{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# The Kernel Trick - Revisited\n", "\n", "The kernel trick is a powerful tool to convert a linear method to a non-linear one. In the following, we will try to explain how and why it works. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Linear Models\n", "\n", "A linear model for an input space $\\mathcal{X}$ and an output space $\\mathcal{Y}$ is a linear function $f:\\mathcal{X}\\rightarrow\\mathcal{Y}$. If $\\mathcal{X}\\subseteq\\mathbb{R}^d$, then we can describe $f$ using a vector of coefficients $\\beta\\in\\mathbb{R}^d$, i.e., $f(x)=\\beta^\\top x = \\langle\\beta,x\\rangle$ (here we are ignoring the intercept).\n", "\n", "## The Dual Problem\n", "\n", "### An Example: Classification with the Hinge Loss\n", "\n", "Let us assume that we want to solve a classification problem, i.e., $\\mathcal{Y}=\\{-1,1\\}$, and we measure the error our model makes by the hinge loss\n", "$$\\ell(f(x),y) = \\max\\{0, 1 - f(x)y\\} = \\max\\{0, 1 - \\langle\\beta,x\\rangle y\\}$$\n", "That is, our model outputs a score $\\beta^\\top x$ and we interpret this score as class $1$ if $\\langle\\beta,x\\rangle\\geq 0$ and as $-1$, otherwise. Thus, the model makes a correct prediction, whenever $sgn(\\langle\\beta,x\\rangle) = y \\Leftrightarrow \\langle\\beta,x\\rangle y \\geq 0$. However, the hinge loss demands not only that the prediction is right, but also that the score is larger than $1$. \n", "\n", "Given a dataset $X\\subset\\mathcal{X}$ of size $n\\in\\mathbb{N}$ and corresponding labels $y\\subset\\mathcal{Y}$, we want to find model parameters that lead to correct predictions, but like in Ridge regression, we also would like to have parameters of small squared norm $\\|\\beta\\|_2^2$. For simplicity, let us assume we could predict $y$ perfectly from $x$. Then we are trying to find the optimal parameters $\\beta$, i.e.,\n", "$$\\min_{\\beta\\in\\mathbb{R}^d}\\frac{1}{2}\\|\\beta\\|_2^2\\ \\ s.t.\\ \\forall i\\in [n]:\\langle\\beta,x_i\\rangle y_i\\geq 1$$\n", "\n", "### The Lagrangian\n", "\n", "We can solve the above optimization problem using the Lagrangian\n", "$$L(\\beta,\\alpha)=\\frac{1}{2}\\beta^\\top\\beta - \\sum_{i=1}^n\\alpha_i\\left(\\langle\\beta,x_i\\rangle y_i - 1\\right)$$\n", "and maximize\n", "$$\\min_{\\beta\\in\\mathbb{R}^d}\\max_{\\alpha\\geq 0}\\frac{1}{2}\\beta^\\top\\beta - \\sum_{i=1}^n\\alpha_i\\left(\\langle\\beta,x_i\\rangle y_i - 1\\right)\\enspace .$$\n", "Now, under some conditions (Slater's condition ensures the Karush-Kuhn-Tucker conditions) we can swap the min and the max and get the dual problem\n", "$$\\max_{\\alpha\\geq 0}\\min_{\\beta\\in\\mathbb{R}^d}\\frac{1}{2}\\beta^\\top\\beta - \\sum_{i=1}^n\\alpha_i\\left(\\langle\\beta,x_i\\rangle y_i - 1\\right)\\enspace .$$\n", "In this form, we can solve this for the optimal $\\beta$ in terms of $\\alpha$ by setting the gradient to zero, i.e.,\n", "$$\\frac{\\partial L}{\\partial\\beta}=\\beta - \\sum_{i=1}^n\\alpha_ix_iy_i \\stackrel{!}{=}0 \\Leftrightarrow \\beta = \\sum_{i=1}^n\\alpha_ix_iy_i\\enspace ,$$\n", "which we can substitue back into our dual problem and get\n", "\\begin{equation*}\n", "\\begin{split}\n", "&\\max_{\\alpha\\geq 0}\\frac{1}{2}\\left(\\sum_{i=1}^n\\alpha_ix_iy_i\\right)^\\top\\left(\\sum_{j=1}^n\\alpha_jx_jy_j\\right) - \\sum_{i=1}^n\\alpha_i\\left(\\langle\\sum_{j=1}^n\\alpha_jx_jy_j,x_i\\rangle y_i - 1\\right)\\\\\n", "&=\\max_{\\alpha\\geq 0}\\frac{1}{2}\\sum_{i,j=1}^n\\alpha_i\\alpha_jy_iy_j\\langle x_i,x_j\\rangle - \\sum_{i,j=1}^n\\alpha_i\\alpha_jy_iy_j\\langle x_i,x_j\\rangle + \\sum_{i=1}^n\\alpha_i\\\\\n", "&=\\max_{\\alpha\\geq 0}\\sum_{i=1}^n\\alpha_i-\\frac{1}{2}\\sum_{i,j=1}^n\\alpha_i\\alpha_jy_iy_j\\langle x_i,x_j\\rangle\\enspace .\n", "\\end{split}\n", "\\end{equation*}\n", "This is a quadratic optimization problem which can be solved using some standard solver. If we found the optimal parameters $\\alpha$, we can then compute the optimal parameters $$\\beta=\\sum_{i=1}^n\\alpha_ix_iy_i\\enspace .$$\n", "Now, how would our linear model then look like? Well, we can just substitute the formula for $\\beta$ directly and get\n", "$$f(x)=\\sum_{i=1}^n\\alpha_iy_i\\langle x_i, x\\rangle\\enspace .$$\n", "If we now rewrite our $\\alpha$'s a bit and say $\\alpha'_i = \\alpha_i y_i$ we get the dual representation of our model $f$, i.e.,\n", "$$f(x)=\\sum_{i=1}^n\\alpha'_i\\langle x_i, x\\rangle\\enspace .