Morten Hjorth-Jensen
4332 lines
707 KiB
Plaintext
4332 lines
707 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 chapteroptimization.do.txt -->"
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"source": [
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"# Optimization, the central part of any Machine Learning algortithm\n",
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"\n",
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"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.\n",
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"\n",
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"In our discussion on Logistic Regression we studied the \n",
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"case of\n",
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"two classes, with $y_i$ either\n",
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"$0$ or $1$. Furthermore we assumed also that we have only two\n",
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"parameters $\\beta$ in our fitting, that is we\n",
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"defined probabilities"
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"$$\n",
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"\\begin{align*}\n",
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"p(y_i=1|x_i,\\boldsymbol{\\beta}) &= \\frac{\\exp{(\\beta_0+\\beta_1x_i)}}{1+\\exp{(\\beta_0+\\beta_1x_i)}},\\nonumber\\\\\n",
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"p(y_i=0|x_i,\\boldsymbol{\\beta}) &= 1 - p(y_i=1|x_i,\\boldsymbol{\\beta}),\n",
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"\\end{align*}\n",
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"$$"
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"source": [
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"where $\\boldsymbol{\\beta}$ are the weights we wish to extract from data, in our case $\\beta_0$ and $\\beta_1$. \n",
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"\n",
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"Our compact equations used a definition of a vector $\\boldsymbol{y}$ with $n$\n",
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"elements $y_i$, an $n\\times p$ matrix $\\boldsymbol{X}$ which contains the\n",
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"$x_i$ values and a vector $\\boldsymbol{p}$ of fitted probabilities\n",
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"$p(y_i\\vert x_i,\\boldsymbol{\\beta})$. We rewrote in a more compact form\n",
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"the first derivative of the cost function as"
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"$$\n",
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"\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}} = -\\boldsymbol{X}^T\\left(\\boldsymbol{y}-\\boldsymbol{p}\\right).\n",
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"$$"
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"source": [
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"If we in addition define a diagonal matrix $\\boldsymbol{W}$ with elements \n",
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"$p(y_i\\vert x_i,\\boldsymbol{\\beta})(1-p(y_i\\vert x_i,\\boldsymbol{\\beta})$, we can obtain a compact expression of the second derivative as"
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"source": [
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"$$\n",
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"\\frac{\\partial^2 \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T} = \\boldsymbol{X}^T\\boldsymbol{W}\\boldsymbol{X}.\n",
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"$$"
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"source": [
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"This defines what is called the Hessian matrix.\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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"source": [
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"$$\n",
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"\\boldsymbol{\\beta}^{\\mathrm{new}} = \\boldsymbol{\\beta}^{\\mathrm{old}}-\\left(\\frac{\\partial^2 \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T}\\right)^{-1}_{\\boldsymbol{\\beta}^{\\mathrm{old}}}\\times \\left(\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}}\\right)_{\\boldsymbol{\\beta}^{\\mathrm{old}}},\n",
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"$$"
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"source": [
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"or in matrix form as"
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"source": [
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"$$\n",
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"\\boldsymbol{\\beta}^{\\mathrm{new}} = \\boldsymbol{\\beta}^{\\mathrm{old}}-\\left(\\boldsymbol{X}^T\\boldsymbol{W}\\boldsymbol{X} \\right)^{-1}\\times \\left(-\\boldsymbol{X}^T(\\boldsymbol{y}-\\boldsymbol{p}) \\right)_{\\boldsymbol{\\beta}^{\\mathrm{old}}}.\n",
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"$$"
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"source": [
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"The right-hand side is computed with the old values of $\\beta$. \n",
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"\n",
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"If we can compute these matrices, in particular the Hessian, the above is often the easiest method to implement. \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.\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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"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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"source": [
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"$$\n",
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"s\\approx x-\\frac{f(x)}{f'(x)}.\n",
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"$$"
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"source": [
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"Having in mind an iterative procedure, it is natural to start iterating with"
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"source": [
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"$$\n",
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"x_{n+1}=x_n-\\frac{f(x_n)}{f'(x_n)}.\n",
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"$$"
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"source": [
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"The above is Newton-Raphson's method. It has a simple geometric\n",
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"interpretation, namely $x_{n+1}$ is the point where the tangent from\n",
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"$(x_n,f(x_n))$ crosses the $x$-axis. Close to the solution,\n",
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"Newton-Raphson converges fast to the desired result. However, if we\n",
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"are far from a root, where the higher-order terms in the series are\n",
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"important, the Newton-Raphson formula can give grossly inaccurate\n",
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"results. For instance, the initial guess for the root might be so far\n",
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"from the true root as to let the search interval include a local\n",
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"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",
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"vanishes, then Newton-Raphson may fail totally\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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"source": [
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"$$\n",
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"\\begin{array}{cc} f_1(x_1,x_2) &=0\\\\\n",
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" f_2(x_1,x_2) &=0,\\end{array}\n",
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"$$"
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]
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"cell_type": "markdown",
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"source": [
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"which we Taylor expand to obtain"
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]
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"source": [
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"$$\n",
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"\\begin{array}{cc} 0=f_1(x_1+h_1,x_2+h_2)=&f_1(x_1,x_2)+h_1\n",
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" \\partial f_1/\\partial x_1+h_2\n",
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" \\partial f_1/\\partial x_2+\\dots\\\\\n",
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" 0=f_2(x_1+h_1,x_2+h_2)=&f_2(x_1,x_2)+h_1\n",
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" \\partial f_2/\\partial x_1+h_2\n",
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" \\partial f_2/\\partial x_2+\\dots\n",
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" \\end{array}.\n",
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"$$"
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"source": [
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"Defining the Jacobian matrix $\\boldsymbol{J}$ we have"
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"source": [
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"$$\n",
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"\\boldsymbol{J}=\\left( \\begin{array}{cc}\n",
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" \\partial f_1/\\partial x_1 & \\partial f_1/\\partial x_2 \\\\\n",
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" \\partial f_2/\\partial x_1 &\\partial f_2/\\partial x_2\n",
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" \\end{array} \\right),\n",
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"$$"
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"source": [
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"we can rephrase Newton's method as"
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"source": [
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"$$\n",
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"\\left(\\begin{array}{c} x_1^{n+1} \\\\ x_2^{n+1} \\end{array} \\right)=\n",
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"\\left(\\begin{array}{c} x_1^{n} \\\\ x_2^{n} \\end{array} \\right)+\n",
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"\\left(\\begin{array}{c} h_1^{n} \\\\ h_2^{n} \\end{array} \\right),\n",
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"$$"
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]
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"cell_type": "markdown",
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"source": [
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"where we have defined"
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]
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"source": [
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"$$\n",
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"\\left(\\begin{array}{c} h_1^{n} \\\\ h_2^{n} \\end{array} \\right)=\n",
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" -\\boldsymbol{J}^{-1}\n",
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" \\left(\\begin{array}{c} f_1(x_1^{n},x_2^{n}) \\\\ f_2(x_1^{n},x_2^{n}) \\end{array} \\right).\n",
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||
"$$"
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"cell_type": "markdown",
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"id": "8d67266e",
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"source": [
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"We need thus to compute the inverse of the Jacobian matrix and it\n",
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"is to understand that difficulties may\n",
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"arise in case $\\boldsymbol{J}$ is nearly singular.\n",
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"\n",
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"It is rather straightforward to extend the above scheme to systems of\n",
|
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"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."
