{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "### HW 2: Gradient descent\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Total: 25 pts__" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Start date: Friday Sept. 13
\n", "Due date: Tuesday Sept. 24" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this homework, you will learn to code one of the building block of many learning algorithms. When one wants to fit a model $f_{\\beta}$ (with parameters $\\beta$) to some training dataset $\\mathcal{D}_T$, as we saw in regression, we usually solve an optimization problem of the form \n", "\n", "\\begin{align}\n", "\\min_{f_{\\beta}} \\sum_{i\\in \\mathcal{D}_T} \\left|f_{\\beta}(x_i) - t_i\\right|^2\n", "\\end{align}\n", "\n", "When the learning model is relatively simple, such as in linear regression, an explicit solution can be computed in closed form as we saw this week. However, for most models (and particularly for the more interesting ones), such explicit expression does not exists or is not straightforward and we thus need an alternative. \n", "\n", "The gradient descent algorithm takes any loss function $\\ell(\\beta, x)$ for which one wants to find a local minimum, i.e.\n", "\n", "\\begin{align}\n", "\\min_{\\beta} \\ell(\\beta; x, t)\n", "\\end{align}\n", "\n", "and iterates and the following step\n", "\n", "\\begin{align}\n", "\\beta^{t+1} \\leftarrow \\beta^{t} - \\alpha\\; \\text{grad}\\; f(\\beta^t)\n", "\\end{align}\n", "\n", "for a learning rate $\\alpha$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a starting point, consider the following function whose plot is given below. You can uncomment the first line to activate interactive plot on jupyter and use the \"plt.ioff()\n", "%matplotlib inline\" cell below to turn the interactive mode off\n", "\n", "$$f(x,y) = 3(1-x)^2 e^{-(x^2) - (y+1)^2}- 10(x/5 - x^3 - y^5)e^{-x^2-y^2}- \\frac{1}{3} e^{-(x+1)^2 - y^2}$$\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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bczC9IySFZZbMVWxcXL9GRHCwfRnDLWKb65GTJPbgCSdxvUmWPJuBKAhCLw4u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\nOIsYkK8HP/30E+644w52U42aA9FSx6lTp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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#%matplotlib notebook # use to activate interactive plotting \n", "import numpy as np\n", "\n", "x = np.linspace(-2,2,100)\n", "y = np.linspace(-3,3,100)\n", "\n", "xx, yy = np.meshgrid(x, y, indexing='xy')\n", "\n", "z = 3*((1-xx)**2) * np.exp(-(xx**2) - (yy+1)**2) \\\n", "- 10*(xx/5 - xx**3 - yy**5) * np.exp(-xx**2 - yy**2)- (1/3)* np.exp(-(xx+1)**2 - yy**2)\n", "\n", "from matplotlib import cm\n", "\n", "from mpl_toolkits.mplot3d import Axes3D\n", "from mpl_toolkits.mplot3d import axes3d \n", "\n", "\n", "fig = plt.figure()\n", "\n", "ax = fig.add_subplot(111, projection='3d')\n", "ax.plot_surface(xx, yy, z, cmap=cm.viridis,alpha=.4,\n", " linewidth=0, antialiased=False)\n", "\n", "\n", "plt.show()\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__1a.(10 pts)__ Code a function __'gradient_descent'__ that takes as argument a function 'f(x,y)' in two variables and a learning rate $\\alpha$ as well as a maximum number of iterations $N$ and return the location $(x,y)$ of a local minimum as well as the value of the function and gradient after the $N$ iterations.\n", "\n", "(Hint: note that you don't need to know the explicit expression for the derivative of f(x,y), you can simply use the definition of the derivative \n", "$$\\frac{\\partial f}{\\partial y} \\approx \\frac{[f(x, y+h) - f(x,y)]}{h}$$ \n", "for a sufficiently small step size h and similarly for $x$.\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# First defining the function\n", "\n", "def my_function(x,y):\n", "\n", " z = 3*((1-x)**2) * np.exp(-(x**2) - (y+1)**2) \\\n", " - 10*(x/5 - x**3 - y**5) * np.exp(-x**2 - y**2)- (1/3)* np.exp(-(x+1)**2 - y**2)\n", " \n", " return z\n", " \n", "\n", "\n", "def gradient_descent(my_function,x0,learning_rate, epsilong, N_iter):\n", " \n", " \n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__1b.(5pts)__ Extend your algorithm to a function of $D$ variables, $f(x_1, x_2, \\ldots, x_D)$" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# put the code here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__1b.(10 pts)__ Now that you have a gradient descent algorithm, we want to use it on a simple regression problem. Apply your GD iterations to the regression problem below." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Generate and plot the line $t(x) = \\beta_0 + \\beta_1 x$ for $\\beta_0 = 1$ and $\\beta_1 = 2$. (use linspace with 100 points between $-5$ and $5$)\n", "\n", "- Generate $20$ samples along the line (use linspace with 20). For each of those samples, generate the data/feature vectors $(t_i, x_i, x_i^2)$ where $t_i$ si defined as \n", "\\begin{align}\n", "t_i = x_i + \\varepsilon_i\n", "\\end{align}\n", "\n", "and $\\varepsilon_i$ is some random gaussian noise with mean $0$ and variance $3$.\n", "\n", "- Solve the minimization problem \n", "\n", "\\begin{align}\n", "\\min_{\\beta_0, \\beta_1, \\beta_2} \\sum_{i=1}^{20}\\left|t_i - \\left(\\beta_0 + \\beta_1x_i + \\beta_2 x_i^2\\right)\\right|^2 + \\lambda \\|\\mathbf{\\beta}\\|_2^2\n", "\\end{align}\n", "\n", "where $\\mathbf{\\beta} = (\\beta_0, \\beta_1,\\beta_2)$, with your gradient descent algorithm. \n", "\n", "\n", "- Repeat the steps above for a few values of $\\lambda$. For each value of $\\lambda$, apply the model you get on a new set of $20$ points between $-5$ and $5$ that you perturb with the same gaussian noise as before, i.e. $t_i = x_i + \\varepsilon_i$, apply your model to those __new__ points and compute the error \n", "\n", "\\begin{align}\n", "\\text{err}(\\lambda) = \\frac{1}{20}\\sum_{i=1}^{20} \\left|t_i - \\left(\\beta_0 + \\beta_1x_i +\\beta_2 x_i^2 \\right)\\right|^2\n", "\\end{align}\n", "\n", "Then plot the values $\\text{err}(\\lambda)$ as a function of $\\lambda$.\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "\n", "\n", "# put your code here\n", "\n", "\n", "\n", "\n" ] } ], "metadata": { "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": "2.7.13" } }, "nbformat": 4, "nbformat_minor": 2 }