$$\n", "\n", "Now, we found that nice representation for this special case. However, the representer theorem (Schölkopf, Herbrich, Smola) guarantees that we can always find such a representation. In a simplified form it says that if we have a loss function $\\ell$, a training set $X,y$ of size $n$, a strictly increasing real-valued function $g$, and an inner product $\\langle\\cdot,\\cdot\\rangle$, then the linear function minimizing the regularized loss, i.e., \n", "$$f^* = \\arg\\min_{f\\in\\mathcal{H}}\\sum_{i=1}^n\\ell(f(x_i),y_i) + g(\\|f\\|)$$\n", "can be represented as\n", "$$f^*(\\cdot)=\\sum_{i=1}^n\\alpha_i\\langle x_i, \\cdot\\rangle\\enspace .$$\n", "Here, $f(\\cdot)$ means we can insert any $x\\in\\mathcal{X}$. Moreover, $\\mathcal{H}$ is the Hilbert of linear functions from $\\mathcal{X}$ to $\\mathcal{Y}$. Now, this is a simplified version only for the standard dot product. We will discuss the full version below.\n", "\n", "### Excursion: Max-Margin Classifiers\n", "Before we go to the kernel trick, let us just do a small excercise to show why using the hinge loss for classification makes sense. For that let's assume a simple 2d binary classification example." ] }, { "cell_type": "code", "execution_count": 283, "metadata": {}, "outputs": [], "source": [ "#some general imports\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import math\n", "%matplotlib inline\n", "import warnings\n", "warnings.filterwarnings('ignore')" ] }, { "cell_type": "code", "execution_count": 284, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sklearn.datasets.samples_generator import make_blobs, make_moons\n", "X, y = make_blobs(n_samples = 40, centers = 2, random_state = 43, cluster_std = 1.8)\n", "plt.scatter(X[:,0], X[:,1], c=y, cmap='Spectral')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now there are many possible linear models that perfectly fit the data." ] }, { "cell_type": "code", "execution_count": 285, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.scatter(X[:,0], X[:,1], c=y, cmap='Spectral')\n", "lspace = np.linspace(-12,-3)\n", "plt.plot(lspace, -0.5*lspace -5.5, '-k', linewidth=1.)\n", "plt.plot(lspace, 0.5*lspace +2.0, '-k', linewidth=1.)\n", "plt.plot(lspace, -0.1*lspace -2.5, '-k', linewidth=1.)\n", "\n", "plt.annotate('?', (-11,-3), color='red', fontsize='xx-large')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So which of these models is better? Well, the one with the largest margin!" ] }, { "cell_type": "code", "execution_count": 286, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.scatter(X[:,0], X[:,1], c=y, cmap='Spectral')\n", "lspace = np.linspace(-12,-3)\n", "plt.plot(lspace, -0.5*lspace -5.5, '-k', linewidth=1.)\n", "plt.plot(lspace, 0.5*lspace +2.0, '-k', linewidth=1.)\n", "plt.plot(lspace, -0.1*lspace -2.5, '-k', linewidth=1.)\n", "\n", "plt.fill_between(lspace, -0.5*lspace -5.5 -0.5, -0.5*lspace -5.5 +0.5, edgecolor='none', color='k', alpha=0.1)\n", "plt.fill_between(lspace, 0.5*lspace +2.0 -0.2, 0.5*lspace +2.0 +0.2, edgecolor='none', color='k', alpha=0.1)\n", "plt.fill_between(lspace, -0.1*lspace -2.5 -1.2, -0.1*lspace -2.5 +1.2, edgecolor='none', color='k', alpha=0.1)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So, our goal is to find the linear model with the largest margin, the maximum margin classifier. So given our function $f(x)=\\beta^\\top x=$, what is its margin? Well, since we optimize for the hinge loss, we know that the closest points to our decision boundary fulfill $\\langle\\beta,x\\rangle y - 1 = 0$ and thus the two hyperplanes defining the boarders of the margin $H_1$ and $H_{-1}$ are given by $\\langle\\beta,x\\rangle = 1$, respectively $\\langle\\beta,x\\rangle = -1$. The linear model is the hyperplane $H_0$ in between with $\\langle\\beta,x\\rangle = 0$. \n" ] }, { "cell_type": "code", "execution_count": 287, "metadata": {}, "outputs": [], "source": [ "from sklearn.svm import SVC # \"Support vector classifier\"\n", "f = SVC(kernel='linear', C=1E10)\n", "f.fit(X, y)\n", "def plotDecisionFunction(ax, f, showSVs = False, cmap=None):\n", " x = np.linspace(ax.get_xlim()[0], ax.get_xlim()[1], 30)\n", " y = np.linspace(ax.get_ylim()[0], ax.get_ylim()[1], 30)\n", " Y, X = np.meshgrid(y, x)\n", " \n", " grid = np.vstack([X.ravel(), Y.ravel()]).T\n", " decFunc = f.decision_function(grid).reshape(X.shape)\n", " if