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]
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},
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"source": [
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"## Steepest descent\n",
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"\n",
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"The basic idea of gradient descent is\n",
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"that a function $F(\\mathbf{x})$, \n",
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"$\\mathbf{x} \\equiv (x_1,\\cdots,x_n)$, decreases fastest if one goes from $\\bf {x}$ in the\n",
|
||
"direction of the negative gradient $-\\nabla F(\\mathbf{x})$.\n",
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"\n",
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||
"It can be shown that if"
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]
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"source": [
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||
"$$\n",
|
||
"\\mathbf{x}_{k+1} = \\mathbf{x}_k - \\gamma_k \\nabla F(\\mathbf{x}_k),\n",
|
||
"$$"
|
||
]
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},
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"cell_type": "markdown",
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"source": [
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||
"with $\\gamma_k > 0$.\n",
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"\n",
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"For $\\gamma_k$ small enough, then $F(\\mathbf{x}_{k+1}) \\leq\n",
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"F(\\mathbf{x}_k)$. This means that for a sufficiently small $\\gamma_k$\n",
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"we are always moving towards smaller function values, i.e a minimum.\n",
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"\n",
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"The previous observation is the basis of the method of steepest\n",
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||
"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"
|
||
]
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},
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"metadata": {
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"source": [
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||
"$$\n",
|
||
"\\mathbf{x}_{k+1} = \\mathbf{x}_k - \\gamma_k \\nabla F(\\mathbf{x}_k), \\ \\ k \\geq 0.\n",
|
||
"$$"
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]
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},
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{
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"cell_type": "markdown",
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"id": "9a43f87d",
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"metadata": {
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},
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"source": [
|
||
"The parameter $\\gamma_k$ is often referred to as the step length or\n",
|
||
"the learning rate within the context of Machine Learning.\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",
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||
"global or local minimum. In the special case when $F$ is a convex\n",
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||
"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.\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": "c271932e",
|
||
"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...).\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\n",
|
||
"$f(tx_1 + (1-t)x_2) \\leq tf(x_1) + (1-t)f(x_2)$\n",
|
||
"for all\n",
|
||
"$x_1, x_2 \\in X$ and for all $t \\in [0,1]$.\n",
|
||
"\n",
|
||
"If $\\leq$ is replaced with a strict inequality 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 discussed below.\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/, 2004).\n",
|
||
"\n",
|
||
"**First order condition**: 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 $x,y \\in D_f$. This condition means that for a convex function\n",
|
||
"the first order Taylor expansion (right hand side above) at any point\n",
|
||
"is 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**: 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.\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": "87f52dcb",
|
||
"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": "5add3827",
|
||
"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": "d54a453e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{A}\\boldsymbol{x} = \\boldsymbol{b}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b1b84a57",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"In the iterative process we end up with a problem like"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "880db06e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{r}= \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d2cc7ff0",
|
||
"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, $\\boldsymbol{r}=0$.\n",
|
||
"\n",
|
||
"The residual is zero when we reach the minimum of the quadratic equation"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8dc530e6",
|
||
"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": "813d3073",
|
||
"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. \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": "3d0d9d18",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{x}_0=0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "fe5d0507",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"or consider the system"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "bfabfe26",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{A}\\boldsymbol{z} = \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "27b361b6",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"instead.\n",
|
||
"\n",
|
||
"One can show that the solution $\\boldsymbol{x}$ is also the unique minimizer of the quadratic form"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "402e450f",
|
||
"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": "fa3d7c41",
|
||
"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": "3e6d73b8",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{A}\\boldsymbol{x}_0-\\boldsymbol{b},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "02c8e436",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"and \n",
|
||
"$\\boldsymbol{x}_0=0$ it is equal $-\\boldsymbol{b}$.\n",
|
||
"\n",
|
||
"We can compute the residual iteratively as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "18100e11",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{r}_{k+1}=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_{k+1},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ac2290e7",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which equals"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "33b872cd",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{b}-\\boldsymbol{A}(\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{r}_k),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b0ef2463",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"or"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9bdb71be",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"(\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k)-\\alpha_k\\boldsymbol{A}\\boldsymbol{r}_k,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8b526371",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which gives"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f2304289",
|
||
