{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Linear Regression and Kernel Methods\n", "====================================\n", "\n", "*Important:* Please read the [installation page](http://gpeyre.github.io/numerical-tours/installation_matlab/) for details about how to install the toolboxes.\n", "$\\newcommand{\\dotp}[2]{\\langle #1, #2 \\rangle}$\n", "$\\newcommand{\\enscond}[2]{\\lbrace #1, #2 \\rbrace}$\n", "$\\newcommand{\\pd}[2]{ \\frac{ \\partial #1}{\\partial #2} }$\n", "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$\n", "$\\newcommand{\\umax}[1]{\\underset{#1}{\\max}\\;}$\n", "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$\n", "$\\newcommand{\\uargmin}[1]{\\underset{#1}{argmin}\\;}$\n", "$\\newcommand{\\norm}[1]{\\|#1\\|}$\n", "$\\newcommand{\\abs}[1]{\\left|#1\\right|}$\n", "$\\newcommand{\\choice}[1]{ \\left\\{ \\begin{array}{l} #1 \\end{array} \\right. }$\n", "$\\newcommand{\\pa}[1]{\\left(#1\\right)}$\n", "$\\newcommand{\\diag}[1]{{diag}\\left( #1 \\right)}$\n", "$\\newcommand{\\qandq}{\\quad\\text{and}\\quad}$\n", "$\\newcommand{\\qwhereq}{\\quad\\text{where}\\quad}$\n", "$\\newcommand{\\qifq}{ \\quad \\text{if} \\quad }$\n", "$\\newcommand{\\qarrq}{ \\quad \\Longrightarrow \\quad }$\n", "$\\newcommand{\\ZZ}{\\mathbb{Z}}$\n", "$\\newcommand{\\CC}{\\mathbb{C}}$\n", "$\\newcommand{\\RR}{\\mathbb{R}}$\n", "$\\newcommand{\\EE}{\\mathbb{E}}$\n", "$\\newcommand{\\Zz}{\\mathcal{Z}}$\n", "$\\newcommand{\\Ww}{\\mathcal{W}}$\n", "$\\newcommand{\\Vv}{\\mathcal{V}}$\n", "$\\newcommand{\\Nn}{\\mathcal{N}}$\n", "$\\newcommand{\\NN}{\\mathcal{N}}$\n", "$\\newcommand{\\Hh}{\\mathcal{H}}$\n", "$\\newcommand{\\Bb}{\\mathcal{B}}$\n", "$\\newcommand{\\Ee}{\\mathcal{E}}$\n", "$\\newcommand{\\Cc}{\\mathcal{C}}$\n", "$\\newcommand{\\Gg}{\\mathcal{G}}$\n", "$\\newcommand{\\Ss}{\\mathcal{S}}$\n", "$\\newcommand{\\Pp}{\\mathcal{P}}$\n", "$\\newcommand{\\Ff}{\\mathcal{F}}$\n", "$\\newcommand{\\Xx}{\\mathcal{X}}$\n", "$\\newcommand{\\Mm}{\\mathcal{M}}$\n", "$\\newcommand{\\Ii}{\\mathcal{I}}$\n", "$\\newcommand{\\Dd}{\\mathcal{D}}$\n", "$\\newcommand{\\Ll}{\\mathcal{L}}$\n", "$\\newcommand{\\Tt}{\\mathcal{T}}$\n", "$\\newcommand{\\si}{\\sigma}$\n", "$\\newcommand{\\al}{\\alpha}$\n", "$\\newcommand{\\la}{\\lambda}$\n", "$\\newcommand{\\ga}{\\gamma}$\n", "$\\newcommand{\\Ga}{\\Gamma}$\n", "$\\newcommand{\\La}{\\Lambda}$\n", "$\\newcommand{\\si}{\\sigma}$\n", "$\\newcommand{\\Si}{\\Sigma}$\n", "$\\newcommand{\\be}{\\beta}$\n", "$\\newcommand{\\de}{\\delta}$\n", "$\\newcommand{\\De}{\\Delta}$\n", "$\\newcommand{\\phi}{\\varphi}$\n", "$\\newcommand{\\th}{\\theta}$\n", "$\\newcommand{\\om}{\\omega}$\n", "$\\newcommand{\\Om}{\\Omega}$\n", "$\\newcommand{\\eqdef}{\\equiv}$" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "This tour studies linear regression method, and its non-linear variant\n", "using kernlization.\n", "\n", "\n", "We recommend that after doing this Numerical Tours, you apply it to your\n", "own data, for instance using a dataset from [LibSVM](https://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/).\n", "\n", "_Disclaimer:_ these machine learning tours are intended to be\n", "overly-simplistic implementations and applications of baseline machine learning methods.