cmap is None:\n", " ax.contour(X, Y, decFunc, levels=[-1, 0, 1], colors='k', linestyles=['--', '-', '--'], alpha=0.6)\n", " else:\n", " ax.contourf(X, Y, decFunc, cmap=cmap, alpha=0.3)\n", " if showSVs:\n", " ax.scatter(f.support_vectors_[:,0], f.support_vectors_[:,1], linewidth=1.1, facecolors='None', edgecolor = 'k', s=250)" ] }, { "cell_type": "code", "execution_count": 288, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.scatter(X[:,0], X[:,1], c=y, cmap='Spectral')\n", "ax = plt.gca()\n", "plotDecisionFunction(ax,f)\n", "plt.annotate(r'$H_1$', (-4,-0.4), fontsize='large')\n", "plt.annotate(r'$H_0$', (-4,-2.4), fontsize='large')\n", "plt.annotate(r'$H_{-1}$', (-4,-4.4), fontsize='large')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The distance of a point $x$ to a hyperplane $\\beta^\\top x = 0$ is given by \n", "$$\\frac{|\\beta^\\top x|}{\\|\\beta\\|}\\enspace .$$\n", "(this is because $\\beta$ is a normal vector to the plane; the signed distance of a point $x$ to a plane $\\beta^\\top x = 0$ can be obtained by first normalizing $\\widehat{\\beta}=\\frac{\\beta}{\\|\\beta\\|}$ and then computing the dot product $\\widehat{\\beta}^\\top x = \\frac{\\beta^\\top x}{\\|\\beta\\|}$; the unsigned distance is the absolute of this).\n", "\n", "Pick any point on $H_1$, then its distance to $H_0$ is $\\frac{1}{\\|\\beta\\|}$, since $\\beta^\\top x = 1$. Similarly, for any point on $H_{-1}$. Thus, the total margin is \n", "$$\\frac{2}{\\|\\beta\\|}\\enspace .$$\n", "If we want to maximize this margin, we need to minimize $\\beta$ and use the hinge loss. And that was exactly what we were doing! \n", "\n", "### A Side-Note\n", "\n", "We are already in an excursion and I am making another side note. I am sorry, bear with me. In the example above, we found that there will be some points directly on the margin. Actually, the hyperplane $H_0$ and with it the model $f$ is uniquely defined by the points on the margin. The position of all other points is utterly irrelevant. That is why these points are called support vectors. \n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 289, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.scatter(X[:,0], X[:,1], c=y, cmap='Spectral')\n", "ax = plt.gca()\n", "plotDecisionFunction(ax,f, True)\n", "plt.annotate(r'$H_1$', (-4,-0.4), fontsize='large')\n", "plt.annotate(r'$H_0$', (-4,-2.4), fontsize='large')\n", "plt.annotate(r'$H_{-1}$', (-4,-4.4), fontsize='large')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And now the loop closes. In our newly found representation \n", "$$f(\\cdot)=\\sum_{i=1}^n\\alpha_i\\langle x_i, \\cdot\\rangle$$\n", "we define the hyperplane that is our linear model as a linear combination of elements in our training set. And guess what? All $\\alpha_i=0$ except for those $x_i$ that are directly on the boundary of the margin. Thus, all $x_i$ with $\\alpha_i\\neq 0$ are our support vectors. So, we just derived a hard-margin SVM. \n", "\n", "But now, back to the kernel trick." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### What have we achieved?\n", "\n", "So far, a bit less than nothing. We found a more complicated way to find our linear model, and we can now represent our model in a slightly more complicated way. Now, there are special cases in which this dual represenation can actually be advantageous. If the number of features is far larger than the number of samples, i.e., $d>>n$, then computing the dual representation is cheaper than the primal. The same holds for solving the optimization problem (please recall Mario's presentation on kernel methods that showed this in detail).\n", "\n", "However, this dual represenation will come in very handy when we apply the kernel trick. So let's get there.\n", "\n", "## Non-Linear Models\n", "\n", "To motivate the kernel trick, I will follow the example given here: https://jakevdp.github.io/PythonDataScienceHandbook/05.07-support-vector-machines.html.