juliaL23demo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Kernels demo\n",
    "\n",
    "2018 Winter Term 1\n",
    "\n",
    "By Mike Gelbart (converted to Julia by Jason Chau)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RBF_features (generic function with 1 method)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using LinearAlgebra\n",
    "include(\"__init__.jl\")\n",
    "using PyCall\n",
    "SkPreprocessing = pyimport(\"sklearn.preprocessing\")\n",
    "using PyPlot\n",
    "plt = pyimport(\"matplotlib.pyplot\")\n",
    "using Random\n",
    "SkSVM = pyimport(\"sklearn.svm\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## \"Other normal equations\" demo\n",
    "\n",
    "- The normal equations: $$w=(X^TX+\\lambda I)^{-1}X^Ty$$\n",
    "- Alternate form: $$w=X^T(XX^T+\\lambda I)^{-1}y$$\n",
    "\n",
    "Let's test this out:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 1000\n",
    "d = 10\n",
    "X = randn(n,d)\n",
    "y = rand(n)\n",
    "\n",
    "λ=1;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10-element Array{Float64,1}:\n",
       "  0.03184633062803163 \n",
       " -0.02604234569496713 \n",
       "  0.024617575996351282\n",
       " -0.014383354285724372\n",
       " -0.013709525197413449\n",
       " -0.005962299922601739\n",
       " -0.04171102545381545 \n",
       "  0.007655923021691462\n",
       " -0.010429980293493816\n",
       " -0.022603514202397496"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w1 = (X'*X + λ*Array{Int64}(I,d,d))\\ (X'*y)\n",
    "w1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10-element Array{Float64,1}:\n",
       "  0.03184633062800657 \n",
       " -0.026042345694962776\n",
       "  0.0246175759963565  \n",
       " -0.014383354285717687\n",
       " -0.013709525197418415\n",
       " -0.00596229992259012 \n",
       " -0.041711025453827766\n",
       "  0.007655923021687272\n",
       " -0.010429980293510166\n",
       " -0.02260351420240614 "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w2 = X'*((X*X'+λ*Array{Int64}(I,n,n))\\y)\n",
    "w2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "allClose(w1,w2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This isn't a proof but they seem to yield the same results for this randomly generated dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Number of polynomial features\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 35)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 2\n",
    "d = 4\n",
    "p = 3\n",
    "\n",
    "X = randn(n,d)\n",
    "y = randn(n)\n",
    "\n",
    "pf = SkPreprocessing.PolynomialFeatures(degree=p)\n",
    "Z = pf.fit_transform(X)\n",
    "size(Z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above: we get $k=35$ as in the slides."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Polynonial kernel vs. polynomial features (for regression)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 10\n",
    "x = rand(n)\n",
    "y = x.^2 + randn(n)*0.1;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x,y,\".\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PyObject Ridge(alpha=1e-10, copy_X=True, fit_intercept=False, max_iter=None,\n",
       "      normalize=False, random_state=None, solver='auto', tol=0.001)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SkKernelRidge = pyimport(\"sklearn.kernel_ridge\")\n",
    "SkLinearModel = pyimport(\"sklearn.linear_model\")\n",
    "\n",
    "k=10  # polynomial degree\n",
    "λ=1e-10 # L2 regularization strength\n",
    "\n",
    "X = reshape(x,length(x),1)\n",
    "pf = SkPreprocessing.PolynomialFeatures(degree=k)\n",
    "Z = pf.fit_transform(X)\n",
    "\n",
    "ridge = SkLinearModel.Ridge(alpha=λ, fit_intercept=false) \n",
    "# fit_intercept=False because features already include intercept feature\n",
    "# could alternatively set include_bias=False for the PolynomialFeatures\n",
    "ridge.fit(Z,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "grid = reshape(range(minimum(x),stop=maximum(x),length=1000),1000,1)\n",
    "plt.plot(x,y,\".\")\n",
    "plt.plot(grid, ridge.predict(pf.transform(grid)));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11-element Array{Float64,1}:\n",
