{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2017-07-21T08:04:51.423823", "start_time": "2017-07-21T08:04:33.547918" }, "collapsed": true, "hide_input": false }, "outputs": [], "source": [ "# Run this cell first (shit+enter) to import all packages\n", "\n", "from numpy import array, matrix, meshgrid, invert, ones,\\\n", "hstack, vstack, dot, linspace, sin, diag, abs, arange,\\\n", "cos, exp, identity\n", "import numpy as np\n", "from numpy.linalg import inv\n", "from numpy.ma import masked_where\n", "from matplotlib.pyplot import plot, fill_between\n", "\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Gaussian Process Regression Demonstration\n", "\n", "## About\n", "\n", "This notebook is supplementary material for the lecture [\"Maschinelles Lernen 2\" at the Karlsruhe Insitute of Technology](https://his.anthropomatik.kit.edu/28_327.php). It is intended to give the class' participants a feeling for the discussed algorithm and a brief introduction to numerical computation with python and [jupyter](http://jupyter.org). You are invited to modify the code but please do not share it outside the scope of the lecture.\n", "To install it on windows, it is recommended to use the [anaconda distribution](https://docs.continuum.io/anaconda/install). Please inform us if you encounter problems with this notebook.\n", "\n", "© 2017, Stefan Ulbrich, Forschungszentrum Informatik, All rights reserved.\n", "\n", "## Kernel functions\n", "\n", "The kernel functions in this notebook use a [python decorator](http://wiki.python.org/moin/PythonDecorators/) that transforms the *first two* arguments into matrices which yield all combinations of the input vectors when compared element-wise (cf. Cartesian product). Note that this works only for vectors and not for matrices (see [this thread](http://stackoverflow.com/questions/1827489/numpy-meshgrid-in-3d) to handle higher dimensions).\n", "\n", "Example:\n", "$$ k\\left((x_1,x_2)^T,(y_1,y_2)^T\\right) \\rightarrow \\begin{pmatrix} k(x_1,y_1) & k(x_1,y_2) \\\\ k(x_2,y_1) & k(x_2,y_2) \\end{pmatrix} $$\n" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "ExecuteTime": { "end_time": "2017-07-21T08:29:27.684165", "start_time": "2017-07-21T08:29:27.666268" }, "collapsed": false }, "outputs": [], "source": [ "# Press shift+enter to execute this cell \n", "# and add the kernel functions\n", "\n", "def kernel_function(f):\n", " def decorator(x,y,*args, **kwargs):\n", " xx,yy = meshgrid(x,y)\n", " val = f(xx,yy, *args, **kwargs)\n", " return matrix(val)\n", " return decorator\n", "\n", "class kernels(object):\n", " @kernel_function\n", " def periodic(x,y):\n", " return np.exp(np.cos((x-y)))\n", "\n", " @kernel_function\n", " def squared_exponential(x,y):\n", " return np.exp(-((x-y)**2)/2)\n", " \n", " @kernel_function\n", " def exponential(x,y):\n", " return np.exp(-((x-y))/0.5)\n", " \n", " @kernel_function\n", " def symmetric(x,y):\n", " return np.exp(-((abs(x)-abs(y))**2)/3)\n", " \n", " @kernel_function\n", " def squared_exponential_param(x,y,signal_variance=1.0,\n", " length_scale=0.1):\n", " return signal_variance * \\\n", " np.exp(-((x-y)**2)/length_scale)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Regression Examples\n", "\n", "### Squared Exponential\n", "\n", "#### Definition\n", "Kernel function **(stationary)**: \n", "\n", "$$ k(d) = \\exp\\left(-\\frac{d^2}{2}\\right), \\quad \\text{ where } d= \\| x-y \\| $$\n", "\n", "#### Evaluation\n", "\n", "Remind that the evaluation of a GPR is based on the following formulas:\n", "\n", "$$ \\bar {\\mathbf f_{L}} = \\text{E}[\\mathbf f_{\\star}|X,X_{\\star},\\mathbf y] = K(X_{\\star},X) \\cdot (K(X,X)+\\sigma^2I)^{-1} \\cdot \\mathbf f $$\n", "\n", "$$ \\text{cov} (\\mathbf f_{\\star}) = K(X_{\\star},X_{\\star}) - K(X_{\\star},X) \\cdot (K(X,X)+\\sigma^2I)^{-1}\\cdot