{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline\n", "from __future__ import division\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from utils import NormalDistribution\n", "\n", "plt.rcParams['figure.figsize'] = (10,4)\n", "\n", "np.random.seed(42)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## How to estimate the background distribution\n", "\n", "As we saw in the previous example, if we know the _background_ distribution we can get the optimal Bayes, thus achieving the minimum possible error. However we need to estimate this _background_ with little or no samples.\n", "\n", "### (k+1)-class posterior probabilities\n", "\n", "Lets formalize the problem by deffining the different classes and their probabilities. Following the previous example we will have $k$ known classes; that we call _foreground_, and $1$ extra class that aggregates all the unknown classes; that we call _background_. These classes are $y \\in \\{1,\\dots,k,k+1\\}$ where $k+1$ corresponds to the aggregated _background_. Then, given the instantiation $X=x$ we can compute the posterior probabilites $p(Y=y_i|X=x)$. We will simplify our notation refering to $Y=y_i$ with $i \\in \\{1, \\dots, k\\}$ as $f_i$, and to $Y=y_{k+1}$ as $b$, also we will use $x$ to deonte $X=x$. Then we have the following posterior probabilities as:\n", "\n", "$$p(f_1|x),\\dots ,p(f_k|x), p(b|x)$$\n", "\n", "where\n", "\n", "$$ p(b|x) + \\sum_{i \\in \\{1,\\dots , k\\}} p(f_i|x) = 1$$\n", "\n", "We call this (k+1)-class posterior probabilities.\n", "\n", "### Class posterior probabiliites within foreground\n", "\n", "However, given the lack of _background_ information we can only get the posterior probabilities from the _foerground_ classes. In this case, if we use any multi-class classifier trained on the _foreground_ classes what we really obtain is:\n", "\n", "$$p(f_1|f,x), \\dots, p(f_k|f,x)$$\n", "\n", "where\n", "\n", "$$ \\sum_{i \\in \\{1,\\dots , k\\}} p(f_i|f,x) = 1$$\n", "\n", "This posterior probabilites also sum to one, and we refere to this ones as class posterior probabilities withing foreground." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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1pmqXHr+BTpPh+t0QbTcv7cR7sG4clJ9y33m9mC9eo6Jp0p/Oay7xmmT58yZg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\nsc+e3bPn/O65m2oe5LbGv0Tr+BEc/RoETmY/yb8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "norm_f1 = NormalDistribution(mu=0.9, sigma=0.2)\n", "norm_f2 = NormalDistribution(mu=1.1, sigma=0.3)\n", "\n", "p_f1 = 0.4\n", "p_f2 = 0.6\n", "\n", "x_min = np.min([norm_f1.mu-4*norm_f1.sigma, norm_f2.mu-4*norm_f2.sigma])\n", "x_max = np.max([norm_f1.mu+4*norm_f1.sigma, norm_f2.mu+4*norm_f2.sigma])\n", "\n", "x_lin = np.linspace(x_min, x_max, 100)\n", "\n", "p_x_g_f1 = norm_f1.pdf(x_lin)\n", "p_x_g_f2 = norm_f2.pdf(x_lin)\n", "\n", "plt.plot(x_lin, p_x_g_f1, color='yellowgreen', label='$p(x|f_1)$', linewidth=3)\n", "plt.plot(x_lin, p_x_g_f2, color='orange', label='$p(x|f_2)$', linewidth=3)\n", "plt.ylabel('Class densities')\n", "plt.legend()\n", "plt.xlim([x_min, x_max])\n", "plt.grid(True)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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2LuG5Dj4GJ563tYf8Ga5bol08Qghdas+E8dFAKpAOVAPvAXOvOuZHwMeohRM0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\nYwpiTt+3CffvrXFkQghnkzlPOnY4+50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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "p_x = p_x_g_f1*p_f1 + p_x_g_f2*p_f2\n", "\n", "p_f1_g_f_x = (p_x_g_f1*p_f1)/p_x\n", "p_f2_g_f_x = (p_x_g_f2*p_f2)/p_x\n", "\n", "plt.plot(x_lin, p_f1_g_f_x, color='yellowgreen', label='$p(f_1|f, x)$', linewidth=3)\n", "plt.plot(x_lin, p_f2_g_f_x, color='orange', label='$p(f_2|f, x)$', linewidth=3)\n", "plt.legend()\n", "plt.xlim([x_min, x_max])\n", "plt.grid(True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Obtaining the (k+1)-class posterior probabilities\n", "\n", "It is possible to obtain the (k+1)-class posterior probabilities only with the class posterior probabilities within the foreground and a familiarity ratio defined as:\n", "\n", "$$r(x) = \\frac{p(f|x)}{p(b|x)}$$\n", "\n", "From