\n", "For more advanced uses and implementations, we recommend\n", "to use a state-of-the-art library, the most well known being\n", "[Scikit-Learn](http://scikit-learn.org/)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "WARNING: Method definition ndgrid(AbstractArray{T<:Any, 1}) in module NtToolBox at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:3 overwritten at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:3.\n", "WARNING: Method definition ndgrid(AbstractArray{#T<:Any, 1}, AbstractArray{#T<:Any, 1}) in module NtToolBox at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:6 overwritten at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:6.\n", "WARNING: Method definition ndgrid_fill(Any, Any, Any, Any) in module NtToolBox at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:13 overwritten at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:13.\n", "WARNING: Method definition ndgrid(AbstractArray{#T<:Any, 1}...) in module NtToolBox at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:19 overwritten at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:19.\n", "WARNING: Method definition meshgrid(AbstractArray{T<:Any, 1}) in module NtToolBox at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:33 overwritten at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:33.\n", "WARNING: Method definition meshgrid(AbstractArray{#T<:Any, 1}, AbstractArray{#T<:Any, 1}) in module NtToolBox at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:36 overwritten at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:36.\n", "WARNING: Method definition meshgrid(AbstractArray{#T<:Any, 1}, AbstractArray{#T<:Any, 1}, AbstractArray{#T<:Any, 1}) in module NtToolBox at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:44 overwritten at /Users/gpeyre/.julia/v0.5/NtToolBox/src/ndgrid.jl:44.\n" ] } ], "source": [ "using PyPlot\n", "using NtToolBox" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Dataset Loading\n", "---------------\n", "We test the method on the\n", "[Boston house prices dataset](http://scikit-learn.org/stable/modules/generated/sklearn.datasets.load_boston.html), consisting in $n=506$ samples with\n", "features $x_i \\in \\RR^p$ in dimension $p=13$. The goal is to predict the price value\n", "$y_i \\in \\RR$.\n", "\n", "\n", "Helpers." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "# SetAR = @(ar)set(gca, 'PlotBoxAspectRatio', [1 ar 1], 'FontSize', 10);\n", "Xm = X -> X - repeat(mean(X,1), outer=(size(X,1), 1))\n", "Cov = X -> Xm(X)'*Xm(X);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Load the dataset." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "A = readdlm(\"NtToolBox/src/data/boston_house_prices.csv\", ',');" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Randomly permute it." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "A = A[randperm(size(A,1)),:];" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Separate the features $X$ from the data $y$ to predict information." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "X = A[:,1:end-1]\n", "y = A[:,end];" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "$n$ is the number of samples, $p$ is the dimensionality of the features," ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "n,p = size(X);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Dimenionality Reduction and PCA\n", "-------------------------------\n", "In order to display in 2-D or 3-D the data, dimensionality is needed.