]\n",
|
||
" [3.]]\n",
|
||
"Eigenvalues of Hessian Matrix:[0.30306759 4.65944342]\n",
|
||
"0 [-20.62275788] [-25.73690387]\n",
|
||
"1 [-0.03662823] [0.02925855]\n",
|
||
"2 [-0.0342458] [0.02735547]\n",
|
||
"3 [-0.03201832] [0.02557617]\n",
|
||
"4 [-0.02993573] [0.0239126]\n",
|
||
"5 [-0.0279886] [0.02235723]\n",
|
||
"6 [-0.02616812] [0.02090304]\n",
|
||
"7 [-0.02446604] [0.01954342]\n",
|
||
"8 [-0.02287468] [0.01827225]\n",
|
||
"9 [-0.02138683] [0.01708375]\n",
|
||
"10 [-0.01999575] [0.01597256]\n",
|
||
"11 [-0.01869515] [0.01493365]\n",
|
||
"12 [-0.01747915] [0.01396231]\n",
|
||
"13 [-0.01634224] [0.01305415]\n",
|
||
"14 [-0.01527928] [0.01220505]\n",
|
||
"15 [-0.01428546] [0.01141119]\n",
|
||
"16 [-0.01335628] [0.01066897]\n",
|
||
"17 [-0.01248754] [0.00997502]\n",
|
||
"18 [-0.0116753] [0.0093262]\n",
|
||
"19 [-0.01091589] [0.00871959]\n",
|
||
"20 [-0.01020588] [0.00815244]\n",
|
||
"21 [-0.00954206] [0.00762217]\n",
|
||
"22 [-0.0089214] [0.0071264]\n",
|
||
"23 [-0.00834112] [0.00666287]\n",
|
||
"24 [-0.00779859] [0.00622949]\n",
|
||
"25 [-0.00729134] [0.0058243]\n",
|
||
"26 [-0.00681708] [0.00544547]\n",
|
||
"27 [-0.00637367] [0.00509128]\n",
|
||
"28 [-0.0059591] [0.00476012]\n",
|
||
"29 [-0.0055715] [0.0044505]\n",
|
||
"theta from own gd\n",
|
||
"[[3.98281205]\n",
|
||
" [3.0137297 ]]\n",
|
||
"0 [-0.00520911] [0.00416103]\n",
|
||
"1 [-0.00487029] [0.00389038]\n",
|
||
"2 [-0.00445186] [0.00355614]\n",
|
||
"3 [-0.00403677] [0.00322456]\n",
|
||
"4 [-0.00364967] [0.00291535]\n",
|
||
"5 [-0.00329616] [0.00263296]\n",
|
||
"6 [-0.00297571] [0.00237699]\n",
|
||
"7 [-0.00268602] [0.00214559]\n",
|
||
"8 [-0.00242441] [0.00193661]\n",
|
||
"9 [-0.00218823] [0.00174795]\n",
|
||
"10 [-0.00197505] [0.00157766]\n",
|
||
"11 [-0.00178263] [0.00142396]\n",
|
||
"12 [-0.00160895] [0.00128523]\n",
|
||
"13 [-0.0014522] [0.00116001]\n",
|
||
"14 [-0.00131072] [0.001047]\n",
|
||
"15 [-0.00118302] [0.00094499]\n",
|
||
"16 [-0.00106776] [0.00085292]\n",
|
||
"17 [-0.00096373] [0.00076983]\n",
|
||
"18 [-0.00086984] [0.00069482]\n",
|
||
"19 [-0.00078509] [0.00062713]\n",
|
||
"20 [-0.0007086] [0.00056603]\n",
|
||
"21 [-0.00063957] [0.00051088]\n",
|
||
"22 [-0.00057726] [0.00046111]\n",
|
||
"23 [-0.00052102] [0.00041619]\n",
|
||
"24 [-0.00047025] [0.00037564]\n",
|
||
"25 [-0.00042444] [0.00033904]\n",
|
||
"26 [-0.00038309] [0.00030601]\n",
|
||
"27 [-0.00034576] [0.0002762]\n",
|
||
"28 [-0.00031208] [0.00024929]\n",
|
||
"29 [-0.00028167] [0.000225]\n",
|
||
"theta from own gd wth momentum\n",
|
||
"[[3.99916114]\n",
|
||
" [3.00067008]]\n"
|
||
]
|
||
}
|
||
],
|
||
"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": "641a2e50",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## But none of these can compete with Newton's method"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 29,
|
||
"id": "ca6775b3",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Own inversion\n",
|
||
"[[4.26281735]\n",
|
||
" [2.84478178]]\n",
|
||
"Eigenvalues of Hessian Matrix:[0.33978889 4.51659846]\n",
|
||
"0 [-14.67490857] [-18.08539155]\n",
|
||
"1 [-4.46170878e-15] [-1.45781905e-14]\n",
|
||
"2 [-1.21430643e-15] [-1.24768421e-15]\n",
|
||
"3 [4.92661467e-16] [4.50610071e-16]\n",
|
||
"4 [4.92661467e-16] [4.50610071e-16]\n",
|
||
"beta from own Newton code\n",
|
||
"[[4.26281735]\n",
|
||
" [2.84478178]]\n"
|
||
]
|
||
}
|
||
],
|
||
"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": "75ed4c75",
|
||
"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": 30,
|
||
"id": "5a69be60",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Own inversion\n",
|
||
"[[4.0586484]\n",
|
||
" [3.0718316]]\n",