K(X,X_{\\star}) $$\n" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "ExecuteTime": { "end_time": "2017-07-21T10:54:27.468230", "start_time": "2017-07-21T10:54:27.167857" }, "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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y6+Bi9U0USt9EUMg7n4fWmtnTZ5OZlsnl960toRV33TbYdnJY4qKjmbTQ7Jt4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\n7NCxQxTvKUYQpoyawpbXegEw/EodlXAbTSYctGtVd47uTbO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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "latent = lambda x: sin(x) # the latent function\n", "\n", "# input values of the training instances\n", "X = array([1.5,2,3.5,4.5]) \n", "\n", "\n", "## Uncomment the following two lines to see an example \n", "## showing that it is often necessary to determine the \n", "## hyperparameters of akernel:\n", "\n", "# latent = lambda x: exp(-((x)**2)/0.5)\n", "# X = array([-1,-0.25,0,0.25])\n", "\n", "\n", "Y = latent(X) # Compute the function values at \n", "\n", "# for plotting, evaluate the GP at many x-values\n", "x = linspace(-8,8,50) \n", "\n", "kernel = kernels.squared_exponential \n", "\n", "cov_X = kernel(X,X) + identity(X.size)*0.0\n", "cov_Xx = kernel(x,X)\n", "cov_x = kernel(x,x)\n", "\n", "mean = cov_Xx.T * inv(cov_X) * Y.reshape(-1,1)\n", "var = cov_x - cov_Xx.T * inv(cov_X) * cov_Xx\n", "\n", "\n", "upper = mean+var.diagonal().T\n", "lower = mean-var.diagonal().T\n", "\n", "\n", "plot(x,mean,'-g')\n", "fill_between(x, upper.A.flatten(), lower.A.flatten(), \n", " lw=0, facecolor='palegreen', interpolate=True)\n", "plot(X,Y,'*b')\n", "plot(x,latent(x),'-b')\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### A symmetric kernel\n", "\n", "Kernel function **(non-stationary)**: \n", "\n", "$$k(x,y) = \\exp\\left(-\\frac{(|x|-|y|)^2}{2}\\right) $$" ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "ExecuteTime": { "end_time": "2017-07-21T11:01:22.388121", "start_time": "2017-07-21T11:01:22.076158" }, "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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gwCk3/9xzSlulrEynOgJJm2xjr31v0GdsuEPlgTy67yaQnNnP8kdCQ87bF2hnQjMlTTRx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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "latent = lambda x: sin(x)\n", "\n", "X = array([1.5,2,2.5]) \n", "X = array([0,0.5,2,2.5,3,3.5]) # Better results\n", "#X = array([-0.5,0,0.5,2,2.5,3,3.5]) # We need regulazation (A non-zero noise term)\n", "\n", "Y = latent(X) \n", "x = linspace(-8,8,55) \n", "\n", "kernel = kernels.symmetric\n", "\n", "cov_X = kernel(X,X) + identity(X.size)*0.4\n", "cov_Xx = kernel(x,X)\n", "cov_x = kernel(x,x)\n", "\n", "mean = cov_Xx.T * inv(cov_X) * Y.reshape(-1,1)\n", "var = cov_x - cov_Xx.T * inv(cov_X) * cov_Xx\n", "\n", "\n", "upper = mean+var.diagonal().T\n", "lower = mean-var.diagonal().T\n", "\n", "\n", "plot(x,mean,'-g')\n", "fill_between(x, upper.A.flatten(), lower.A.flatten(), \n", " lw=0, facecolor='palegreen', interpolate=True)\n", "plot(X,Y,'*b')\n", "plot(x,latent(x),'-b')\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Periodic kernel\n", "\n", "Kernel function **(stationary)**: \n", "\n", "$$ k(d) = \\exp(\\cos(d)$$" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "ExecuteTime": { "end_time": "2017-07-21T11:04:14.346782", "start_time": "2017-07-21T11:04:14.047705" }, "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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xOYaN6srAXpfunOjL3gje0CO+B9cs3Q7Ayn9277ReA7PMiaY6O1/9qcVbMPNJ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\nFzMetCYcJZRwpfdKu7PhWJrMJu7puieutJ1dnfzvL5bz9g9+Bs2BOAg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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "latent = lambda x: sin(x)\n", "\n", "## Experiment with higher frequencies!