"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": "4b00e41e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"leading to the iterative scheme"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0e67a647",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{x}_{k+1}=\\boldsymbol{x}_k-\\alpha_k\\boldsymbol{r}_{k},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 1,
|
||
"id": "f96e45cc",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_9414/483257001.py:18: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().\n",
|
||
" ax = fig.gca(projection=\"3d\")\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"<mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x13b240850>"
|
||
]
|
||
},
|
||
"execution_count": 1,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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\n",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_61_2.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"%matplotlib inline\n",
|
||
"\n",
|
||
"import numpy as np\n",
|
||
"import numpy.linalg as la\n",
|
||
"\n",
|
||
"import scipy.optimize as sopt\n",
|
||
"\n",
|
||
"import matplotlib.pyplot as pt\n",
|
||
"from mpl_toolkits.mplot3d import axes3d\n",
|
||
"\n",
|
||
"def f(x):\n",
|
||
" return 0.5*x[0]**2 + 2.5*x[1]**2\n",
|
||
"\n",
|
||
"def df(x):\n",
|
||
" return np.array([x[0], 5*x[1]])\n",
|
||
"\n",
|
||
"fig = pt.figure()\n",
|
||
"ax = fig.gca(projection=\"3d\")\n",
|
||
"\n",
|
||
"xmesh, ymesh = np.mgrid[-2:2:50j,-2:2:50j]\n",
|
||
"fmesh = f(np.array([xmesh, ymesh]))\n",
|
||
"ax.plot_surface(xmesh, ymesh, fmesh)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "16ce9afc",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"And then as countor plot"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 2,
|
||
"id": "de682254",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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\n",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_63_0.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"pt.axis(\"equal\")\n",
|
||
"pt.contour(xmesh, ymesh, fmesh)\n",
|
||
"guesses = [np.array([2, 2./5])]"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ebbe4b30",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Find guesses"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 3,
|
||
"id": "5f2c4a9c",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"x = guesses[-1]\n",
|
||
"s = -df(x)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "83f88bfa",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Run it!"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 4,
|
||
"id": "2da02da5",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[ 1.33333333 -0.26666667]\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": "02d36ca5",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"What happened?"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 5,
|
||
"id": "53313492",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"[<matplotlib.lines.Line2D at 0x13b8c72e0>]"
|
||
]
|
||
},
|
||
"execution_count": 5,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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\n",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_69_1.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"pt.axis(\"equal\")\n",
|
||
"pt.contour(xmesh, ymesh, fmesh, 50)\n",
|
||
"it_array = np.array(guesses)\n",
|
||
"pt.plot(it_array.T[0], it_array.T[1], \"x-\")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
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||
"id": "c39319be",
|
||
"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": "6f709878",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{s}^T\\boldsymbol{A}\\boldsymbol{t}= 0.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "321f39ff",
|
||
"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": "ddf2d65f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{x}_i^T\\boldsymbol{A}\\boldsymbol{x}_j= 0.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "3245eaab",
|
||
"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 $\\boldsymbol{s}$.\n",
|
||
"\n",
|
||
"An example is given by the eigenvectors of the matrix"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "69cc7635",
|
||
"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": "e4a46e89",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which is zero unless $i=j$. \n",
|
||
"\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": "69c46421",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{x}_{i+1}=\\boldsymbol{x}_{i}+\\alpha_i\\boldsymbol{p}_{i}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "90770121",
|
||
"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": "3a5e36b1",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{x} = \\sum^{n}_{i=1} \\alpha_i \\boldsymbol{p}_i.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c144cca2",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"The coefficients are given by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "dd5316be",
|
||
"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": "d22dc91f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Multiplying with $\\boldsymbol{p}_k^T$ from the left gives"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e07ec0c1",
|
||
"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": "63340018",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"and we can define the coefficients $\\alpha_k$ as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c41887ce",
|
||
"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": "b161780a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"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": "1abed167",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{x}_0=0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "bd840c05",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"or consider the system"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d47ce82a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{A}\\boldsymbol{z} = \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a7d6e5ee",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"instead.\n",
|
||
"\n",
|
||
"One can show that the solution $\\boldsymbol{x}$ is also the unique minimizer of the quadratic form"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8e31bd0e",
|
||
"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": "b337f9b4",
|
||
"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": "6740500b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{A}\\boldsymbol{x}_0-\\boldsymbol{b},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "03216125",
|
||
"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.\n",
|
||
"\n",
|
||
"Let $\\boldsymbol{r}_k$ be the residual at the $k$-th step:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9b45c7ad",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{r}_k=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1c275ef3",
|
||
"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": "099132d8",
|
||