\n", "The simplest method is the principal component analysis, which perform an\n", "orthogonal linear projection on the principal axsis (eigenvector) of the\n", "covariance matrix.\n", "\n", "\n", "Display the covariance matrix." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "imshow(Cov(X), extent=[0, 1, 0, 1], cmap = get_cmap(\"jet\"));" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Compute PCA ortho-basis and\n", "the feature in the PCA basis." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "U,D,V = svd(Xm(X),thin=true)\n", "Z = Xm(X) * V;" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Plot sqrt of the eigenvalues." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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7BmSE+M7Lym5WIqLhjgEZIT7XQ3Ickoho2GNARkhGsg7jUuMBAO83X0Kvg+OQRETDGQMyguZcPop0ugTMZy/JXA0REd0MAzKCZvP+kEREUYMBGUGcMICIKHowICMoTR+HiaMTAAD/OGdFt71f5oqIiOhGGJARNnA2a79b4PDHHTJXQ0REN8KAjLD8CaO8z3k9JBHR8MWAjLDZE4ze57wekoho+GJARlhqohafSU8CAHxw3gpbn1PmioiIaDAMSBkMjEO6BXC4keOQRETDEQNSBrN5uQcR0bDHgJTB7AlGSJLnOU/UISIanhiQMkiO12CqSQ8AOP6JDZYeh8wVERHRtRiQMhkYhxQCqOM4JBHRsMOAlAmnnSMiGt4YkDKZNcEIxeVxyIMchyQiGnYYkDLRx6lx520GAMDJ1k5c7LLLXBEREV2NASmjq7tZOQ5JRDS8MCBlNHsixyGJiIYrBqSM7hlvhPLyQCSvhyQiGl4YkDJK1KowfaxnHPLD9i60d/bJXBEREQ1gQMrs6nHIg2c4DklENFz4FZBlZWW45557kJSUhLS0NCxatAgNDQ0+bYQQ2LhxI8aMGQOdToeCggKcPn3ap01fXx9KSkqQmpqKxMRELFmyBG1tbT5tOjo6UFRUBL1ej+TkZCxfvhxdXV0B7ubwlc9xSCKiYcmvgKypqUFJSQkOHjyIqqoqOJ1OfP7zn0d3d7e3zebNm1FeXo6KigrU1dUhISEBhYWF6Ou70n24Zs0a7NmzB7t27UJNTQ1aWlqwePFin20VFRXh2LFjqKqqQmVlJQ4cOIAVK1YEubvDT+44I9RKzzgkr4ckIhpGRBDa29sFAFFTUyOEEMLtdguTySS2bNnibWOxWIRWqxU7d+70vlar1WLXrl3eNidOnBAARG1trRBCiOPHjwsA4vDhw942e/fuFZIkifPnzw+pNqvVKgAIq9UazC5GxMPb3hXj1lWKcesqRYulR+5yiIhiSqB5ENQYpNVqBQAYjUYAQGNjI1pbW1FQUOBtYzAYkJeXh9raWgCA2WyG0+n0aTNlyhRkZWV529TW1iI5ORm5ubneNgUFBVAoFKirqxu0FrvdDpvN5vOIFpx2joho+Ak4IN1uN1avXo25c+fizjvvBAC0trYCANLT033apqene9e1trZCo9EgOTn5pm3S0tJ81qtUKhiNRm+ba5WVlcFgMHgfmZmZge5axPF6SCKi4SfggCwpKcHRo0fx6quvhrKegK1fvx5Wq9X7aG5ulrukIZuZlQKNyvNPweshiYiGh4ACsrS0FJWVldi/fz/Gjh3rXW4ymQDgujNS29ravOtMJhMcDgcsFstN27S3t/us7+/vR0dHh7fNtbRaLfR6vc8jWsSplZiZ5TmiPnepF80dPTJXREREfgWkEAKlpaXYvXs39u3bh+zsbJ/12dnZMJlMqK6u9i6z2Wyoq6tDfn4+ACAnJwdqtdqnTUNDA5qamrxt8vPzYbFYYDabvW327dsHt9uNvLw8//cyCuRPGOV9zqNIIiL5qfxpXFJSgh07duCPf/wjkpKSvOOBBoMBOp0OkiRh9erV2LRpEyZNmoTs7Gxs2LABGRkZWLRokbft8uXLsXbtWhiNRuj1eqxatQr5+fmYPXs2AGDq1Kl48MEH8cQTT6CiogJOpxOlpaVYunQpMjIyQvxXMDzkT0zFL//ieV7T0I78CalI0KqQEq+GJEnyFkdENAJJQggx5MY3+KDevn07Hn/8cQCeo8wf/ehHePHFF2GxWDBv3jxs3boVkydP9rbv6+vDd77zHezcuRN2ux2FhYXYunWrT/dpR0cHSktLsWfPHigUCixZsgTl5eVITEwcUq02mw0GgwFWqzUqulsvdPYhv2wf+t2+/xzjjPFYNmc8luSMhUGnlqk6IqLoFWge+BWQ0SSaArLm1AWsfNmMHofrunUDX0l0GiW2PZqD+ZNHR7Y4IqIoF2gecC5WmdWcuoDi7YfQ67w+HAFAXH70Ol0o3n4INacuRLQ+IqKRigEpI2uvEytfNntC8BbH8UJ4gnLly2ZYe52RKI+IaERjQMroD+Zz6HW4bhmOA4QAeh0uvH7kXHgLIyIiBqRchBD43d8+Dui9L737MWJ06JiIaNhgQMrkUo8TZzt64G/MCQBnO3pg6WE3KxFRODEgZdJt7w/q/V1Bvp+IiG6OASmTBK1fczRcJzHI9xMR0c0xIGWSEq/GOGM8/J0jR4Jn8oDkeE4aQEQUTgxImUiShGVzxgf03sfnjuf0c0REYcaAlNGSnLHQaZQYatYpJM+MOotnjr11YyIiCgoDUkYGnRrbHs2BBNwyJAdWVzyawzlZiYgigAEps/mTR2N78Szo1EpPUN6gnSQBLxXPwr2ci5WIKCIYkMPA/MmjUbt+ATYunIYsY7zPOpXCE5luASTG8cxVIqJI4d08hhkhBCw9TnTZ+5GoVeHNo59g/e6jAID7p6Tht4/fI3OFRETRhXfziBGSJCElQYNMYzxSEjRYkpOJ25J1AIB9J9tx9LxV5gqJiEYGBuQwp1Ep8M35E7yvn9v3oYzVEBGNHAzIKPDV3EykJWkBAG8ea0VDa6fMFRERxT4GZBSIUyux4t6rjiL38yiSiCjcGJBR4v/kZcGYoAEAVP6jBR9d6JK5IiKi2MaAjBLxGhX+5XPZADw