{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "***\n", "# Problem Sheet 2\n", "***\n", "$\\newcommand{\\vct}[1]{\\mathbf{#1}}$\n", "$\\newcommand{\\mtx}[1]{\\mathbf{#1}}$\n", "$\\newcommand{\\e}{\\varepsilon}$\n", "$\\newcommand{\\norm}[1]{\\|#1\\|}$\n", "$\\newcommand{\\minimize}{\\text{minimize}\\quad}$\n", "$\\newcommand{\\maximize}{\\text{maximize}\\quad}$\n", "$\\newcommand{\\subjto}{\\quad\\text{subject to}\\quad}$\n", "$\\newcommand{\\R}{\\mathbb{R}}$\n", "$\\newcommand{\\trans}{T}$\n", "$\\newcommand{\\ip}[2]{\\langle {#1}, {#2} \\rangle}$\n", "$\\newcommand{\\zerovct}{\\vct{0}}$\n", "$\\newcommand{\\diff}[1]{\\mathrm{d}{#1}}$\n", "$\\newcommand{\\dom}{\\mathrm{dom} }$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "## Part A\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Problem 2.1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let $\\{\\vct{x}_k\\}_{k\\geq 0}$ be a sequence of vectors in $\\R^n$ and assume that this sequence converges linearly to some $\\vct{x}^*\\in \\R^n$ with respect to a norm $\\norm{\\cdot}$,\n", "\n", "\\begin{equation*}\n", " \\norm{\\vct{x}_{k+1}-\\vct{x}^*} \\leq r\\cdot \\norm{\\vct{x}_k-\\vct{x}^*}, \\quad k\\geq 0,\n", "\\end{equation*}\n", "\n", "for some constant $r\\in (0,1)$. \n", "\n", "(a) Show that for $M=\\norm{\\vct{x}_0-\\vct{x}^*}$, \n", "\n", "\\begin{equation*}\n", " \\norm{\\vct{x}_k-\\vct{x}^*} \\leq r^k \\cdot M.\n", " \\end{equation*}\n", "\n", "(b) Let $\\e>0$ be given. Show that if $N$ is an integer such that\n", "\n", "\\begin{equation*}\n", " N> \\frac{1}{1-r}\\left(\\ln(M)+\\ln\\left(\\frac{1}{\\e}\\right)\\right),\n", "\\end{equation*}\n", "\n", "then $\\norm{\\vct{x}_N-\\vct{x}^*}\\leq \\e$. In words, $N$ iterations are sufficient to reach accuracy $\\e$.\n", "\n", "(c) Now assume that the sequence converges quadratically,\n", "\n", "\\begin{equation*}\n", " \\norm{\\vct{x}_k-\\vct{x}^*}\\leq C\\norm{\\vct{x}_k-\\vct{x}^*}^2\n", "\\end{equation*}\n", "\n", "for some constant $C>0$. Show that\n", "\n", "\\begin{equation*}\n", " \\norm{\\vct{x}_k-\\vct{x}^*}\\leq C^k \\cdot M^{2^k}.\n", "\\end{equation*}\n", "\n", "How many steps will guarantee a solution up to an error $\\e$?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Problem 2.2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider the function\n", "\n", " \\begin{equation*}\n", " f(x) = \\sqrt{x^2+1}.\n", " \\end{equation*}\n", "\n", "Determine a value $\\overline{x}\\in \\R$ such that\n", "\n", "* for $x_0<\\overline{x}$, Newton's method converges to a minimizer,\n", "* for $x_0>\\overline{x}$, Newton's method does not converge.\n", "\n", "What happens if $x_0=\\overline{x}$ is chosen as starting point?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Problem 2.3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Describe a steepest descent method with respect to the norm \n", "\n", " \\begin{equation*}\n", " \\norm{\\vct{x}}_{\\infty} = \\max_{1\\leq i\\leq n} |x_i|.\n", " \\end{equation*}\n", "\n", "What are the descent directions? How can the best descent direction be found?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "## Part B\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Problem 2.4" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Iterative algorithms will never find the exact solution, so it is important to have suitable criteria for stopping an algorithm. Given a tolerance $\\e>0$, consider the following candidates for stopping criteria:\n", "\n", "(a) $\\norm{\\vct{x}_{k+1}-\\vct{x}_k}<\\e$;\n", "\n", "(b) $\\norm{\\nabla f(\\vct{x}_k)}<\\e$;\n", "\n", "(c) $k=100$.\n", "\n", "Apply Newton's method for minimizing the function\n", "\n", "\\begin{equation*}\n", " f(x) = (x-1)^6\n", "\\end{equation*}\n", "\n", "with each of the given stopping criteria. Which of these is the most efficient? In general, describe the benefits or disadvantages of each of these stopping criteria. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Problem 2.5" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When implementing descent algorithms one often uses **backtracking** to select a good step length. Given a descent direction $\\vct{p}_k$, one first tries the step length $1$ and then successively scales it down until the *sufficient decrease* condition (see Lecture 4) is satisfied.\n", "\n", "Fixing a decrease parameter $c\\in (0,1/2)$ and a scaling parameter $s\\in (0,1)$, backtracking works as follows.