"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": "2a0c62f2",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"We can also compute the residual iteratively as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d04ba7fb",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{r}_{k+1}=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_{k+1},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b0846f39",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which equals"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a467360c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{b}-\\boldsymbol{A}(\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{p}_k),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d41094c1",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"or"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1740a0a7",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"(\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k)-\\alpha_k\\boldsymbol{A}\\boldsymbol{p}_k,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "df099649",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which gives"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "75ea0e90",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{r}_{k+1}=\\boldsymbol{r}_k-\\boldsymbol{A}\\boldsymbol{p}_{k},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "69cad896",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Revisiting our Linear Regression Solvers\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.\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": "b7c5dad0",
|
||
"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": "f97fbc43",
|
||
"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": "7e249cc0",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"h_\\beta(x) = \\boldsymbol{y} = \\beta_0 + \\beta_1 x,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7335ac71",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"such that"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "fa5ee00d",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{y}_i = \\beta_0 + \\beta_1 x_i.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c5e55d7b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"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": "80980c3d",
|
||
"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": "bd680445",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"The cost/loss/risk function is given by ("
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e6d47679",
|
||
"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": "ee872c38",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"and we want to find $\\beta$ such that $C(\\beta)$ is minimized.\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": "c286e8a4",
|
||
"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": "268e5249",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where $X$ is the design matrix defined above.\n",
|
||
"\n",
|
||
"The Hessian matrix of $C(\\beta)$ is given by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "43dead94",
|
||
"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": "32db94fc",
|
||
"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.\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": "11418e4d",
|
||
"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": "1d0005da",
|
||
"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",
|
||
"$\\beta= (X^TX)^{-1} X^T \\mathbf{y}$.\n",
|
||
"\n",
|
||
"Here is our simple example"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 7,
|
||
"id": "bbbaf736",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[0.25881631 4.66111673]\n",
|
||
"[[4.01840062]\n",
|
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" [2.89545727]]\n",
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"[[4.01840062]\n",
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" [2.89545727]]\n"
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]
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},
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{
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"data": {
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\n",
|
||
"text/plain": [
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||
"<Figure size 640x480 with 1 Axes>"
|
||
]
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||
},
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"metadata": {
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"filenames": {
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"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_123_1.png"
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||
}
|
||
},
|
||
"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(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": "00a02162",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Alternatively, we can use **Scikit-Learn** as done here"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 8,
|
||
"id": "5e5c5cec",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[[3.79441434]\n",
|
||
" [3.07608141]]\n",
|
||
"[3.80994952] [3.12302855]\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": "215a1d5f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"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": "b88e153c",
|
||
"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": "9ab32b33",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"In order to minimize $C_{\\text{ridge}}(\\beta)$ using GD we only have adjust the gradient as follows"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6f285d39",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\nabla_\\beta C_{\\text{ridge}}(\\beta) = \\frac{2}{n}\\begin{bmatrix} \\sum_{i=1}^{100} \\left(\\beta_0+\\beta_1x_i-y_i\\right) \\\\\n",
|
||
"\\sum_{i=1}^{100}\\left( x_i (\\beta_0+\\beta_1x_i)-y_ix_i\\right) \\\\\n",
|
||
"\\end{bmatrix} + 2\\lambda\\begin{bmatrix} \\beta_0 \\\\ \\beta_1\\end{bmatrix} = 2 (X^T(X\\beta - \\mathbf{y})+\\lambda \\beta).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "98b1fab8",
|
||
"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": "1d731c50",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\beta_{\\text{ridge}} = \\left(X^T X + \\lambda I_{2 \\times 2} \\right)^{-1} X^T \\mathbf{y}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 9,
|
||
"id": "9e58f547",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[[3.78596961]\n",
|
||
" [3.12387751]]\n",
|
||
"[[3.71441535]\n",
|
||
" [3.17942122]]\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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\n",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_132_1.png"
|
||
}
|
||
},
|
||
"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 = lmbda* np.eye(XT_X.shape[0])\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 = 0.1\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": "bba77347",
|
||
"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": "d888b6a7",
|
||
"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.\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": "bb7f68c3",
|
||
"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": "8f0504db",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"This in turn means that the gradient can be\n",
|
||
"computed as a sum over $i$-gradients"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a8b282a3",
|
||
"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": "97da117c",
|
||
"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",
|
||
"$k=1,\\cdots,n/M$.\n",
|
||
"\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": "4dc0d7a8",
|
||
"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": "a92a3c90",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Thus a gradient descent step now looks like"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "80c357e0",
|
||
"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": "fe754d21",
|
||
"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": "code",
|
||
"execution_count": 10,
|
||
"id": "ae39eaed",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"import numpy as np \n",
|
||
"\n",
|
||
"n = 100 #100 datapoints \n",
|
||
"M = 5 #size of each mini-batche\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": "4b5ab1a0",
|
||