\n", "\n", "So far, we have seen that we can represent a linear model using the training set and we have seen that we can directly optimize the model using this representation by solving the Lagrangian dual. We also have seen that using the hinge loss and minimizing $\\beta$ leads to a maximum margin classifier and that the points exactly on the margin are the support vectors. \n", "\n", "But what about data distributions that cannot be described by a linear model? Let's look at a simple example." ] }, { "cell_type": "code", "execution_count": 290, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sklearn.datasets.samples_generator import make_circles\n", "X, y = make_circles(100, factor=.1, noise=.1)\n", "\n", "f = SVC(kernel='linear').fit(X, y)\n", "pred = f.predict(X)\n", "\n", "fig, (ax1,ax2) = plt.subplots(1, 2, figsize = (12,4))\n", "ax1.set_title('True Label')\n", "ax2.set_title('Prediction')\n", "ax1.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='Spectral')\n", "plotDecisionFunction(ax1,f, False)\n", "ax2.scatter(X[:, 0], X[:, 1], c=pred, s=50, cmap='Spectral')\n", "plotDecisionFunction(ax2,f, False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we can see, the linear model is utterly useless. But what if we would preprocess our data? That is, what if we have a function $\\varphi:\\mathbb{R}^d\\rightarrow F$ that maps our original data from $\\mathcal{X}\\subseteq\\mathbb{R}^d$ into a (typically higher dimensional) feature space $F$? Let's construct one such $\\varphi$ for our example. For that we add to the features a Gaussian centered around the origin, i.e., \n", "$$\\varphi(x) = \\left(x_1,x_2,\\dots,x_d,e^{-\\|x\\|_2^2}\\right)\\enspace .$$\n", "In this case, we know that how the feature space looks like, i.e., $F\\subseteq\\mathbb{R}^{d+1}$. For our example, we can even visualize this." ] }, { "cell_type": "code", "execution_count": 291, "metadata": { "scrolled": false }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "20f0c0fb77b74632a127b97d966e2ebe", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(IntSlider(value=25, description='tilt', max=50, min=-50), IntSlider(value=-40, descripti…" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from mpl_toolkits import mplot3d\n", "from ipywidgets import interact, fixed\n", "\n", "phi = np.exp(-(X ** 2).sum(1))\n", "\n", "def plotPhi(X=X, y=y, tilt=25, turn=-40):\n", " f = plt.figure(figsize=(7,7))\n", " ax = plt.subplot(projection='3d')\n", " ax.scatter3D(X[:, 0], X[:, 1], phi, c=y, s=50, cmap='Spectral')\n", " ax.view_init(elev=tilt, azim=turn)\n", " ax.set_xlabel(r'$x_1$')\n", " ax.set_ylabel(r'$x_2$')\n", " ax.set_zlabel(r'$e^{-\\|x\\|_2^2}$')\n", "\n", "interact(plotPhi, X=fixed(X), y=fixed(y), tilt=(-50, 50), turn=(-180, 180))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can find a trivial linear model by simply deciding the class based on $e^{-\\|x\\|_2^2}$, e.g., whether it is smaller than $0.5$.\n", "\n", "However, this feature map was tuned to the example. In general, this feature map does not work. If we would shift the data just a bit (e.g. by 1 in each direction), this does not work anymore." ] }, { "cell_type": "code", "execution_count": 292, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "474a5877e9cc4029802526666f8931a4", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(IntSlider(value=25, description='tilt', max=50, min=-50), IntSlider(value=-40, descripti…" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X_shift = X + np.ones(X.shape)\n", "phi_shift = np.exp(-(X_shift ** 2).sum(1))\n", "\n", "def plotPhi(X=X, y=y, tilt=25, turn=-40):\n", " f = plt.figure(figsize=(7,7))\n", " ax = plt.subplot(projection='3d')\n", " ax.scatter3D(X[:, 0], X[:, 1], phi_shift, c=y, s=50, cmap='Spectral')\n", " ax.view_init(elev=tilt, azim=turn)\n", " ax.set_xlabel(r'$x_1$')\n", " ax.set_ylabel(r'$x_2$')\n", " ax.set_zlabel(r'$e^{-\\|x\\|_2^2}$')\n", "\n", "interact(plotPhi, X=fixed(X_shift), y=fixed(y), tilt=(-50, 50), turn=(-180, 180))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So, what we need is a feature map that always works. Let's stay with a two-dimensional example.\n", "\n", "### Polynomial Feature Maps\n", "\n", "Let's try to create a feature map that could work for this example. For that, let's try to get some non-linearities in the feature map, but fairly generic ones. At let's stay modest with the non-linearity. E.g., let's fix a constant $c\\in\\mathbb{R}$ and define\n", "$$\\varphi_{poly}(x)=\\left(x_1^2,x_2^2,\\sqrt{2}x_1x_2,\\sqrt{2c}x_1,\\sqrt{2c}x_2,c\\right)\\enspace .$$\n", "Now, of course, we cannot plot the feature space anymore. But we can check how well a linear model would work with this feature space.