       "    -2.2648086547851562\n",
       "    54.46995747089386  \n",
       "  -348.4217441082001   \n",
       "   791.0944981575012   \n",
       "  -297.8525207042694   \n",
       "  -929.5056574344635   \n",
       "   240.59610676765442  \n",
       "  1208.8515241146088   \n",
       "   150.2549387216568   \n",
       " -1670.6712690591812   \n",
       "   804.4347157478333   "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### And now the same with a kernel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PyObject KernelRidge(alpha=1e-10, coef0=1, degree=10, gamma=None, kernel='polynomial',\n",
       "            kernel_params=None)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kr = SkKernelRidge.KernelRidge(alpha=λ, kernel=\"polynomial\", degree=k)\n",
    "kr.fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x,y,\".\")\n",
    "plt.plot(grid, kr.predict(grid));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are slight differences due to different implementations and different interpretations of $\\lambda$, but they are essentially the same."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### RBF kernel vs. RBF features\n",
    "\n",
    "Next we'll try to show how the RBF kernel relates to the RBF features. We implement the RBF features (from Lecture 14) below, and compare with the above. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "sys:1: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.\r\n"
     ]
    }
   ],
   "source": [
    "# generate synthetic 2D data set\n",
    "Random.seed!(0)\n",
    "n = 20\n",
    "X = randn(n,2)\n",
    "y = rand([-1,+1],n)\n",
    "\n",
    "plt.scatter(X[y.<0,1], X[y.<0,2], color=\"b\", label=\"class -1\")\n",
    "plt.scatter(X[y.>0,1], X[y.>0,2], color=\"r\", label=\"class +1\")\n",
    "plt.legend(loc=\"best\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\jasonsyc.STUDENTS.000\\.julia\\conda\\3\\lib\\site-packages\\sklearn\\svm\\base.py:193: FutureWarning: The default value of gamma will change from 'auto' to 'scale' in version 0.22 to account better for unscaled features. Set gamma explicitly to 'auto' or 'scale' to avoid this warning.\r\n",
      "  \"avoid this warning.\", FutureWarning)\r\n"
     ]
    }
   ],
   "source": [
    "svm = SkSVM.SVC(kernel=\"rbf\")\n",
    "svm.fit(X,y)\n",
    "plot_classifier(X, y, svm,ax=plt.gca())\n",
    "plt.scatter(svm.support_vectors_[:,1],svm.support_vectors_[:,2], marker=\"o\", edgecolor=\"yellow\", facecolor=\"none\", s=120);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Z = RBF_features(X,X)\n",
    "svm2 = SkSVM.SVC(kernel=\"linear\")\n",
    "svm2.fit(Z,y)\n",
    "plot_classifier(X, y, svm2, transformation=Xtest-> RBF_features(X,Xtest), ax=plt.gca())\n",
    "plt.scatter(X[svm2.support_.+1,:][:,1],X[svm2.support_.+1,:][:,2], marker=\"o\", edgecolor=\"yellow\", facecolor=\"none\", s=120);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "They look pretty similar. Let's time them though. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  0.050502 seconds (26 allocations: 1.203 KiB)\n"
     ]
    }
   ],
   "source": [
    "n = 1000\n",
    "d = 10\n",
    "X = randn(n,d)\n",
    "y = rand([-1,+1],n)\n",
    "\n",
    "svm = SkSVM.SVC(kernel=\"rbf\",gamma=\"scale\")\n",
    "\n",
    "@time svm.fit(X,y);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  0.027283 seconds (43 allocations: 9.953 KiB)\n"
     ]
    }
   ],
   "source": [
    "@time svm.predict(X);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  1.095040 seconds (26 allocations: 1.203 KiB)\n"
     ]
    }
   ],
   "source": [
    "Z = RBF_features(X,X)\n",
    "svm2 = SkSVM.SVC(kernel=\"linear\")\n",
    "\n",
    "@time svm2.fit(Z,y);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  1.101239 seconds (43 allocations: 9.953 KiB)\n"
     ]
    }
   ],
   "source": [
    "@time svm2.predict(Z);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 0.7.0",
   "language": "julia",
   "name": "julia-0.7"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "0.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}