"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.\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.\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.\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": 11,
|
||
"id": "1aa9624a",
|
||
"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": "5a1b9a95",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"We note that we have defined several hyperparameters. These are now the number of epochs, the number of mini-batches and the parameters $t_0$ and $t_1$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "eece48be",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"### Program for stochastic gradient"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 12,
|
||
"id": "15a1c324",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Own inversion\n",
|
||
"[[4.42130182]\n",
|
||
" [2.83757843]]\n",
|
||
"Eigenvalues of Hessian Matrix:[0.27660123 4.17938393]\n",
|
||
"theta from own gd\n",
|
||
"[[4.42130182]\n",
|
||
" [2.83757843]]\n",
|
||
"theta from own sdg\n",
|
||
"[[4.44198566]\n",
|
||
" [2.79512696]]\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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\n",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_148_1.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Importing various packages\n",
|
||
"# 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",
|
||
"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",
|
||
"\n",
|
||
"\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": "360cca72",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"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. More material will be added later."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1a0e415c",
|
||
"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": "1def9354",
|
||
"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": "391f8e0d",
|
||
"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": "ca5f2b4a",
|
||
"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": "6d6e32d1",
|
||
"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": "8cec056e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where we have defined $\\Delta \\boldsymbol{\\theta}_{t}= \\boldsymbol{\\theta}_t-\\boldsymbol{\\theta}_{t-1}$.\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": "57d668cd",
|
||
"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": "90802b47",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"We can discretize this equation in the usual way to get"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ad5b8b19",
|
||
"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": "925285b7",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Rearranging this equation, we can rewrite this as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "74962fe4",
|
||
"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": "4532fe7b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"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": "c513fcdc",
|
||
"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": "d9ce9d46",
|
||
"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": "f7c21684",
|
||
"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": "196d654d",
|
||
"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": "252fb3d1",
|
||
"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 $\\gamma$.\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."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "de9bbf4a",
|
||
"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": "82921918",
|
||
"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": "d100fcf9",
|
||
"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": "5c6dd6a5",
|
||
"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": "91a73753",
|
||
"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": "482ace07",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"### ADAM optimizer\n",
|
||
"\n",
|
||
"A related algorithm is the ADAM optimizer. In ADAM, we keep a running\n",
|
||
"average of both the first and second moment of the gradient and use\n",
|
||
"this information to adaptively change the learning rate for different\n",
|
||
"parameters. 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": "bdf3643f",
|
||
"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": "210ec4d9",
|
||
"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": "3eff0da8",
|
||
"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": "b1479583",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{\\mathbf{m}}_t={\\mathbf{m}_t \\over 1-\\beta_1^t} \\nonumber\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ae6c4d9f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{\\mathbf{s}}_t ={\\mathbf{s}_t \\over1-\\beta_2^t} \\nonumber\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "213c59cd",
|
||
"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": "4a418e6b",
|
||
"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": "5a8ff160",
|
||
"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": "125d7fef",
|
||
"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": "bcf9e94e",
|
||
"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."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e18768d0",
|
||
"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": "e0f3885d",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"f(x) = \\sin\\left(2\\pi x + x^2\\right)\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "67b8af63",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which has the following derivative"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "98709557",
|
||
"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": "3660eaa4",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Using **autograd** we have"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 13,
|
||
"id": "045c878d",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
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\n",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_188_0.png"
|
||
}
|
||
},
|
||
"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": "f7f7a1fb",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"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": 14,
|
||
"id": "aafa5873",
|
||
"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": "6758a831",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"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": 15,
|
||
"id": "a01d4e52",
|
||
"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": "f2871382",
|
||
"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": "code",
|
||
"execution_count": 16,
|
||
"id": "b0060765",
|
||
"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": "743f91b4",
|
||
"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": "code",
|
||
"execution_count": 17,
|
||
"id": "eb6c8a53",
|
||
"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": "code",
|
||
"execution_count": 18,
|
||
"id": "5d332825",
|
||
"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": "code",
|
||
"execution_count": 19,
|
||
"id": "f5cfd0ff",
|
||
"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": 20,
|
||
"id": "fed0da90",
|
||
"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": "code",
|
||
"execution_count": 21,
|
||
"id": "7cc40c34",
|
||
"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": "1343bf83",
|
||
"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.\n",
|
||
"\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": 22,
|
||
"id": "5d283e6c",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"'\\nimport autograd.numpy as np\\nfrom autograd import grad\\ndef f8(x): # Assume x is an array\\n x[2] = 3\\n return x*2\\n\\nf8_grad = grad(f8)\\n\\nx = 8.4\\n\\nprint(\"The derivative of f8 is:\",f8_grad(x))\\n'"