\n" ] }, { "cell_type": "code", "execution_count": 293, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "c = 1.0\n", "phiX = np.array([[x[0]**2,x[1]**2,math.sqrt(2)*x[0]*x[1],math.sqrt(2*c)*x[0],math.sqrt(2*c)*x[1],c] for x in X])\n", "\n", "flin = SVC(kernel='linear').fit(X, y)\n", "pred = flin.predict(X)\n", "\n", "fig, (ax1,ax2) = plt.subplots(1, 2, figsize = (12,4))\n", "ax1.set_title('Original Space')\n", "ax1.scatter(X[:, 0], X[:, 1], c=pred, s=50, cmap='Spectral')\n", "plotDecisionFunction(ax1,flin, False)\n", "\n", "fphi = SVC(kernel='linear').fit(phiX, y)\n", "pred = fphi.predict(phiX)\n", "ax2.set_title('Feature Space')\n", "ax2.scatter(X[:, 0], X[:, 1], c=pred, s=50, cmap='Spectral')\n", "\n", "#We need to plot the decision boundary a bit differently here. Maybe I should make the initial function a bit more modular.\n", "x1_c = np.linspace(ax2.get_xlim()[0], ax2.get_xlim()[1], 30)\n", "x2_c = np.linspace(ax2.get_ylim()[0], ax2.get_ylim()[1], 30)\n", "X1c, X2c = np.meshgrid(x1_c, x2_c)\n", "\n", "grid = np.vstack([X1c.ravel(), X2c.ravel()]).T\n", "phiGrid = np.array([[x[0]**2,x[1]**2,math.sqrt(2)*x[0]*x[1],math.sqrt(2*c)*x[0],math.sqrt(2*c)*x[1],c] for x in grid])\n", "decFunc = fphi.decision_function(phiGrid).reshape(X2c.shape)\n", "ax2.contour(X1c, X2c, decFunc, levels=[-0.8, 0, 0.8], colors='k', linestyles=['--', '-', '--'], alpha=0.6)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This feature map $\\varphi_{poly}$ seems to work quite well and it is pretty generic. So let us write our model in the dual representation using the feature map. We get\n", "$$f(x)=\\sum_{i=1}^n\\alpha_i\\langle\\varphi_{poly}(x_i),\\varphi_{poly}(x)\\rangle\\enspace .$$\n", "Let us look at this inner product a bit more closely. Assume to vectors $x,z\\in\\mathcal{X}$ (and let's abbreviate $\\varphi_{poly}=\\varphi$ for the moment), what does it look like?\n", "\\begin{equation*}\n", "\\begin{split}\n", "\\langle\\varphi(x),\\varphi(z)\\rangle =& \\left\\langle\\left(x_1^2,x_2^2,\\sqrt{2}x_1x_2,\\sqrt{2c}x_1,\\sqrt{2c}x_2,c\\right), \\left(z_1^2,z_2^2,\\sqrt{2}z_1z_2,\\sqrt{2c}z_1,\\sqrt{2c}z_2,c\\right) \\right\\rangle\\\\\n", "=& x_1^2z_1^2 + x_2^2z_2^2 + 2x_1x_2z_1z_2 + 2x_1z_1c + 2x_2z_2c + c^2\\\\\n", "=& (\\underbrace{x_1z_1}_{=:\\xi_1})^2 + (\\underbrace{x_2z_2}_{=:\\xi_2})^2 + 2(x_1z_1)(x_2z_2) + 2c(x_1z_1) + 2c(x_2z_2) + c^2\\\\\n", "=& \\xi_1^2 + 2\\xi_1\\xi_2 + \\xi_2^2 + 2c\\xi_1 + 2c\\xi_2 + c^2\\\\\n", "=& (\\xi_1 + \\xi_2)^2 + 2c(\\xi_1+\\xi_2) + c^2\\\\\n", "=&\\left((\\xi_1 + \\xi_2) + c\\right)^2\\\\\n", "=&\\left((x_1z_1 + x_2z_2) + c\\right)^2\\\\\n", "=&\\left(\\langle x,z \\rangle + c\\right)^2\n", "\\end{split}\n", "\\end{equation*}\n", "So, what we have seen is that we can explress the inner product in feature space $\\langle\\varphi(x),\\varphi(z)\\rangle$ by a much simpler function $\\left(\\langle x,z \\rangle + c\\right)^2$.\n", "\n", "## An Intuitive Perspective on the Kernel Function\n", "\n", "In our model representation and in our optimization problem, we only ever need to compute $\\langle\\varphi_{poly}(x),\\varphi_{poly}(z)\\rangle$ and never need the actual point in feature space $\\varphi_{poly}(x)$. That is good, because it means we can instead use our simpler function $k_{poly}(x,z) = \\left(\\langle x,z \\rangle + c\\right)^2$ to compute that inner product. \n", "\n", "For this particular function $k$ we can guarantee that if we replace the inner product in the model and the Lagrangian with $k_{poly}$, we get the linear model in the feature space that $\\varphi_{poly}$ maps to. Our new model then is\n", "$$f(\\cdot) = \\sum_{i=1}^n \\alpha_i k_{poly}(x_i,\\cdot)$$\n", "and the Lagrangian optimization problem is\n", "$$\\max_{\\alpha\\geq 0}\\sum_{i=1}^n\\alpha_i-\\frac{1}{2}\\sum_{i,j=1}^n\\alpha_i\\alpha_jy_iy_jk_{poly}(x_i,x_j)\\enspace .$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Kernel Functions\n", "\n", "We have seen that for a particular choice of $\\varphi_{poly}$, we found a function $k_{poly}(\\dot,\\cdot)$ so that $k_{poly}(x,z) = \\langle\\varphi_{poly}(x),\\varphi_{poly}(z)\\rangle$. This implies that $k_{poly}$ is an inner product in the feature space $F$ that $\\varphi_{poly}$ maps to. What about other functions $k$? \n", "\n", "**Mercer's thorem** states that if $k$ is positive semi-definite, i.e., for all finite sets $x_1,\\dots,x_n$ and all real numbers $c_1,\\dots,c_n$, it holds that\n", "$$\\sum_{i=1}^n\\sum_{j=1}^n k(x_i,x_j)c_1c_j \\geq 0\\enspace ,$$\n", "then there exists _some_ $\\varphi$ such that $k(x,z)$ corresponds to _some_ inner product $\\langle\\varphi(x),\\varphi(z)\\rangle_F$ in $F$. Let's look at that a bit more closely.