{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "# Maximum likelihood estimation and numerical optimization" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "import autograd.numpy as np\n", "np.seterr(all=\"ignore\")\n", "import autograd as ag\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "deletable": true, "editable": true }, "source": [ "Suppose we want to estimate the probability of a coin landing heads (H), tails (T), or on the edge (E):" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3 2 1\n" ] } ], "source": [ "data = \"HTTHEH\"\n", "ch = sum([1 for c in data if c == \"H\"])\n", "ct = sum([1 for c in data if c == \"T\"])\n", "ce = sum([1 for c in data if c == \"E\"])\n", "print(ch, ct, ce)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Our model has two parameters, $\\theta_H$ and $\\theta_T$, the probability of heads and tails, respectively. In terms of these two parameters, the probability of seeing the data that we saw would be:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "deletable": true, "editable": true, "scrolled": false }, "outputs": [ { "data": { "image/png": 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PPQ0YMICNGzeSlpaGubk5x48fp169eu+dx0aSpJzR+3BXFEXVcNflxdTjx49j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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def likelihood(theta):\n", " ph, pt = theta\n", " pe = 1-ph-pt\n", " return ph**ch * pt**ct * pe**ce\n", "eps = 1e-2\n", "X, Y = np.meshgrid(np.arange(eps, 1-eps, 0.01), np.arange(eps, 1-eps, 0.01))\n", "\n", "def plot():\n", " fig = plt.figure(figsize=(6,6))\n", " CS = plt.contour(X, Y, likelihood((X, Y)), [0,1e-5,1e-4,5e-4,1e-3,1.5e-3,2e-3,2.3e-3], colors='k')\n", " plt.clabel(CS, inline=1, fontsize=10, fmt=\"%1.4f\")\n", " \n", "plot()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Below, we're going to make use of the gradient (vector of first derivatives) of the function, which we compute using a magic package called Autograd:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "g = ag.grad(likelihood)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "In stochastic gradient ascent/descent, at each step, we move a little bit in the direction that the surface rises/falls most steeply. The _step size_ or _learning rate_ $\\eta$ controls how quickly we move. If it is too high, then we can overshoot, as seen below." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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PPQ0dOpRNmzaRkZGBqakpR44coWHDhm9cx0aSpLej9+GuKIqq4a7Li6lHjhzB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\nX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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_path(path):\n", " plot()\n", " x0, y0 = path[0]\n", " plt.plot(x0, y0, marker='o', color='k')\n", " for xy1 in path[1:]:\n", " x1, y1 = xy1\n", " plt.arrow(x0, y0, x1-x0, y1-y0, head_width=0.01, color='k')\n", " x0, y0 = x1, y1\n", "\n", "theta0 = np.array([0.1, 0.4])\n", "theta = theta0\n", "path = [theta]\n", "eta = 1\n", "for iteration in range(100):\n", " theta1 = theta + eta*g(theta)\n", " path.append(theta1)\n", " theta = theta1\n", "plot_path(path)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "One way to fix this is to make the step size decrease over time. But be careful not to decrease it too much, or convergence may take a long time." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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HBwcW8AwjAwof7gB/V+7FxcVQUVHhpa3qiI+PBwDY2dnJrQa+NGzYEKGhofjh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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "theta = theta0\n", "path = [theta]\n", "eta = 20\n", "for iteration in range(100):\n", " theta1 = theta + eta/(iteration+1)*g(theta)\n", " path.append(theta1)\n", " theta = theta1\n", "plot_path(path)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Another trick is to halve the learning rate when the objective function doesn't improve." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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yxoeeRo0axc6dO0lPT8fU1JSTJ0/SpEmTt65jI0lS3uh9uCuKomq46/Ji6smT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\nRK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "theta = theta0\n", "path = [theta]\n", "eta = 10\n", "for iteration in range(100):\n", " theta1 = theta + eta*g(theta)\n", " path.append(theta1)\n", " if likelihood(theta1) <= likelihood(theta): eta /= 2\n", " theta = theta1\n", "plot_path(path)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.0" } }, "nbformat": 4, "nbformat_minor": 1 }