|
||
]
|
||
},
|
||
"execution_count": 22,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"\"\"\"\n",
|
||
"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))\n",
|
||
"\"\"\""
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "2125f374",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Here, Autograd tells us that an 'ArrayBox' does not support item assignment. The item assignment is done when the program tries to assign x[2] to the value 3. However, Autograd has implemented the computation of the derivative such that this assignment is not possible."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 23,
|
||
"id": "da6fd9e3",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"ename": "AttributeError",
|
||
"evalue": "'ArrayBox' object has no attribute 'dot'",
|
||
"output_type": "error",
|
||
"traceback": [
|
||
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
||
"\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)",
|
||
"Input \u001b[0;32mIn [23]\u001b[0m, in \u001b[0;36m<cell line: 11>\u001b[0;34m()\u001b[0m\n\u001b[1;32m 7\u001b[0m f9_grad \u001b[38;5;241m=\u001b[39m grad(f9)\n\u001b[1;32m 9\u001b[0m x \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39marray([\u001b[38;5;241m1.0\u001b[39m,\u001b[38;5;241m0.0\u001b[39m])\n\u001b[0;32m---> 11\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mThe derivative of f9 is:\u001b[39m\u001b[38;5;124m\"\u001b[39m,\u001b[43mf9_grad\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m)\n",
|
||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:20\u001b[0m, in \u001b[0;36munary_to_nary.<locals>.nary_operator.<locals>.nary_f\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m 18\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m 19\u001b[0m x \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mtuple\u001b[39m(args[i] \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m argnum)\n\u001b[0;32m---> 20\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43munary_operator\u001b[49m\u001b[43m(\u001b[49m\u001b[43munary_f\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_args\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_kwargs\u001b[49m\u001b[43m)\u001b[49m\n",
|
||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:25\u001b[0m, in \u001b[0;36mgrad\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m 18\u001b[0m \u001b[38;5;129m@unary_to_nary\u001b[39m\n\u001b[1;32m 19\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mgrad\u001b[39m(fun, x):\n\u001b[1;32m 20\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m 21\u001b[0m \u001b[38;5;124;03m Returns a function which computes the gradient of `fun` with respect to\u001b[39;00m\n\u001b[1;32m 22\u001b[0m \u001b[38;5;124;03m positional argument number `argnum`. The returned function takes the same\u001b[39;00m\n\u001b[1;32m 23\u001b[0m \u001b[38;5;124;03m arguments as `fun`, but returns the gradient instead. The function `fun`\u001b[39;00m\n\u001b[1;32m 24\u001b[0m \u001b[38;5;124;03m should be scalar-valued. The gradient has the same type as the argument.\"\"\"\u001b[39;00m\n\u001b[0;32m---> 25\u001b[0m vjp, ans \u001b[38;5;241m=\u001b[39m \u001b[43m_make_vjp\u001b[49m\u001b[43m(\u001b[49m\u001b[43mfun\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 26\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m vspace(ans)\u001b[38;5;241m.\u001b[39msize \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m1\u001b[39m:\n\u001b[1;32m 27\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mGrad only applies to real scalar-output functions. \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m 28\u001b[0m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mTry jacobian, elementwise_grad or holomorphic_grad.\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n",
|
||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:10\u001b[0m, in \u001b[0;36mmake_vjp\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mmake_vjp\u001b[39m(fun, x):\n\u001b[1;32m 9\u001b[0m start_node \u001b[38;5;241m=\u001b[39m VJPNode\u001b[38;5;241m.\u001b[39mnew_root()\n\u001b[0;32m---> 10\u001b[0m end_value, end_node \u001b[38;5;241m=\u001b[39m \u001b[43mtrace\u001b[49m\u001b[43m(\u001b[49m\u001b[43mstart_node\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mfun\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 11\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m end_node \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m 12\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mvjp\u001b[39m(g): \u001b[38;5;28;01mreturn\u001b[39;00m vspace(x)\u001b[38;5;241m.\u001b[39mzeros()\n",
|
||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:10\u001b[0m, in \u001b[0;36mtrace\u001b[0;34m(start_node, fun, x)\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m trace_stack\u001b[38;5;241m.\u001b[39mnew_trace() \u001b[38;5;28;01mas\u001b[39;00m t:\n\u001b[1;32m 9\u001b[0m start_box \u001b[38;5;241m=\u001b[39m new_box(x, t, start_node)\n\u001b[0;32m---> 10\u001b[0m end_box \u001b[38;5;241m=\u001b[39m \u001b[43mfun\u001b[49m\u001b[43m(\u001b[49m\u001b[43mstart_box\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 11\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m isbox(end_box) \u001b[38;5;129;01mand\u001b[39;00m end_box\u001b[38;5;241m.\u001b[39m_trace \u001b[38;5;241m==\u001b[39m start_box\u001b[38;5;241m.\u001b[39m_trace:\n\u001b[1;32m 12\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m end_box\u001b[38;5;241m.\u001b[39m_value, end_box\u001b[38;5;241m.\u001b[39m_node\n",
|
||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:15\u001b[0m, in \u001b[0;36munary_to_nary.<locals>.nary_operator.<locals>.nary_f.<locals>.unary_f\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m 13\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m 14\u001b[0m subargs \u001b[38;5;241m=\u001b[39m subvals(args, \u001b[38;5;28mzip\u001b[39m(argnum, x))\n\u001b[0;32m---> 15\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mfun\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43msubargs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
|
||
"Input \u001b[0;32mIn [23]\u001b[0m, in \u001b[0;36mf9\u001b[0;34m(a)\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mf9\u001b[39m(a): \u001b[38;5;66;03m# Assume a is an array with 2 elements\u001b[39;00m\n\u001b[1;32m 4\u001b[0m b \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39marray([\u001b[38;5;241m1.0\u001b[39m,\u001b[38;5;241m2.0\u001b[39m])\n\u001b[0;32m----> 5\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43ma\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdot\u001b[49m(b)\n",
|
||
"\u001b[0;31mAttributeError\u001b[0m: 'ArrayBox' object has no attribute 'dot'"
|
||
]
|
||
}
|
||
],
|
||
"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": "b26b3471",
|
||
"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": 24,
|
||
"id": "18b1ae5f",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"import autograd.numpy as np\n",
|
||
"from autograd import grad\n",
|
||
"def f9_alternative(x): # Assume a is an array with 2 elements\n",
|
||
" b = np.array([1.0,2.0])\n",
|
||
" return np.dot(x,b) # The same as x_1*b_1 + x_2*b_2\n",
|
||
"\n",
|
||
"f9_alternative_grad = grad(f9_alternative)\n",
|
||
"\n",
|
||
"x = np.array([3.0,0.0])\n",
|
||
"\n",
|
||
"print(\"The gradient of f9 is:\",f9_alternative_grad(x))\n",
|
||
"\n",
|
||
"# The analytical gradient of the dot product of vectors x and b with two elements (x_1,x_2) and (b_1, b_2) respectively\n",
|
||