\n", "\n", "## Mercer's Theorem\n", "\n", "If we have a function $k:\\mathcal{X}\\times\\mathcal{X}\\rightarrow \\mathbb{R}$ that is positive semi-definite then we can define the associated Hilbert-Schmidt integral operator (a linear operator) over the space $\\mathcal{L}^2$ of square-integrable real-valued functions\n", "$$[T_k f](x) = \\int_\\mathcal{X}k(z,x)\\varphi(z)dz$$\n", "for all $f\\in\\mathcal{L}^2$ and $x\\in\\mathcal{X}$. Now, what Mercer's theorem says is the following.\n", "\n", "If $k$ is symmetric and positive-semidefinite, then there exists an orthonormal basis $\\{e_i\\}_{i=1}^\\infty$ of $\\mathcal{L}^2$ where the $e_i$ are the Eigenfunctions of $T_k$ such that the corresponding sequence of Eigenvalues $\\{\\lambda_i\\}_{i=1}^\\infty$ is non-negative. The Eigenfunctions corresponding to non-zero Eigenvalues of $T_k$ are continuous on $\\mathcal{X}$ and $k$ has the representation\n", "$$k(x,z) = \\sum_{i=1}^\\infty \\lambda_i e_i(x) e_i(z)\\enspace .$$\n", "\n", "Now what does that mean for us? We can basically ignore the whole part about the integral operator and just look at that last equation. It guarantees that for any **symmetric and positive-semidefinite** function $k(\\cdot,\\cdot)$ there exists a feature map $\\varphi(x)=(e_1(x),e_2(x),\\dots)$ such that $k$ is an inner product in the feature space that $\\varphi$ maps to. \n", "\n", "_Note:_ It is not the standard inner product, but one where each dimension is scaled by a non-negative factor $\\lambda_i$. \n", "\n", "## Reproducing Kernel Hilbert Spaces\n", "\n", "Assume a Hilbert space $\\mathcal{H}$ (vector space with inner product and norm) of real-valued functions over $\\mathcal{X}$. The evaluation functional $L_x:\\mathcal{H}\\rightarrow\\mathbb{R}$ evaluates each function $f\\in\\mathcal{H}$ at the point $x\\in\\mathcal{X}$, i.e., $L_x(f) = f(x)$. \n", "\n", "_Note:_ That's a very weird way to describe the evaluation of a function. Usually, you fix $f$ and then evaluate $f$ at all possible $x$. Here, you fix one $x$ with corresponding $L_x$ and then evaluate it at all possible $f$. In both cases, what you get in the end is simply $f(x)$.\n", "\n", "Now $\\mathcal{H}$ is a reproducing kernel Hilbert space, if $L_x$ is continuous at any $f\\in\\mathcal{H}$. This means, for every $L_x$ there exists a corresponding function $k_x$ such that \n", "$$L_x(f) = \\langle k_x, f\\rangle = f(x)\\enspace .$$\n", "With this, we can define the **reproducing kernel**\n", "$$k(x,z) = \\langle k_x, k_z\\rangle$$\n", "which is symmetric and positive-semidefinite.\n", "\n", "Now, the Moore–Aronszajn theorem guarantees that the converse is also true: if we have a symmetric and positive-semidefinite function $k$, then there existis a corresponding reproducing kernel Hilbert space of real-valued functions.\n", "\n", "## Feature Maps and RKHS\n", "\n", "We have seen above that for our symmetric and positive-semidefinite function $k$ there always exists some feature map $\\varphi$ such that $k(x,z)=\\langle\\varphi(x),\\varphi(z)\\rangle_F$ for some feature space $F$. Moreover, we know that there always exists a reproducing kernel Hilbert space $H_k$ of real-valued functions over $\\mathcal{X}$. What kind of functions are in that space? \n", "\n", "Let's construct a Hilbert space of linear functions\n", "$$H_\\varphi = \\{f:\\mathcal{X}\\rightarrow\\mathbb{R} \\mid \\exists \\beta\\in F, f(x)=\\langle\\beta,\\varphi(x)\\rangle_F, \\forall x\\in\\mathcal{X}\\}$$\n", "which has the norm\n", "$$\\|f\\|_\\varphi = \\inf\\{\\|\\beta\\|_F:\\beta\\in F, f(x)=\\langle\\beta,\\varphi(x)\\rangle_F, \\forall x\\in\\mathcal{X}\\}\\enspace .$$\n", "\n", "**Check the source for the following!**\n", "It can be shown that $H_\\varphi$ is the reproducing kernel Hilbert space defined by $k(x,z)=\\langle\\varphi(x),\\varphi(z)\\rangle_F$. \n", "\n", "This implies that the real-valued functions over $\\mathcal{X}$ in $\\mathcal{H}_k$ are linear functions over the feature space $F$.