3Tt66/yOZKyIiim0MyCjy9dnjvLPovFF/Hs0dPTJXREQUuxiQUSQpTo3iueMBAC63wNa3eRRJRBQuDMgoUzwn23svyP82N6PF0itzRUREsYkBGWUM8WosmzMOAOB0Cbx44IzMFRERxSYGZBT6xtxs6NRKAMDOQ01o7+yTuSIiotjDgIxCqYlaPDo7CwBg73fj1zyKJCIKOQZklHri3gnQqDz/fC8fbEJHt0PmioiIYgsDMkqlJcXhkXsyAQC9Thf+8x0eRRIRhRIDMor96/yJUCs994v83d/OwtrjlLkiIqLYwYCMYhnJOjycMxYA0GXvx0t/+1jegoiIYggDMsqtnH87lArPUeRv321EZx+PIomIQoEBGeWyUuOx6O7bAADWXidePtgkc0VERLGBARkDvvVPEyF5DiLxm7+eQY+jX96CiIhiAAMyBkwcnYgvTc8AAFzsdmBHHY8iiYiCxYCMEaX/dLv3+YsHzqDP6ZKxGiKi6MeAjBGfMSWh8I50AEB7px273muWuSIioujGgIwhq+6f5H1eUXMGjn63jNUQEUU3BmQMufM2A+6fkgYAOG/pxe73z8lcERFR9GJAxpjS+6+MRT6//yP0u3gUSUQUCAZkjJmZlYJ5t48CADR19GDPP1pkroiIKDoxIGPQ1UeRz+37EC63kLEaIqLoxICMQbMnpGLWeCMA4KML3XjzaKvMFRERRR+/A/LAgQNYuHAhMjIyIEkS3njjDZ/1Qghs3LgRY8aMgU6nQ0FBAU6fPu3Tpq+vDyUlJUhNTUViYiKWLFmCtrY2nzYdHR0oKiqCXq9HcnIyli9fjq6urgB2cWRateDKUeSz+07DzaNIIiK/+B2Q3d3dmDFjBp5//vlB12/evBnl5eWoqKhAXV0dEhISUFhYiL6+Pm+bNWvWYM+ePdi1axdqamrQ0tKCxYsX+/ycoqIiHDt2DFVVVaisrMSBAwewYsUKf8sdsebdPgozMpMBACdbO/GXE223eAcREfkQQQAgdu/e7X3tdruFyWQSW7Zs8S6zWCxCq9WKnTt3el+r1Wqxa9cub5sTJ04IAKK2tlYIIcTx48cFAHH48GFvm7179wpJksT58+eHVJvVahUAhNVqDWYXo9pfjreKcesqxbh1lWLhs38Vbrdb7pKIiCIu0DwI6RhkY2MjWltbUVBQ4F1mMBiQl5eH2tpaAIDZbIbT6fRpM2XKFGRlZXnb1NbWIjk5Gbm5ud42BQUFUCgUqKurC2XJMe3+KWmYNkYPAPjHOStqTl2QuSIiougR0oBsbfWcDJKenu6zPD093buutbUVGo0GycnJN22Tlpbms16lUsFoNHrbXMtut8Nms/k8RjpJkrDq/qvHIj+EEByLJCIaipg5i7WsrAwGg8H7yMzMlLukYaHwDhMmpSUCAMxnL6H2zEWZKyIiig4hDUiTyQQA152R2tbW5l1nMpngcDhgsVhu2qa9vd1nfX9/Pzo6OrxtrrV+/XpYrVbvo7mZk3UDgEIh+VwX+Wz1hzJWQ0QUPUIakNnZ2TCZTKiurvYus9lsqKurQ35+PgAgJycHarXap01DQwOampq8bfLz82GxWGA2m71t9u3bB7fbjby8vEG3rdVqodfrfR7k8aXpGcgelQAAqD1zEe993CFzRUREw5/fAdnV1YX6+nrU19cD8JyYU19fj6amJkiShNWrV2PTpk3405/+hA8++ACPPfYYMjIysGjRIgCek3aWL1+OtWvXYv/+/TCbzSguLkZ+fj5mz54NAJg6dSoefPBBPPHEEzh06BDeffddlJaWYunSpcjIyAjh7o8MSoWEb9030fv62X08iiQiuiV/T5fdv3+/AHDdY9myZUIIz6UeGzZsEOnp6UKr1YoFCxaIhoYGn5/R29srvvWtb4mUlBQRHx8vvvKVr4hPPvnEp83FixfFI488IhITE4VerxfFxcWis7NzyHXyMg9fjn6XmPt0tfeyj/qmS3KXREQUEYHmgSREbJ7WaLPZYDAYYLVa2d162St1Z/HD3UcBAA9MS8evH8u9xTuIiKJfoHkQM2ex0q09nDMWJn0cAKDqeBtOfMJLYYiIboQBOYJoVUr86/wJ3tfPcSySiOiGGJAjzCOzsjAqUQsA+PPRT/Bhe6fMFRERDU8MyBEmTq3EinuzAQBCAM/v/0jmioiIhicG5AhUlDcOKfFqAMAf68/j7MVumSsiIhp+GJAjUIJWheXzPEeRbgFs3f8RhBDo6HaguaMHHd0OztlKRCOeSu4CSB6PzRmPFw6cQWdfP3aZm/HOh5/ivKXXu36cMR7L5ozHkpyxMOjUMlZKRCQPHkGOUPo4Ne7/zGgAnqPIq8MRAJo6evBU5XHkl1XzNllENCIxIEeomlMXsOcfn9xw/cAUSb1OF4q3H2JIEtGIw4Acgay9Tqx82YyhjDIK4QnKlS+bYe11hrs0IqJhgwE5Av3BfA69DheGeh6OEECvw4XXj5wLb2FERMMIA3KEEULgd3/7OKD3vvTuxzy7lYhGDAbkCHOpx4mzHT1D6l69mgBwtqMHlh52sxLRyMCAHGG67f1Bvb8ryPcTEUULBuQIk6AN7tLXxCDfT0QULRiQI0xKvBrjjPGQAnivUgLeeP8c+pyukNdFRDTcMCBHGEmSsGzO+IDe6xLATypPYP6W/Xjp3UYGJRHFNAbkCLQkZyx0GiWkIR5GSgCUVzVus9nx4z3Hce9mBiURxS4G5Ahk0Kmx7dEcSMAtQ1KSPI/txffgf749D4V3pHvXtXcyKIkodkkiRi9ss9lsMBgMsFqt0Ov1cpczLNWcuoCVL5vR6/AE29W/CAO5qdMoUfFoDu6dPNq77liLFeXVp/HWsTafn5eWpMW37puIpbOyEKdW3nL7Qghc6nGi296PBK0KKfFqSEM9rCUiGqJA84ABOcJZe514/cg5vPTuxzjb0eNdPs4Yj8fneu7moY8b/G4egQaltdeJP5jP4Xd/u36bvIMIEYUaA/IaDEj/CCFg6XGiy96PRK0KyX4czd0sKFfeNxGPXBWUQz1q3fZoDuZfddRKRBQoBuQ1GJCRd6ugHJuiw7/+P88k6Tf7rZMkT1huL57FkCSioDEgr8GAlM/xFhvKq0/jzWOtAf8MSQJ0aiVq1y9gdysRBSXQPOBZrBRy0zL0qPh6Dv787c/hwTtMAf0M3kGEiOTGgKSwGQjK/1k1D7ohnNU6GN5BhIjkwoCksBuTrENvANdI8g4iRCQnBiSFHe8gQkTRiAFJYRfsHUS0av6aElHk8ZOHwi6YO4gAwBee+St++j/H0dDaGdK6iIhuhgFJYRfMHUQA4GK3A7/+ayMKnzmALz/3Dv6r9mNYehwB/SwhBDq6HWju6EFHt4NogukBAAAQPElEQVQnABHRDfE6SIoIa68T+WXV6HW6bjpJwACFBKiVCtw7eRTebrgAp8v3TRqlAg9MS8fDuWPxudtHQaW8+Xc9Tm9HNHJxooBrMCCHn5pTF1C8/dCQZ9J5qXgW7p08Gpe6HfjT31vw3+Zz+OC89br2aUlafGXmbfhqzljcnpY06HY5vR3RyMWAvAYDcngK9A4iA058YsN/m8/hjffP42L39d2sd2cm46u5Y/Gl6Rkw6NR+h3K4prfjnUuI5MOAvAYDcvgK5g4iA5wuN95uuIBd7zVj38l29Lt9f421KgXun5KGfSfb4XC5h9StG47p7eTs2mUoE3kwIK/BgBz+grmDyNUudtnxRn0Ldr3XjJNBnukqAdi4cBqK52YH9XMA+bp2GcpEvhiQ12BAjkzHWqzY9d45vPH+OVh6/Z9gQAKQZYzH29+9L6gPdrm6dkdiKBPdCgPyGgzIka3V2ofZZdUBv3/9F6fgtmQdknUaJMerkZKgQUq8Gjq18pbB6e8Zu6Hq2h1poXw1HrnSzQSaB8FNcUI0TDld7qDeX/bnk4Mu1ygVnsCM9wTnleeXgzReDfPZS+h1uDDUb55X37kk0K5da68TK1++9b02B7YHCVj5sjm0oTzYti7/2et0oXj7oZCfBDXSupP5RSCyGJAUk4Kd3u5GHC432jvtaO+0h/TnCgC/qj4NlUKCXqdGgkaFBK0KiVoVEuNUSNAqkahV3fAI9g/mcyMmlAdce+R6taaOHjxVeRz//r8NMdGdLHcX9kj9MsAuVopJQgjct+VtNHX0DDk0AE+X4KgkLb77+cmw9vbjUo8Dl3qcsPY6cKnbiUs9Dlh6nLD0OtDnDO4oNRAKCd7gTBh4aBR4v8nq9x1TJAC3pehQvXY+NCqF3x8+v32nEU9VHvf77zcUJ0GNpO5kObuwY+XLAMcgr8GApHB/gPc5XZ4A7fYEpqXHiTMXuvDv/3sq4JrlolRIiFMpoNMooVUpodMooVMrEadWIE498Nzzp06jhEYl4bXD52Dt9e9WZKE4CWokjfHKeR1vLH0ZYEBegwFJgUxvFxfkB2lHtwMzn6oK6L0A8KOF0yCE5xZhXY5+dNv70W13obPv8nNHP7rsnuddff3oHqR7MRpMSktEcrzaexScqBnoSlYhUatEolbt7VYeOFoe6G5+/cg5lP35ZESPXOUIZbm+CACx92UgZk/Sef7557Flyxa0trZixowZePbZZzFr1iy5y6IoYNCpse3RHBRvPwRIt/5PBwAVj+YE9eEycOeSQLp2s4zxeHzOeL+OrNxugfOWXnxu836/ax3w2axkuNwCvQ4X+vpd6HW40ed0odfpgssdnu/Pp9u7wvJzb0QA+NVfTsPR70KcWgWNSgGtSnH5T6X39dXLrn792uHmiI/xyjGuDMgztiz3ePaNDOuAfO2117B27VpUVFQgLy8PzzzzDAoLC9HQ0IC0tDS5y6MoMH/yaGwvnnXrbhv1jae388fAnUueqjzu93sfn+tfOAKAQiFhbIouqFB+feWcG27X6XKj1+lCn9OFPseV522dfVjxX2a/ar2aWildNwF9uFl6nSjb2xCx7QkAW95qwPtNl6BRKaFWKqBRSlArFVCrFL6vLy8beK1SSNj29kd+/XsO+M93GvGVu2+DUilBIUlQKjx/KiRPV/qtfsfkCGa5vgzcyrDuYs3Ly8M999yD5557DgDgdruRmZmJVatW4fvf//5N38suVrpaKKa382dbke7ajfQJM8GcBDUwBtnvFui293u6jx2eLuOuy13KXXYnuuwuT1ey/Uq38gWbHX87c9HveukKSYInOCUJCgU8f0oSFApPiFp7nQik40CjVOCOjCQoFQooJMm7HYUCl197fv5AWA+8lgAcOP0pevwcLvBnPDvmulgdDgfMZjPWr1/vXaZQKFBQUIDa2trr2tvtdtjtV069t9lsEamTooNBp0bx3Gw8Pmd8SKa3u9W2It21uyRnLP79fxv8DuXFM8cGtL1QHCmrldLl60c1Q35vsGO8mx+eDrVSgt3phsPlvupPF+w+r68st/Y5UXemI+BtDjdCAC4h4IIAQjiE7XC58X7z9XfbCRcB4GxHDyw9TqQkDP13yB/DNiA//fRTuFwupKen+yxPT0/HyZPXX8RdVlaGn/zkJ5Eqj6KUJEmeWXHC9B9qQKS7dkdCKAPBj/F+NWes31+Igg3lPaXzoNMo4XS5vQ9Hv7jquSeMna4ryyw9Dvyi6nTA25wzMRVKhQS3EHC5BdxuTyi6hYDbLTwB6fb0BLguvxYCsDtdaLH2BbxdOXTZ+0deQPpr/fr1WLt2rfe1zWZDZmamjBXRSDd/8mjUrl8waNduVhi6dkdCKEd6jBcIPpTvvE3v93aFEPiD+XzA23zlX/IC2tdgvwyY/28BDDo13AIQ8ISuWwi4L/8p3AOvPcuEEOjoduDBX/014G0mhmlSEGAYB+SoUaOgVCrR1tbms7ytrQ0mk+m69lqtFlqtNlLlEQ1JJLt2gdgPZSA6u5OjYZtA8F8GjAkav7c9Okkb1DaT48N3FqsibD85SBqNBjk5OaiuvjLhtNvtRnV1NfLz82WsjMh/A127mcZ4pATwIeKPgVB++7v34f0ND+Cv3/snvL/hAbz93ftQPDc7ZOE4YCCUNy6chixjvM+6LGM8Ni6choM/WBCScASuHLlKuHJkeiOh7E7WaZS33N4AheS5oD2Y7mQ5tjkQzIEI9stAJLc5VMP6LNbXXnsNy5YtwwsvvIBZs2bhmWeewe9//3ucPHnyurHJa/EsVqLIC9U9PodiqLOuhOrI1d8L2V8qnhX0duXYphxnYYd7mzE7k85zzz3nnSjg7rvvRnl5OfLy8m75PgYkUeyL5OU7QORDWc5txtKXgZgNyEAxIIlGjkgeuUY6lOXaZix9GWBAXoMBSUThFMlQlmubsfJlgAF5DQYkEVFoRPuXgZibSSdYA7nPGXWIiIKnBGBQAXD1o7MzMpMJhGqbAzng7/FgzAZkZ2cnAHCyACIiAuDJBYPBMOT2MdvF6na70dLSgqSkpKC6AgZm5Glubo75rtqRsq8jZT8B7mssGin7CYRuX4UQ6OzsREZGBhSKoV/+H7NHkAqFAmPHBn7B7LX0en3M/zIOGCn7OlL2E+C+xqKRsp9AaPbVnyPHAcN2Jh0iIiI5MSCJiIgGofzxj3/8Y7mLGO6USiXuu+8+qFQx2yPtNVL2daTsJ8B9jUUjZT8Befc1Zk/SISIiCga7WImIiAbBgCQiIhoEA5KIiGgQDEgiIqJBMCBv4vnnn8f48eMRFxeHvLw8HDp0SO6SQq6srAz33HMPkpKSkJaWhkWLFqGhoUHusiLi6aefhiRJWL16tdylhMX58+fx6KOPIjU1FTqdDnfddRfee+89ucsKKZfLhQ0bNiA7Oxs6nQ4TJ07EU0895fecm8PRgQMHsHDhQmRkZECSJLzxxhs+64UQ2LhxI8aMGQOdToeCggKcPn1apmqDc7N9dTqdWLduHe666y4kJCQgIyMDjz32GFpaWsJeFwPyBl577TWsXbsWP/rRj3DkyBHMmDEDhYWFaG9vl7u0kKqpqUFJSQkOHjyIqqoqOJ1OfP7zn0d3d7fcpYXV4cOH8cILL2D69OlylxIWly5dwty5c6FWq7F3714cP34c//Ef/4GUlBS5Swupn//859i2bRuee+45nDhxAj//+c+xefNmPPvss3KXFrTu7m7MmDEDzz///KDrN2/ejPLyclRUVKCurg4JCQkoLCxEX19kJhIPpZvta09PD44cOYINGzbgyJEjeP3119HQ0IAvf/nL4S9M0KBmzZolSkpKvK9dLpfIyMgQZWVlMlYVfu3t7QKAqKmpkbuUsOns7BSTJk0SVVVVYv78+eLJJ5+Uu6SQW7dunZg3b57cZYTdQw89JL7xjW/4LFu8eLEoKiqSqaLwACB2797tfe12u4XJZBJbtmzxLrNYLEKr1YqdO3fKUWLIXLuvgzl06JAAIM6ePRvWWngEOQiHwwGz2YyCggLvMoVCgYKCAtTW1spYWfhZrVYAgNFolLmS8CkpKcFDDz3k8+8ba/70pz8hNzcXX/3qV5GWlobPfvaz+PWvfy13WSE3Z84cVFdX49SpUwCAv//973jnnXfwhS98QebKwquxsRGtra0+v8MGgwF5eXkx/xkFeD6nJElCcnJyWLcT+9MwBODTTz+Fy+VCenq6z/L09HScPHlSpqrCz+12Y/Xq1Zg7dy7uvPNOucsJi1dffRVHjhzB4cOH5S4lrM6cOYNt27Zh7dq1+MEPfoDDhw/j29/+NjQaDZYtWyZ3eSHz/e9/HzabDVOmTIFSqYTL5cJPf/pTFBUVyV1aWLW2tgLAoJ9RA+tiVV9fH9atW4dHHnkk7JO1MyDJq6SkBEePHsU777wjdylh0dzcjCeffBJVVVWIi4uTu5ywcrvdyM3Nxc9+9jMAwGc/+1kcPXoUFRUVMRWQv//97/HKK69gx44duOOOO1BfX4/Vq1cjIyMjpvaTPJxOJ772ta9BCIFt27aFfXvsYh3EqFGjoFQq0dbW5rO8ra0NJpNJpqrCq7S0FJWVldi/f39IbxM2nJjNZrS3t2PmzJlQqVRQqVSoqalBeXk5VCoVXC6X3CWGzJgxYzBt2jSfZVOnTkVTU5NMFYXHd7/7Xaxbtw5Lly7FXXfdha9//etYs2YNysrK5C4trAY+h0bSZ9RAOJ49exZVVVURudUXA3IQGo0GOTk5qK6u9i5zu92orq5Gfn6+jJWFnhACpaWl2L17N/bt24fs7Gy5SwqbBQsW4IMPPkB9fb33kZubi6KiItTX10OpVMpdYsjMnTv3ust1Tp06hXHjxslUUXj09PRcN4m1UqmE2+2WqaLIyM7Ohslk8vmMstlsqKuri7nPKOBKOJ4+fRp/+ctfkJqaGpHtsov1BtauXYtly5YhNzcXs2bNwjPPPIPu7m4UFxfLXVpIlZSUYMeOHfjjH/+IpKQk7/iFwWCATqeTubrQSkpKum5sNSEhAampqTE35rpmzRrMmTMHP/vZz/C1r30Nhw4dwosvvogXX3xR7tJCauHChdi0aRMyMzNxxx134P3338cvfvELfOMb35C7tKB1dXXhww8/9L5ubGxEfX09jEYjsrKysHr1amzatAmTJk1CdnY2NmzYgIyMDCxatEjGqgNzs30dM2YMHn74YRw5cgSVlZVwuVzezymj0QiNRhO+wsJ6jmyUe/bZZ0VWVpbQaDRi1qxZ4uDBg3KXFHIABn1s375d7tIiIlYv8xBCiD179og777xTaLVaMWXKFPHiiy/KXVLI2Ww28eSTT4qsrCwRFxcnJkyYIH74wx8Ku90ud2lB279//6D/N5ctWyaE8FzqsWHDBpGeni60Wq1YsGCBaGhokLfoAN1sXxsbG2/4ObV///6w1sXbXREREQ2CY5BERESDYEASERENggFJREQ0CAYkERHRIBiQREREg2BAEhERDYIBSURENAgGJBER0SAYkERERINgQBIREQ2CAUlERDQIBiQREdEg/j95/cdK4WM1MQAAAABJRU5ErkJggg==", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure(figsize=(5,3))\n", "plot(D, \".-\", linewidth= 2, markersize= 20); axis(\"tight\");" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display the points cloud of feature vectors in 3-D PCA space." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "ename": "LoadError", "evalue": "UndefVarError: plot_multiclasses not defined", "output_type": "error", "traceback": [ "UndefVarError: plot_multiclasses not defined", "", " in include_string(::String, ::String) at ./loading.jl:441", " in include_string(::String, ::String) at /Applications/Julia-0.5.app/Contents/Resources/julia/lib/julia/sys.dylib:?" ] } ], "source": [ "figure(figsize=(6,4))\n", "plot_multiclasses(X,ones(n,1),disp_dim=3, ms=5);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "1D plot of the function to regress along the main eigenvector axes." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "col = [\"blue\" \"green\" \"red\" \"cyan\" \"magenta\" \"yellow\" \"black\"]\n", "for i=1:min(p,3)\n", " subplot(3,1,i)\n", " plot(Z[:,i], y, \".