"# w.r.t x is (b_1, b_2)."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "138f3f1e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"The documentation recommends to avoid inplace operations such as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 25,
|
||
"id": "caebcdc6",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"a += b\n",
|
||
"a -= b\n",
|
||
"a*= b\n",
|
||
"a /=b"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "73211a47",
|
||
"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": "a38103f7",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Using Autograd\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": 26,
|
||
"id": "89f0a17f",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Using Autograd to calculate gradients for OLS\n",
|
||
"from random import random, seed\n",
|
||
"import numpy as np\n",
|
||
"import autograd.numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from autograd import grad\n",
|
||
"\n",
|
||
"def CostOLS(beta):\n",
|
||
" return (1.0/n)*np.sum((y-X @ beta)**2)\n",
|
||
"\n",
|
||
"n = 100\n",
|
||
"x = 2*np.random.rand(n,1)\n",
|
||
"y = 4+3*x+np.random.randn(n,1)\n",
|
||
"\n",
|
||
"X = np.c_[np.ones((n,1)), x]\n",
|
||
"XT_X = X.T @ X\n",
|
||
"theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
|
||
"print(\"Own inversion\")\n",
|
||
"print(theta_linreg)\n",
|
||
"# Hessian matrix\n",
|
||
"H = (2.0/n)* XT_X\n",
|
||
"EigValues, EigVectors = np.linalg.eig(H)\n",
|
||
"print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
|
||
"\n",
|
||
"theta = np.random.randn(2,1)\n",
|
||
"eta = 1.0/np.max(EigValues)\n",
|
||
"Niterations = 1000\n",
|
||
"# define the gradient\n",
|
||
"training_gradient = grad(CostOLS)\n",
|
||
"\n",
|
||
"for iter in range(Niterations):\n",
|
||
" gradients = training_gradient(theta)\n",
|
||
" theta -= eta*gradients\n",
|
||
"print(\"theta from own gd\")\n",
|
||
"print(theta)\n",
|
||
"\n",
|
||
"xnew = np.array([[0],[2]])\n",
|
||
"Xnew = np.c_[np.ones((2,1)), xnew]\n",
|
||
"ypredict = Xnew.dot(theta)\n",
|
||
"ypredict2 = Xnew.dot(theta_linreg)\n",
|
||
"\n",
|
||
"plt.plot(xnew, ypredict, \"r-\")\n",
|
||
"plt.plot(xnew, ypredict2, \"b-\")\n",
|
||
"plt.plot(x, y ,'ro')\n",
|
||
"plt.axis([0,2.0,0, 15.0])\n",
|
||
"plt.xlabel(r'$x$')\n",
|
||
"plt.ylabel(r'$y$')\n",
|
||
"plt.title(r'Random numbers ')\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c6607dea",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Same code but now with momentum gradient descent"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 27,
|
||
"id": "d3818505",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Using Autograd to calculate gradients for OLS\n",
|
||
"from random import random, seed\n",
|
||
"import numpy as np\n",
|
||
"import autograd.numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from autograd import grad\n",
|
||
"\n",
|
||
"def CostOLS(beta):\n",
|
||
" return (1.0/n)*np.sum((y-X @ beta)**2)\n",
|
||
"\n",
|
||
"n = 100\n",
|
||
"x = 2*np.random.rand(n,1)\n",
|
||
"y = 4+3*x#+np.random.randn(n,1)\n",
|
||
"\n",
|
||
"X = np.c_[np.ones((n,1)), x]\n",
|
||
"XT_X = X.T @ X\n",
|
||
"theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
|
||
"print(\"Own inversion\")\n",
|
||
"print(theta_linreg)\n",
|
||
"# Hessian matrix\n",
|
||
"H = (2.0/n)* XT_X\n",
|
||
"EigValues, EigVectors = np.linalg.eig(H)\n",
|
||
"print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
|
||
"\n",
|
||
"theta = np.random.randn(2,1)\n",
|
||
"eta = 1.0/np.max(EigValues)\n",
|
||
"Niterations = 30\n",
|
||
"\n",
|
||
"# define the gradient\n",
|
||
"training_gradient = grad(CostOLS)\n",
|
||
"\n",
|
||
"for iter in range(Niterations):\n",
|
||
" gradients = training_gradient(theta)\n",
|
||
" theta -= eta*gradients\n",
|
||
" print(iter,gradients[0],gradients[1])\n",
|
||
"print(\"theta from own gd\")\n",
|
||
"print(theta)\n",
|
||
"\n",
|
||
"# Now improve with momentum gradient descent\n",
|
||
"change = 0.0\n",
|
||
"delta_momentum = 0.3\n",
|
||
"for iter in range(Niterations):\n",
|
||
" # calculate gradient\n",
|
||
" gradients = training_gradient(theta)\n",
|
||
" # calculate update\n",
|
||
" new_change = eta*gradients+delta_momentum*change\n",
|
||
" # take a step\n",
|
||
" theta -= new_change\n",
|
||
" # save the change\n",
|
||
" change = new_change\n",
|
||
" print(iter,gradients[0],gradients[1])\n",
|
||
"print(\"theta from own gd wth momentum\")\n",
|
||
"print(theta)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8bc11302",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"We note indeed a considerable increase in efficiency here, we less iterations needed.\n",
|
||
"However, if we can invert the Hessian matrix, this is the preferred approach, as shown in the example here."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 28,
|
||
"id": "e04cac92",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Using Newton's method\n",
|
||
"from random import random, seed\n",
|
||
"import numpy as np\n",
|
||
"import autograd.numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from autograd import grad\n",
|
||
"\n",
|
||
"def CostOLS(beta):\n",
|
||
" return (1.0/n)*np.sum((y-X @ beta)**2)\n",
|
||
"\n",
|
||
"n = 100\n",
|
||
"x = 2*np.random.rand(n,1)\n",
|
||
"y = 4+3*x+np.random.randn(n,1)\n",
|
||
"\n",
|
||
"X = np.c_[np.ones((n,1)), x]\n",
|
||
"XT_X = X.T @ X\n",
|
||
"beta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
|
||
"print(\"Own inversion\")\n",
|
||
"print(beta_linreg)\n",
|
||
"# Hessian matrix\n",
|
||
"H = (2.0/n)* XT_X\n",
|
||
"# Note that here the Hessian does not depend on the parameters beta\n",
|
||
"invH = np.linalg.pinv(H)\n",
|
||
"EigValues, EigVectors = np.linalg.eig(H)\n",
|
||
"print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
|
||
"\n",
|
||
"beta = np.random.randn(2,1)\n",
|
||
"Niterations = 5\n",
|
||
"\n",
|
||
"# define the gradient\n",
|
||
"training_gradient = grad(CostOLS)\n",
|
||
"\n",
|
||
"for iter in range(Niterations):\n",
|
||
" gradients = training_gradient(beta)\n",
|
||
" beta -= invH @ gradients\n",
|
||
" print(iter,gradients[0],gradients[1])\n",
|
||
"print(\"beta from own Newton code\")\n",
|
||
"print(beta)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "fabacfbb",
|
||
"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": 29,
|
||
"id": "850fbafa",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Using Autograd to calculate gradients using SGD\n",
|
||
"# OLS example\n",
|
||
"from random import random, seed\n",
|
||
"import numpy as np\n",
|
||
"import autograd.numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from autograd import grad\n",
|
||
"\n",
|
||
"# Note change from previous example\n",
|
||
"def CostOLS(y,X,theta):\n",
|
||
" return np.sum((y-X @ theta)**2)\n",
|
||
"\n",
|
||
"n = 100\n",
|
||
"x = 2*np.random.rand(n,1)\n",
|
||
"y = 4+3*x+np.random.randn(n,1)\n",
|
||
"\n",
|
||
"X = np.c_[np.ones((n,1)), x]\n",
|
||
"XT_X = X.T @ X\n",
|
||
"theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
|
||
"print(\"Own inversion\")\n",
|
||
"print(theta_linreg)\n",
|
||
"# Hessian matrix\n",
|
||
"H = (2.0/n)* XT_X\n",
|
||
"EigValues, EigVectors = np.linalg.eig(H)\n",
|
||
"print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
|
||
"\n",
|
||
"theta = np.random.randn(2,1)\n",
|
||
"eta = 1.0/np.max(EigValues)\n",
|
||
"Niterations = 1000\n",
|
||
"\n",
|
||
"# Note that we request the derivative wrt third argument (theta, 2 here)\n",
|
||
"training_gradient = grad(CostOLS,2)\n",
|
||
"\n",
|
||
"for iter in range(Niterations):\n",
|
||
" gradients = (1.0/n)*training_gradient(y, X, theta)\n",
|
||
" theta -= eta*gradients\n",
|
||
"print(\"theta from own gd\")\n",
|
||
"print(theta)\n",
|
||
"\n",
|
||
"xnew = np.array([[0],[2]])\n",
|
||
"Xnew = np.c_[np.ones((2,1)), xnew]\n",