\n", "# latent = lambda x: sin(x*2)\n", "\n", "X = array([1.5,2,3,4.5])\n", "Y = latent(X) \n", "x = linspace(0,20,100) \n", "\n", "kernel = kernels.periodic\n", "\n", "cov_X = kernel(X,X) + identity(X.size)*0.0\n", "cov_Xx = kernel(x,X)\n", "cov_x = kernel(x,x)\n", "\n", "mean = cov_Xx.T * inv(cov_X) * Y.reshape(-1,1)\n", "var = cov_x - cov_Xx.T * inv(cov_X) * cov_Xx\n", "\n", "\n", "upper = mean+var.diagonal().T\n", "lower = mean-var.diagonal().T\n", "\n", "\n", "plot(x,mean,'-g')\n", "fill_between(x, upper.A.flatten(), lower.A.flatten(), \n", " lw=0, facecolor='palegreen', interpolate=True)\n", "plot(X,Y,'*b')\n", "plot(x,latent(x),'-b')\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Paramterized Squared Exponential\n", "\n", "Kernel **(stationary)**:\n", "$$ k(d) = \\sigma_f^2 \\cdot \\exp(\\frac{-d^2}{2\\cdot l^2}) + \\sigma_n^2 \\delta(d) $$" ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "ExecuteTime": { "end_time": "2017-07-21T11:06:21.327396", "start_time": "2017-07-21T11:06:21.012294" }, "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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OpX9cf7y9vN38HZwoRacwUU9s7b/941xdeNlYLbXkkksvern83jLFITozS5OJdpgELD/p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\nKUyIJEgBBRRS6HUZkqaydRFmUzrutZX/enk2Q09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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "latent = lambda x: sin(x)\n", "\n", "X = array([1.5,2,2.5])\n", "Y = latent(X) \n", "x = linspace(0,4,50) \n", "\n", "\n", "# setup the hyperparameters\n", "\n", "signal_variance=1.5\n", "length_scale=0.1\n", "noise_variance=0\n", "\n", "\n", "# Shortcut (no need to modify successing code)\n", "kernel = lambda a,b: \\\n", " kernels.squared_exponential_param(a,b, signal_variance, \n", " length_scale)\n", "\n", "\n", "cov_X = kernel(X,X) + identity(X.size)*noise_variance\n", "cov_Xx = kernel(x,X)\n", "cov_x = kernel(x,x)\n", "\n", "mean = cov_Xx.T * inv(cov_X) * Y.reshape(-1,1)\n", "var = cov_x - cov_Xx.T * inv(cov_X) * cov_Xx\n", "\n", "\n", "upper = mean+var.diagonal().T\n", "lower = mean-var.diagonal().T\n", "\n", "\n", "\n", "plot(x,mean,'-g')\n", "fill_between(x, upper.A.flatten(), lower.A.flatten(), \n", " lw=0, facecolor='palegreen', interpolate=True)\n", "plot(X,Y,'*b')\n", "plot(x,latent(x),'-b')\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Polynomial Kernel\n", "\n", "Kernel **(?)**:\n", "$$ k(x,y) = \\phi(x)^t\\cdot\\phi(y) + \\sigma_n^2 \\delta(d) $$" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "ExecuteTime": { "end_time": "2017-07-21T08:35:11.946937", "start_time": "2017-07-21T08:35:11.577351" }, "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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mna/fYc2WNQ6pyxdJMHCAsIAwZo2bRd3guiSmJXLn7DtPm7Q3eLAxKfHzz40t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\nAVERUdQJr0NYSNhp7/798KOlakkb1YZ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "@kernel_function\n", "def polynomial(x,y,deg):\n", " \"\"\"\n", " Polynomial kernel (inefficient as it uses for-loops)\n", " \"\"\"\n", " result = ones(x.shape)\n", " for i in range(x.shape[0]):\n", " for j in range(x.shape[1]):\n", " phi_x = x[i,j]**arange(deg+1)\n", " phi_y = y[i,j]**arange(deg+1)\n", " result[i,j] = dot(phi_x,phi_y) \n", " \n", " return result\n", "\n", "latent = lambda x:sin(x*2)\n", "\n", "X = array([-0.5, 0.25, 0., 0.25, 0.5])\n", "Y = latent(X) \n", "x = linspace(-2,2,50) \n", "\n", "# Experiment with the noise value! \n", "# See what happen for noise=0 (numerical instability).\n", "noise=0.001\n", "\n", "kernel = lambda a,b: polynomial(a,b, 3)\n", "\n", "\n", "cov_X = kernel(X,X) + + identity(X.size)*noise \n", "cov_Xx = kernel(x,X)\n", "cov_x = kernel(x,x)\n", "\n", "mean = cov_Xx.T * inv(cov_X) * Y.reshape(-1,1)\n", "var = cov_x - cov_Xx.T * inv(cov_X) * cov_Xx\n", "\n", "plot(x,mean,'-g')\n", "plot(X,Y,'*b')\n", "plot(x,latent(x),'-b')\n", "\n", "\n", "# Note: Here we cut of values >/< +/- 5 as \n", "# the variance increases quickly!\n", "\n", "upper = (mean+var.diagonal().T).A.flatten()\n", "lower = (mean-var.diagonal().T).A.flatten()\n", "\n", "upper = masked_where(upper > 5.0, upper)\n", "lower = masked_where(lower < -5.0, lower)\n", "\n", "fill_between(x, upper, lower, lw=0, \n", " facecolor='palegreen', interpolate=True)\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "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": "3.4.3" }, "toc": { "colors": { "hover_highlight": "#DAA520", 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