\n", "\n", "* $\\alpha=1$;\n", "* while $f(\\vct{x}_k+\\alpha \\vct{p}_k) \\geq f(\\vct{x}_k)+\\alpha \\cdot c\\cdot \\ip{\\vct{p}_k}{\\nabla f(\\vct{x}_k)}$: \n", " $\\displaystyle \\alpha = \\alpha\\cdot s$;\n", "* $\\displaystyle \\vct{x}_{k+1} = \\vct{x}_k+\\alpha \\vct{p}_k$\n", "\n", "Consider the function\n", "\n", "\\begin{equation*}\n", " f(\\vct{x}) = e^{x_1+3x_2-0.1}+e^{x_1-3x_2-0.1}+e^{-x_1-0.1}\n", "\\end{equation*}\n", "\n", "on $\\R^2$, with level sets given in the contour plot below.\n", "Using the starting point $\\vct{x}_0=(-1,0.7)^{\\trans}$, plot the trajectory of\n", "\n", "(a) Gradient descent with step length $0.1$;\n", "\n", "(b) Gradient descent with backtracking, using $c=0.1$ and $s=0.5$;\n", "\n", "(c) Newton's method." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAAEACAYAAABVtcpZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "# Define the function f and its derivative\n", "def f(x):\n", " return np.exp(x[0]+3*x[1]-0.1)+np.exp(x[0]-3*x[1]-0.1)+np.exp(-x[0]-0.1)\n", "\n", "def df(x):\n", " return np.array([np.exp(x[0]+3*x[1]-0.1)+np.exp(x[0]-3*x[1]-0.1)-np.exp(-x[0]-0.1), 3*np.exp(x[0]+3*x[1]-0.1)-3*np.exp(x[0]-3*y[1]-0.1)])\n", "\n", "# Get a list of values for specifying the level sets\n", "xvals = np.array([[np.linspace(-2,-0.5,20)], [np.zeros(20)]])\n", "yvals = list(reversed(f(xvals)[0]))\n", "\n", "# Create a meshgrid and a contour plot\n", "xx = np.linspace(-2.5,1,100)\n", "yy = np.linspace(-0.8,0.8,100)\n", "X, Y = np.meshgrid(xx, yy)\n", "# The construction inside looks odd: we want to transform the set of input pairs given\n", "# by the meshgrid into a 2 x n array of values that we can apply f to (calling f on such\n", "# an array will apply the function f to each column)\n", "Z = f(np.dstack((X,Y)).reshape((X.size, 2)).transpose())\n", "# the result of applying f is a long list, but we want a matrix\n", "Z = Z.reshape(X.shape)\n", "\n", "% matplotlib inline\n", "cmap = plt.cm.get_cmap(\"coolwarm\")\n", "plt.contour(X, Y, Z, yvals, cmap = cmap)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Problem 2.6" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(Logistic Regression.) Let $Y$ be a random variable that satisfies\n", "\n", " \\begin{equation*}\n", " P\\{Y=1\\} = p, \\quad P\\{Y=0\\} = 1-p.\n", " \\end{equation*}\n", "\n", "This random variable models an event with two possible outcomes. The {\\em logistic model} for $p$ has the form\n", "\n", "\\begin{equation*}\n", " p = \\frac{e^{\\ip{\\vct{a}}{\\vct{u}}+b}}{1+e^{\\ip{\\vct{a}}{\\vct{u}}+b}},\n", "\\end{equation*}\n", "\n", "$\\vct{u}\\in \\R^n$ is a vector of *explanatory variables*, and $\\vct{a}\\in \\R^n, b\\in \\R$ are the *model parameters* that explain how $p$ depends on the variables. For example, the variable $Y$ could represent a choice in an election and the vector $\\vct{u}$ encodes demographic information, or the variable $Y$ could indicate the presence of a disease and $\\vct{u}$ encodes data about a patient.\n", "\n", "Given vectors $\\vct{u}_1,\\dots,\\vct{u}_m$ and corresponding observed outcomes $y_1,\\dots,y_m$, we would like to estimate the parameters $\\vct{a}$ and $b$. Assuming the observed outcomes $y_1=\\cdots =y_k=1$ and $y_{k+1}=\\cdots y_m=0$, the *log likelihood* function is defined as\n", "\n", "\\begin{equation*}\n", " \\sum_{i=1}^k \\ln(p_i) +\\sum_{i=k+1}^m \\ln(1-p_i),\n", "\\end{equation*}\n", "\n", "where $p_i$ is the probability computed using $\\vct{u}_i$,\n", "and the goal is to find parameters $\\vct{a},b$ that maximize this function.\n", "\n", "(a) Show that the negative of the log likelihood function is given by\n", "\n", "\\begin{equation*}\n", " f(\\vct{a},b) = -\\sum_{i=1}^k (\\ip{\\mtx{a}}{\\vct{u}_i}+b)+\\sum_{i=1}^m\\ln\\left(1+e^{\\ip{\\vct{a}}{\\vct{u}_i}+b}\\right)\n", " \\end{equation*}\n", "\n", "Show that the sum of convex functions and the composition of a convex function with a linear one are convex, and deduce that the log likelihood function is convex.\n", "\n", "(b) Consider the following table, in which the first row represents the hours of prepration and the second row whether an exam was passed (1) or not (0).\n", "\n", "| Hours | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 | 3 | 4.5 | 4 |4.5 | 4.75 | 5 |\n", "| ----- | --- | - | --- | - | --- | - | - | --- | - | -- | ---- | - |\n", "| Pass | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |\n", "\n", "\n", "Find the (negative) log likelihood function $f(a,b)$. Solve the corresponding minimization problem \n", "\n", "\\begin{equation*}\n", " \\minimize f(a,b)\n", "\\end{equation*}\n", "\n", "in two dimensions using either gradiend descent or Newton's method, and plot the resulting probability function, giving the relationship of hours of study to probability of success." ] }, { "cell_type": "markdown", "metadata": {}, "source": [] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.12" } }, "nbformat": 4, "nbformat_minor": 0 }