|
||
"ypredict = Xnew.dot(theta)\n",
|
||
"ypredict2 = Xnew.dot(theta_linreg)\n",
|
||
"\n",
|
||
"plt.plot(xnew, ypredict, \"r-\")\n",
|
||
"plt.plot(xnew, ypredict2, \"b-\")\n",
|
||
"plt.plot(x, y ,'ro')\n",
|
||
"plt.axis([0,2.0,0, 15.0])\n",
|
||
"plt.xlabel(r'$x$')\n",
|
||
"plt.ylabel(r'$y$')\n",
|
||
"plt.title(r'Random numbers ')\n",
|
||
"plt.show()\n",
|
||
"\n",
|
||
"n_epochs = 50\n",
|
||
"M = 5 #size of each minibatch\n",
|
||
"m = int(n/M) #number of minibatches\n",
|
||
"t0, t1 = 5, 50\n",
|
||
"def learning_schedule(t):\n",
|
||
" return t0/(t+t1)\n",
|
||
"\n",
|
||
"theta = np.random.randn(2,1)\n",
|
||
"\n",
|
||
"for epoch in range(n_epochs):\n",
|
||
"# Can you figure out a better way of setting up the contributions to each batch?\n",
|
||
" for i in range(m):\n",
|
||
" random_index = M*np.random.randint(m)\n",
|
||
" xi = X[random_index:random_index+M]\n",
|
||
" yi = y[random_index:random_index+M]\n",
|
||
" gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
|
||
" eta = learning_schedule(epoch*m+i)\n",
|
||
" theta = theta - eta*gradients\n",
|
||
"print(\"theta from own sdg\")\n",
|
||
"print(theta)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6325ae4d",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Here we include momentum in the standard gradient descent approach."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 30,
|
||
"id": "cf10fd6b",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Using Autograd to calculate gradients using SGD\n",
|
||
"# OLS example\n",
|
||
"from random import random, seed\n",
|
||
"import numpy as np\n",
|
||
"import autograd.numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from autograd import grad\n",
|
||
"\n",
|
||
"# Note change from previous example\n",
|
||
"def CostOLS(y,X,theta):\n",
|
||
" return np.sum((y-X @ theta)**2)\n",
|
||
"\n",
|
||
"n = 100\n",
|
||
"x = 2*np.random.rand(n,1)\n",
|
||
"y = 4+3*x+np.random.randn(n,1)\n",
|
||
"\n",
|
||
"X = np.c_[np.ones((n,1)), x]\n",
|
||
"XT_X = X.T @ X\n",
|
||
"theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
|
||
"print(\"Own inversion\")\n",
|
||
"print(theta_linreg)\n",
|
||
"# Hessian matrix\n",
|
||
"H = (2.0/n)* XT_X\n",
|
||
"EigValues, EigVectors = np.linalg.eig(H)\n",
|
||
"print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
|
||
"\n",
|
||
"theta = np.random.randn(2,1)\n",
|
||
"eta = 1.0/np.max(EigValues)\n",
|
||
"Niterations = 100\n",
|
||
"\n",
|
||
"# Note that we request the derivative wrt third argument (theta, 2 here)\n",
|
||
"training_gradient = grad(CostOLS,2)\n",
|
||
"\n",
|
||
"for iter in range(Niterations):\n",
|
||
" gradients = (1.0/n)*training_gradient(y, X, theta)\n",
|
||
" theta -= eta*gradients\n",
|
||
"print(\"theta from own gd\")\n",
|
||
"print(theta)\n",
|
||
"\n",
|
||
"\n",
|
||
"n_epochs = 50\n",
|
||
"M = 5 #size of each minibatch\n",
|
||
"m = int(n/M) #number of minibatches\n",
|
||
"t0, t1 = 5, 50\n",
|
||
"def learning_schedule(t):\n",
|
||
" return t0/(t+t1)\n",
|
||
"\n",
|
||
"theta = np.random.randn(2,1)\n",
|
||
"\n",
|
||
"change = 0.0\n",
|
||
"delta_momentum = 0.3\n",
|
||
"\n",
|
||
"for epoch in range(n_epochs):\n",
|
||
" for i in range(m):\n",
|
||
" random_index = M*np.random.randint(m)\n",
|
||
" xi = X[random_index:random_index+M]\n",
|
||
" yi = y[random_index:random_index+M]\n",
|
||
" gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
|
||
" eta = learning_schedule(epoch*m+i)\n",
|
||
" # calculate update\n",
|
||
" new_change = eta*gradients+delta_momentum*change\n",
|
||
" # take a step\n",
|
||
" theta -= new_change\n",
|
||
" # save the change\n",
|
||
" change = new_change\n",
|
||
"print(\"theta from own sdg with momentum\")\n",
|
||
"print(theta)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "450296fc",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"### Similar (second order function now) problem but now with AdaGrad"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 31,
|
||
"id": "e61b44d8",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Using Autograd to calculate gradients using AdaGrad and Stochastic Gradient descent\n",
|
||
"# OLS example\n",
|
||
"from random import random, seed\n",
|
||
"import numpy as np\n",
|
||
"import autograd.numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from autograd import grad\n",
|
||
"\n",
|
||
"# Note change from previous example\n",
|
||
"def CostOLS(y,X,theta):\n",
|
||
" return np.sum((y-X @ theta)**2)\n",
|
||
"\n",
|
||
"n = 10000\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",
|
||
"# Including AdaGrad parameter to avoid possible division by zero\n",
|
||
"delta = 1e-8\n",
|
||
"for epoch in range(n_epochs):\n",
|
||
" # The outer product is calculated from scratch for each epoch\n",
|
||
" Giter = np.zeros(shape=(3,3))\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# Calculate the outer product of the gradients\n",
|
||
" Giter +=gradients @ gradients.T\n",
|
||
"\t# Simpler algorithm with only diagonal elements\n",
|
||
" Ginverse = np.c_[eta/(delta+np.sqrt(np.diagonal(Giter)))]\n",
|
||
" # compute update\n",
|
||
" update = np.multiply(Ginverse,gradients)\n",
|
||
" theta -= update\n",
|
||
"print(\"theta from own AdaGrad\")\n",
|
||
"print(theta)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6ddb5f5e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Running this code we note an almost perfect agreement with the results from matrix inversion.\n",
|
||
"\n",
|
||
"Similarly, here is our implementation of RMSprop."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 32,
|
||
"id": "3d87e7f3",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Using Autograd to calculate gradients using RMSprop and Stochastic Gradient descent\n",
|
||
"# OLS example\n",
|
||
"from random import random, seed\n",
|
||
"import numpy as np\n",
|
||
"import autograd.numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from autograd import grad\n",
|
||
"\n",
|
||
"# Note change from previous example\n",
|
||
"def CostOLS(y,X,theta):\n",
|
||
" return np.sum((y-X @ theta)**2)\n",
|
||
"\n",
|
||
"n = 10000\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 = np.zeros(shape=(3,3))\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# Previous value for the outer product of gradients\n",
|
||
" Previous = Giter\n",
|
||
"\t# Accumulated gradient\n",
|
||
" Giter +=gradients @ gradients.T\n",
|
||
"\t# Scaling with rho the new and the previous results\n",
|
||
" Gnew = (rho*Previous+(1-rho)*Giter)\n",
|
||
"\t# Taking the diagonal only and inverting\n",
|
||
" Ginverse = np.c_[eta/(delta+np.sqrt(np.diagonal(Gnew)))]\n",
|
||
"\t# Hadamard product\n",
|
||
" update = np.multiply(Ginverse,gradients)\n",
|
||
" theta -= update\n",
|
||
"print(\"theta from own RMSprop\")\n",
|
||
"print(theta)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "137ad886",
|
||
"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": 33,
|
||
"id": "07ab244c",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"import jax.numpy as jnp\n",
|
||
"from jax import grad, jit, vmap\n",
|
||
"\n",
|
||
"def sum_logistic(x):\n",
|
||
" return jnp.sum(1.0 / (1.0 + jnp.exp(-x)))\n",
|
||
"\n",
|
||
"x_small = jnp.arange(3.)\n",
|
||
"derivative_fn = grad(sum_logistic)\n",
|
||
"print(derivative_fn(x_small))"
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"language_info": {
|
||
"codemirror_mode": {
|
||
"name": "ipython",
|
||
"version": 3
|
||
},
|
||
"file_extension": ".py",
|
||
"mimetype": "text/x-python",
|
||
"name": "python",
|
||
"nbconvert_exporter": "python",
|
||
"pygments_lexer": "ipython3",
|
||
"version": "3.9.10"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 5
|
||
} |