{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "### Week 1, Numpy, Probability, statistics and gradient descent" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this session, we will review some concepts from probability, linear algebra and multivariate calculus (essentially gradient descent) and start deriving some of the simplest models in machine learning" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__1a.__ Write a function that takes a 2d symmetric matrix as input and return the largest eigenvalue.\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# put your code here\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "__1b__ Do the same with arbitrary rectangular matrices and return the largest singular value" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# put your code here\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__1b__ Modify the function above and write a second function that now takes two arguments. The first argument is a matrix $X$ with singular value decomposition $(\\Sigma, U, V)$. The second argument is an integer $K$. The function should then output the matrix $X_{\\text{approx}}$ defined from the singular value decomposition of your input as\n", "\n", "$$X_{\\text{approx}} = \\sum_{i=1}^K \\sigma_i u_iv_i^T$$\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# put your code here\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__1c__ Consider the image shown below. Using the fact that every image is a 2D matrix. Apply your function to this image for various values of $K$. How large do you need to take $K$ to recover an clear image?" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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d+xU0zNnZmX1PgvD5+bmhSCxGiHyU9wATVGqSLGtjOByakp1Op//ZQBc4T7hV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\nl/qs288KD7Rg+5cv6W9I+tP21z/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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib.image as mpimg\n", "import numpy as np\n", "img=mpimg.imread('subject03.gif')\n", "noisy = np.random.normal(img, 10)\n", "imgplot = plt.imshow(noisy,cmap='gray')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# put your code here\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__1d__ Same question but now change the level of noise in the image. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# put your code here\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__3. MAP and MLE__ Consider a univariate Gaussian distribution " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$p(x) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}} e^{\\frac{-(x-\\mu)^2}{2\\sigma^2}}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pick up a value for the variance and a value for the mean. Then generate a few samples $\\left\\{x_i\\right\\}$ from the distribution. \n", "\n", "- Start by deriving the log-likelihood function. Plot this function for various values of $\\mu$ at $\\sigma$ fixed. Then vary $\\sigma$ and generate a plot for each value of $\\sigma$. How do the plot compare to each other?\n", "\n", "- As a second step, compute the estimators for $\\sigma$ and $\\mu$. Repeat the estimation for various draws of samples $\\left\\{x_i\\right\\}_{i=1}^n$ (keep the size of the sample fixed)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# put the code here\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__3b From MLE to MAP: Coin flipping__\n", "\n", "As a second exercise, we consider flipping a coin. The distribution of heads (resp. tails) can be modelled as a Bernoulli in this case. We thus have \n", "\n", "$$p(x|\\theta) = \\theta^x(1 - \\theta)^{1-x}$$\n", "\n", "for $x = 0$ or $1$. \n", "\n", "- Choose a value for $\\theta$ then generate a sequence of 20 coin tosses using the Bernoulli distribution. Without yet thinking of the MLE or MAP, from your sequence, what would be a reasonable estimator of the probability to get a head?\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# put your code here\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Derive the expression for the MLE and compute its value from the samples you generated above. Justify your developments.\n", "\n", "- Still using your parameter $\\theta$, imagine that you get the following sequence \n", "\n", "$$[1,1,1,1,1,1,1]$$\n", "\n", "What would be the MLE in this case? Does that seems reasonable ?\n", "\n", "- To be more fair, we will now use a prior. Since the Bernoulli distribution is in the exponential family, a good choice of prior is to take the conjugate prior which in this case is a Beta distribution. Plot the Beta distribution for a few pairs of parameters $(\\alpha, \\beta)$. What could be a good choice of prior? \n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# put your code here \n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "- If we neglect the normalizing factor in the Beta distribution, give the expression of the posterior. What distribution does the posterior correspond to?\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " - Pick a value for $\\theta$ (other than 0.5) and generate flipping sequences of length $0$, $5$, $15$ and $30$. For each, plot the resulting posterior, using the expression that you derived above. Approximately, what estimator do you get for the number of heads when taking all $30$ trials into account? " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# put your code here \n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Repeat the experiments above but assuming that surprisingly all your outcomes are '1'. That is, generate the posterior for outcomes given by vectors of all 1, of repsective lengths $0$, $5$, $15$, $30$. Also give the MLE at each step." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# put your code here\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__4a. Towards regression__ We now want to extend the previous result to a multivariate normal distribution. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Start by generating data along a line. I.e generate pairs of $(\\boldsymbol x \\in \\mathbb{R}^n,y)$ with \n", "\n", "$$ y =\\boldsymbol x^T \\boldsymbol b$$\n", "\n", "for some $\\boldsymbol b\\in\\mathbb{R}^n$ and biais $b_0$ that you can choose as you want. \n", "\n", "- Then add some Gaussian noise with variance $1$ to the variables $y$, i.e. you should now have an expression of the form\n", "\n", "$$ y_i =\\boldsymbol x_i^T \\boldsymbol b + \\varepsilon_i$$\n", "\n", "- What is the distribution of the $y_i$ ? Find the expression of the likelihood function in this case. How about the log-likelihood?\n", "\n", "- How can you compute the MLE?\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# put your code here\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__4b From theory to practice__ Download and open (use pandas) the following [salary dataset](https://raw.githubusercontent.com/neurospin/pystatsml/master/datasets/salary_table.csv)\n", "\n", "- Extract the sequences correspondind to the salaries and years of experience. \n", "\n", "- Start by plotting the data with the function scatter from pyplot.\n", "\n", "- We will use the linear gaussian model that we discussed above and assume that the salary can be expressed as directly proportionnal to the number of years of experience. I.e.\n", "\n", "$$s = \\beta_1 y_i + \\beta_0 \\varepsilon_i$$\n", "\n", "we further assume that the samples are independent. Using the MLE, derive an expression for the regression coefficients $\\beta_1$ and $\\beta_0$. What problem do you need to solve to get $\\beta_1$ and $\\beta_0$ ?\n", "(Hint, start by deriving the expression for $\\beta_0$ and $\\beta_1$ by computing the derivatives and setting them to $0$. Then substitute the expression for $\\beta_0$ into the expression for $\\beta_1$ and solve this last expression.)\n", "\n", "- Plot your model (i.e. $\\beta_1 y + \\beta_0$) on top of the data using pyplot. You are done with your first machine learning algorithm. \n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# put your code here\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__4c. From univariate to multivariate__\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__5. Gradient descent: Walking down the hill__\n", "\n", "As we have seen in class, except when there are very simple and can be solved explicitely, the parameters of most models in machine learning are set through optimization. As a first exercise, we will consider a simple model. Let us first consider the simple linear regression landscape\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Exercise 5.a.__ 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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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#%matplotlib notebook # use to activate interactive plotting \n", "import numpy as np\n", "import matplotlib.pyplot as plt\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", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "plt.ioff()\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Code a simple gradient algorithm (see corresponding note on the website). Set the parameters as follows\n", "\n", "- learning rate = step size: 0.1 \n", "- Max number of iterations: 20 \n", "- Stopping criterion: 0.0001 (Your iterations should stop when your gradient is smaller than the threshold)\n", "\n", "Then start your algorithm at \n", "\n", "- (x0 = 0.5, y0 = -0.5)\n", "- (x0 = -0.3, y0 = -0.3)\n", "\n", "And plot the iterations on top of the function (you can use the 3D plotting tools from matplolib or the simpler 'contourf' function). What do you see ?" ] } ], "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 }