|
||
"Eigenvalues of Hessian Matrix:[0.29860173 3.8931686 ]\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"theta from own gd"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"\n",
|
||
"[[4.0586484]\n",
|
||
" [3.0718316]]\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"theta from own sdg\n",
|
||
"[[4.02496085]\n",
|
||
" [3.12081773]]\n"
|
||
]
|
||
}
|
||
],
|
||
"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": "345a84dc",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Same code but now with momentum gradient descent"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 31,
|
||
"id": "656324bd",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Own inversion\n",
|
||
"[[3.96075051]\n",
|
||
" [3.02148021]]\n",
|
||
"Eigenvalues of Hessian Matrix:[0.27470622 4.24106503]\n",
|
||
"theta from own gd\n",
|
||
"[[3.95906059]\n",
|
||
" [3.02296298]]\n",
|
||
"theta from own sdg with momentum\n",
|
||
"[[3.95611042]\n",
|
||
" [2.99475306]]\n"
|
||
]
|
||
}
|
||
],
|
||
"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": "a4f56c77",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Similar (second order function now) problem but now with AdaGrad"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 32,
|
||
"id": "69086c69",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Own inversion\n",
|
||
"[[2.]\n",
|
||
" [3.]\n",
|
||
" [4.]]\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"theta from own AdaGrad\n",
|
||
"[[2.00025662]\n",
|
||
" [2.99802696]\n",
|
||
" [4.00167329]]\n"
|
||
]
|
||
}
|
||
],
|
||
"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": "aaf0ff5c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Running this code we note an almost perfect agreement with the results from matrix inversion."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "adc13d31",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## RMSprop for adaptive learning rate with Stochastic Gradient Descent"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 33,
|
||
"id": "ca22be17",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Own inversion\n",
|
||
"[[2.]\n",
|
||
" [3.]\n",
|
||
" [4.]]\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"theta from own RMSprop\n",
|
||
"[[1.99456598]\n",
|
||
" [2.99848815]\n",
|
||
" [3.99835783]]\n"
|
||
]
|
||
}
|
||
],
|
||
"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": "20bdfaf1",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## And finally [ADAM](https://arxiv.org/pdf/1412.6980.pdf)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 34,
|
||
"id": "aebc385b",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Own inversion\n",
|
||
"[[2.]\n",
|
||
" [3.]\n",
|
||
" [4.]]\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"theta from own ADAM\n",
|
||
"[[1.99989103]\n",
|
||
" [3.00042093]\n",
|
||
" [3.99954925]]\n"
|
||
]
|
||
}
|
||
],
|
||
"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": "59f9e902",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## And Logistic Regression"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 35,
|
||
"id": "0787385b",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Initial loss: 2.772588722239781\n",
|
||
"Trained loss: 1.0672706757870163\n"
|
||
]
|
||
}
|
||
],
|
||
"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": "69ab7a74",
|
||
"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": 36,
|
||
"id": "fec78172",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[0.25 0.19661197 0.10499357]\n"
|
||
]
|
||
}
|
||
],
|
||
"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": "3.9.15"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 5
|
||
} |