\n", "\n", "\n", "# The Kernel Trick\n", "\n", "The kernel trick now means that as soon as we have any symmetric positive-semidefinite function $k(\\cdot,\\cdot)$, we can use it to calculate the inner product in the model representation. However, there is one more problem to solve: in principle this only means we can represent our model as\n", "$$f(\\cdot)=\\sum_{x\\in\\mathcal{X}}\\alpha_xk(x,\\cdot)$$\n", "which is an infinite sum. \n", "\n", "In the beginning, we mentioned the representer theorem and gave a simplified special case. This is the point were the full version of this theorem comes in handy. \n", "\n", "### The Representer Theorem (Schölkopf, Herbrich, Smola)\n", "\n", "Let $k:\\mathcal{X}\\times\\mathcal{X}\\rightarrow\\mathbb{R}$ be a symmetric and positive-semidefinite kernel over the non-empty set $\\mathcal{X}$ with corresponding reproducing kernel Hilbert space $\\mathcal{H}_k$. Given a training set $\\left((x_1,y_1),\\dots,(x_n,y_n)\\right)\\subset\\mathcal{X}\\times\\mathbb{R}$ of size $n\\in\\mathbb{N}$, a loss function $\\ell:\\mathbb{R}\\times\\mathbb{R}\\rightarrow\\mathbb{R}$ and a strictly increasing real-valued function $g:[0,\\infty)\\rightarrow\\mathbb{R}$, the regularized empirical risk on $H_k$ is defined as\n", "$$R(f) = \\sum_{i=1}^n\\ell(f(x_i),y_i) + g(\\|f\\|)\\enspace .$$\n", "Then, any minimizer of the regularized risk\n", "$$f^*=\\arg\\min_{f\\in\\mathcal{H}_k} R(f)$$\n", "admits a representation of the form\n", "$$f(\\cdot) = \\sum_{i=1}^n \\alpha_i k(x_i,\\cdot)$$\n", "\n", "\n", "$\\ell$, a training set $X,y$ of size $n$, a strictly increasing real-valued function $g$, and an inner product $\\langle\\cdot,\\cdot\\rangle$, then the linear function minimizing the regularized loss, i.e., \n", "$$f^* = \\arg\\min_{f\\in\\mathcal{H}}\\sum_{i=1}^n\\ell(f(x_i),y_i) + g(\\|f\\|)$$\n", "can be represented as\n", "$$f^*(\\cdot)=\\sum_{i=1}^n\\alpha_i\\langle x_i, \\cdot\\rangle\\enspace .$$\n", "\n", "# A few Examples\n", "\n", "Let's just try out a few kernel functions on some example data." ] }, { "cell_type": "code", "execution_count": 294, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Polynomial kernel d=1\n", "X, y = make_circles(100, factor=.1, noise=.1)\n", "\n", "fig, (ax1,ax2, ax3) = plt.subplots(1, 3, figsize = (14,4))\n", "f = SVC(kernel='poly', C=1E6, degree = 1)\n", "f.fit(X, y)\n", "pred = f.predict(X)\n", "ax1.set_title(r'$k(x,z)=(x^\\top z + 1)^1$')\n", "ax1.scatter(X[:, 0], X[:, 1], c=pred, s=50, cmap='Spectral')\n", "plotDecisionFunction(ax1,f, True)\n", "\n", "f = SVC(kernel='poly', C=1E6, degree = 2)\n", "f.fit(X, y)\n", "pred = f.predict(X)\n", "ax2.set_title(r'$k(x,z)=(x^\\top z + 1)^2$')\n", "ax2.scatter(X[:, 0], X[:, 1], c=pred, s=50, cmap='Spectral')\n", "plotDecisionFunction(ax2,f, True)\n", "\n", "f = SVC(kernel='rbf', C=1E6)\n", "f.fit(X, y)\n", "pred = f.predict(X)\n", "ax3.set_title(r'$k(x,z)=e^{-\\|\\|x-z\\|\\|_2^2}$')\n", "ax3.scatter(X[:, 0], X[:, 1], c=pred, s=50, cmap='Spectral')\n", "plotDecisionFunction(ax3,f, True)\n", "\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# The Gaussian Kernel\n", "\n", "The polynomial kernel is defined as \n", "$$k(x,z) = e^{-\\frac{\\|x-z\\|_2^2}{2\\sigma}}$$\n", "and it looks as follows." ] }, { "cell_type": "code", "execution_count": 295, "metadata": {}, "outputs": [], "source": [ "import matplotlib.colors as mcolors\n", "def drawKernel(sv, sigma, ax, alpha=1.0, xmin = None, xmax = None):\n", " if xmin is None:\n", " xmin = ax.get_xlim()[0]\n", " if xmax is None:\n", " xmax = ax.get_xlim()[1]\n", " x_c = np.linspace(xmin, xmax, 100)\n", " y = alpha*np.array([np.exp(-1*np.linalg.norm(sv-x)**2 / (2*sigma)) for x in x_c])\n", " ax.plot(x_c, y, color='darkturquoise')\n", " ax.vlines(sv, 0.,alpha,colors='r', linestyles ='dashed')" ] }, { "cell_type": "code", "execution_count": 296, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 1, figsize = (12,4))\n", "sv = 0.4\n", "drawKernel(sv, .01, ax)\n", "ax.set_title(r'Gaussian kernel $e^{-\\frac{\\|x-z\\|_2^2}{2\\sigma}}$ around $x=0.4$')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is called the Gaussian kernel, or RBF kernel (for radial basis function), because it is equal to an unnormalized Gaussian. \n", "\n", "## Example: Regression with the Gaussian Kernel\n", "\n", "So let's do some regression. Assume fome function $f$ that we want to approximate." ] }, { "cell_type": "code", "execution_count": 297, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def f(x):\n", " y = 2.5220937891424464\n", " y -= 1.3205441719052109*x\n", " y += 1.5580077014371324e-001*x**2\n", " y += 1.7371642653756312*x**3\n", " y -= 9.7085004028066801e-001*x**4\n", " y += 2.0053450527785788e-001*x**5\n", " y -= 1.8017813196659842e-002*x**6\n", " y += 5.9348129387248665e-004*x**7\n", " return y\n", "\n", "fig, ax = plt.subplots(1, 1, figsize = (8,4))\n", "X = np.linspace(-1, 10, 1000)\n", "Y = np.array([f(x) for x in X])\n", "ax.plot(X,Y)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How would this look like if we used a support vector regression with a Gaussian kernel?" ] }, { "cell_type": "code", "execution_count": 298, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "16\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sklearn.svm import SVR\n", "gamma = .1\n", "clf = SVR(kernel='rbf', C=100000., gamma=gamma)\n", "X = np.linspace(-1, 10, 1000).reshape(-1,1)\n", "Y = np.array([f(x) for x in X])\n", "fig, ax = plt.subplots(1, 1, figsize = (8,4))\n", "ax.plot(X,Y)\n", "\n", "clf.fit(X,Y)\n", "pred = clf.predict(X)\n", "ax.plot(X,pred, color='purple')\n", "print(len(clf.support_vectors_))\n", "for i in range(len(clf.support_vectors_)):\n", " sv = clf.support_vectors_[i]\n", " alpha = clf.dual_coef_.T[i]\n", " drawKernel(sv, gamma, ax, alpha=1.0, xmin=-2, xmax=11.)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, the coefficients are a bit horrible... (around 20k) so let's regularize a bit and visualize the coefficients. :D" ] }, { "cell_type": "code", "execution_count": 299, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "141\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sklearn.svm import SVR\n", "gamma = 1.9\n", "clf = SVR(kernel='rbf', C=1., gamma=gamma)\n", "X = np.linspace(-1, 10, 1000).reshape(-1,1)\n", "Y = np.array([f(x) for x in X])\n", "fig, ax = plt.subplots(1, 1, figsize = (8,4))\n", "ax.plot(X,Y)\n", "\n", "clf.fit(X,Y)\n", "pred = clf.predict(X)\n", "ax.plot(X,pred, color='purple')\n", "print(len(clf.support_vectors_))\n", "for i in range(len(clf.support_vectors_)):\n", " sv = clf.support_vectors_[i]\n", " alpha = clf.dual_coef_.T[i]\n", " drawKernel(sv, gamma, ax, alpha=alpha, xmin=-2, xmax=11.)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Another Example: Classification with the Gaussian Kernel\n", "\n", "Let us look at how at how the classification depends on the kernel bandwidth sigma ($\\sigma$) and the regularizuation constant $C$." ] }, { "cell_type": "code", "execution_count": 306, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "3a8890d7483b4f2eb9c7b45a2b86921b", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(FloatSlider(value=1.9, description='gamma', min=0.001, step=0.001), FloatSlider(value=49…" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 306, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from ipywidgets import interact, interactive, fixed, interact_manual\n", "import ipywidgets as widgets\n", "%matplotlib notebook\n", "\n", "def plotDecisionFunctionContour(ax, f, showSVs, Xg, Yg, grid, cmap=None):\n", " decFunc = f.decision_function(grid).reshape(Xg.shape)\n", " if cmap is None:\n", " ax.contour(Xg, Yg, decFunc, levels=[-1, 0, 1], colors='k', linestyles=['--', '-', '--'], alpha=0.6)\n", " else:\n", " ax.contourf(Xg, Yg, decFunc, cmap=cmap, alpha=0.3)\n", " if showSVs:\n", " ax.scatter(f.support_vectors_[:,0], f.support_vectors_[:,1], linewidth=1.1, facecolors='None', edgecolor = 'k', s=250)\n", "\n", "def plotSVC(gamma, C,showSVs, X, Y, Xg, Yg, grid):\n", " clf = SVC(kernel='rbf', C=C, gamma=gamma)\n", " clf.fit(X, Y)\n", " pred = clf.predict(X)\n", " \n", " fig = plt.figure(figsize=(8,6))\n", " ax = fig.add_subplot(1, 1, 1)\n", " ax.scatter(X[:,0], X[:,1], c=Y, cmap='Spectral')\n", " plotDecisionFunctionContour(ax, clf, showSVs, Xg, Yg, grid, cmap='Spectral')\n", " \n", " fig.canvas.draw()\n", " \n", "X, Y = make_moons(n_samples = 50, random_state = 43, noise =0.2)\n", "xg = np.linspace(min(X[:,0]), max(X[:,0]), 30)\n", "yg = np.linspace(min(X[:,1]), max(X[:,1]), 30)\n", "Yg, Xg = np.meshgrid(yg, xg)\n", "grid = np.vstack([Xg.ravel(), Yg.ravel()]).T\n", "\n", "interact(plotSVC, gamma = widgets.FloatSlider(min=0.001, max=100., step=0.001, value=1.9), C = (0.0001,10000.,0.1), showSVs = True, X = fixed(X), Y = fixed(Y), Xg = fixed(Xg), Yg = fixed(Yg), grid = fixed(grid))\n", "#gamma = 1/2sigma^2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [] } ], "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": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 2 }