\", c=col[i], ms=10)\n", " axis(\"tight\")\n", "end\n", "tight_layout()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Linear Regression\n", "-----------------\n", "We look for a linear relationship\n", " $y_i = \\dotp{w}{x_i}$\n", "written in matrix format\n", " $y= X w$\n", "where the rows of $X \\in \\RR^{n \\times p}$ stores the features $x_i \\in \\RR^p$.\n", "\n", "\n", "Since here $n > p$, this is an over-determined system, which can\n", "solved in the least square sense\n", " $$\\umin{ w } \\norm{Xw-y}^2$$\n", "whose solution is given using the Moore-Penrose pseudo-inverse\n", " $$w = (X^\\top X)^{-1} X^\\top y$$\n", "\n", "\n", "\n", "Split into training and testing." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "n0 = Int(round(.5*n)); n1 = n-n0\n", "X0 = X[1:n0,:]; y0 = y[1:n0]\n", "X1 = X[n0+1:end,:]; y1 = y[n0+1:end];" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Least square solution." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "w = (X0'*X0) \\ (X0'*y0);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Mean-square error on testing set." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "E = sqrt( sum( (X1*w-y1).^2 ) / n1 );" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Regularization is obtained by introducing a penalty. It is often called\n", "ridge regression, and is defined as\n", " $$\\umin{ w } \\norm{Xw-y}^2 + \\lambda \\norm{w}^2$$\n", "where $\\lambda>0$ is the regularization parameter.\n", "\n", "\n", "The solution is given using the following equivalent formula\n", " $$w = (X^\\top X + \\lambda \\text{Id}_p )^{-1} X^\\top y,$$\n", " $$w = X^\\top ( XX^\\top + \\lambda \\text{Id}_n)^{-1} y,$$\n", "When $p)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "include(\"NtSolutions/ml_2_regression/exo1.jl\");" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "# Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 2__\n", "\n", "Display the regularization path, i.e. the evolution of$w$as a function\n", "of$\\lambda$." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "include(\"NtSolutions/ml_2_regression/exo2.jl\");" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "# Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 3__\n", "\n", "Perform feature selection using$\\ell^1$regularization (aka the Lasso),\n", " $$\\umin{ w } \\frac{1}{2}\\norm{Xw-y}^2 + \\lambda \\norm{w}_1.$$" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "include(\"NtSolutions/ml_2_regression/exo3.jl\");" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "# Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Kernelized Ridge Regression\n", "---------------------------\n", "In order to perform non-linear and non-parametric regression, it is\n", "possible to use kernelization. It is non-parametric in the sense that the number of\n", "parameter grows with the number$n$of samples (while for the initial\n", "linear method, the number of parameter is$p$). This allows in particular to\n", "generate estimator of arbitrary complexity.\n", "\n", "\n", "Given a kernel$ \\kappa(x,z) \\in \\RR $defined for$(x,z) \\in \\RR^p \\times \\RR^p$,\n", "the kernelized method replace the linear approximation functional$f(x) =\n", "\\dotp{x}{w}$by a sum of kernel centered on the samples\n", "$$f_h(x) = \\sum_{i=1}^n h_i k(x_i,x)$$\n", "where$h \\in \\RR^n$is the unknown vector of weight to find.\n", "\n", "\n", "When using the linear kernel$\\kappa(x,y)=\\dotp{x}{y}$, one retrieves\n", "the previously studied linear method.\n", "\n", "\n", "Generate synthetic data in 2D.\n", "Add noise to a deterministic map." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "B = 3\n", "n = 500; p = 2\n", "# X = 2*B*rand(n,2)-B\n", "# rho = .5; # noise level\n", "# y = peaks(X[:,1], X[:,2]) + randn(n,1)*rho;\n", "X = readdlm(\"NtToolBox/src/data/peaks_X.csv\", ',')\n", "y = readdlm(\"NtToolBox/src/data/peaks_y.csv\", ',');" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display as scattered plot." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "scatter(X[:,1], X[:,2], ones(n,1)*20, y, cmap = get_cmap(\"jet\"))\n", "axis([-B B -B B]'); box(\"on\");" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Macro to compute pairwise squared Euclidean distance matrix." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "distmat = (X,Z) -> broadcast(+,sum(X'.*X',1)',sum(Z'.*Z',1))-2*(X*Z');" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The gaussian kernel is the most well known and used kernel\n", "$$\\kappa(x,y) \\eqdef e^{-\\frac{\\norm{x-y}^2}{2\\sigma^2}} .$$\n", "The bandwidth parameter$\\si>0$is crucial and controls the locality of\n", "the model. It is typically tuned through cross validation." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "sigma = .3\n", "kappa = (X,Z) -> exp( -distmat(X,Z)/(2*sigma^2) );" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Once avaluated on grid points, the kernel define a matrix\n", "$$K = (\\kappa(x_i,x_j))_{i,j=1}^n \\in \\RR^{n \\times n}.$$" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "K = kappa(X,X);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The weights$h \\in \\RR^n $are solutions of\n", " $$\\umin{h} \\norm{Kh-y}^2 + \\la \\dotp{Kh}{h}$$\n", "and hence can be computed by solving a linear system\n", " $$h = (K+\\la \\text{Id}_n)^{-1} y$$" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "lambda = 0.01\n", "h = (K+lambda*eye(n))\\y;" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Regressor." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "Y = x-> kappa(x,X)*h;" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Evaluation on a 2D grid." ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "q = 101;\n", "t = linspace(-B,B,q);\n", "v,u = meshgrid(t,t);\n", "Xn = [u[:] v[:]];" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display as an image." ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "yn = reshape(Y(Xn),q,q)\n", "imshow(yn, extent=[0,1, 0,1], cmap = get_cmap(\"jet\"))\n", "axis(\"image\"); axis(\"off\"); " ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 4__\n", "\n", "Display the evolution of the regression as a function of$\\sigma$." ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "include(\"NtSolutions/ml_2_regression/exo4.jl\");" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "# Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 5__\n", "\n", "Apply the kernelize regression to a real life dataset. Study the influence of$\\la$and$\\si\$." ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "include(\"NtSolutions/ml_2_regression/exo5.jl\");" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "# Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "" ] } ], "metadata": { "kernelspec": { "display_name": "Julia 0.5.0", "language": "julia", "name": "julia-0.5" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "0.5.0" } }, "nbformat": 4, "nbformat_minor": 1 }