it we can get the posterior probability of the _background_\n", "\n", "$$p(b|x) = \\frac{1}{1/p(b|x)} = \\frac{1}{(p(b|x)+p(f|x))/p(b|x)} = \\frac{1}{1+r(x)}$$\n", "\n", "Similarly it is possible to compute the k-class posterior probabilities\n", "\n", "$$p(f_c|x) = p(f_c, f|x) = p(f_c|f,x)\\frac{p(f|x)}{p(b|x)}p(b|x) = \\frac{p(f_c|f,x)r(x)}{1+r(x)}$$\n", "\n", "### E.g. constant familiarity ratio\n", "\n", "As an example, imagine that we assume that the _foreground_ and the _background_ densities are the same trhough all the input space but with a different ratio. Here there is an example with different ratio values." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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4eu3Tj0NxReM782gF745FpVeSgnCYUtd+BhdmkjLlVstxtDWmq1KfcCUc+Yvl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\ny7QX9gG3m1/tpztwb/M3X3kfeF+V/o2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pyU+LhLiN7LzL+Z6ep9fCtpssjlPXsXDx6y2a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\nHu1T4r3X64wDHiIOn3ltxHp3Svk+KI2h9HVNxJsTdzXmoAjJZUjNaOQ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rs = [0.5, 1, 1.5, 2]\n", "\n", "for i, r in enumerate(rs):\n", " plt.subplot(1,len(rs),i+1)\n", " p_b_g_x = np.ones_like(x_lin)/(1+r)\n", "\n", " p_f1_g_x = p_f1_g_f_x*r/(1+r)\n", " p_f2_g_x = p_f2_g_f_x*r/(1+r)\n", "\n", " plt.plot(x_lin, p_f1_g_x, color='yellowgreen', label='$p(f_1,f| x)$', linewidth=3)\n", " plt.plot(x_lin, p_f2_g_x, color='orange', label='$p(f_2,f| x)$', linewidth=3)\n", " plt.plot(x_lin, p_b_g_x, color='red', label='$p(b|x)$', linewidth=3)\n", " plt.plot(x_lin, p_f1_g_x+p_f2_g_x, '--', color='blue', label='$p(f|x)$', linewidth=2)\n", " plt.xlim([x_min, x_max])\n", " plt.ylim([0,1])\n", " plt.grid(True)\n", " plt.title(\"$r(x) = {}$\".format(r))\n", " \n", " if i == 1:\n", " plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### E.g. non-constant familiarity ratio\n", "\n", "Another example could be if we assume that the _background_ class comes from a Normal distribution with more variance than the _foreground_. In this case the _foreground_ posterior probability will be higher on its mean, while it will be lower in farther regions.\n", "\n", "$$ r(x) = \\frac{p(f|x)}{p(b|x)} = \\frac{p(f,x)p(x)}{p(b,x)p(x)} = \\frac{p(f,x)}{p(b,x)}$$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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djgqgkjahIoErFDWdyy8Hp68Z8fEwrmz8QvuSlQX7nG7FR4/KWIeffw5NmsCt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\nk5bWGY6x191Wajz9mljXP+f2gNrWHsCCa9YbT7q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tmKtpKCGvfJ91dBhDSYmcXVSp1E/p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\n8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "norm_f = NormalDistribution(mu=1, sigma=0.3)\n", "p_f_x = norm_f.pdf(x_lin)\n", "\n", "sigmas = [0.3,1,2]\n", "\n", "for i, sigma in enumerate(sigmas):\n", " norm_b = NormalDistribution(mu=1, sigma=sigma)\n", "\n", " p_b_x = norm_b.pdf(x_lin)\n", "\n", " r = p_f_x/p_b_x\n", " \n", " plt.subplot(1,len(sigmas),i+1)\n", " p_b_g_x = np.ones_like(x_lin)/(1+r)\n", "\n", " p_f1_g_x = p_f1_g_f_x*r/(1+r)\n", " p_f2_g_x = p_f2_g_f_x*r/(1+r)\n", "\n", " plt.plot(x_lin, p_f1_g_x, color='yellowgreen', label='$p(f_1,f| x)$', linewidth=3)\n", " plt.plot(x_lin, p_f2_g_x, color='orange', label='$p(f_2,f| x)$', linewidth=3)\n", " plt.plot(x_lin, p_b_g_x, color='red', label='$p(b|x)$', linewidth=3)\n", " plt.plot(x_lin, p_f1_g_x+p_f2_g_x, '--', color='blue', label='$p(f|x)$', linewidth=2)\n", " plt.xlim([x_min, x_max])\n", " plt.ylim([0,1])\n", " plt.grid(True)\n", " plt.title(\"$\\sigma = {}$\".format(sigma))\n", " if i==0:\n", " plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Familiarity ratio\n", "\n", "Because we are only interested in the ratio between the _foreground_ and the _background_ classes we can define a relative density $q_f(x)$ for the _foreground_ and $q_b(x)$ for the _background_ as follows:\n", "\n", "$$\n", "q_f(x) = \\frac{p(x,f)}{\\max_x p(x,f)}, \\\\\n", "q_b(x) = \\frac{p(x,b)}{\\max_x p(x,f)}\n", "$$\n", "\n", "Then we can use these two functions instead of the real densities to compute the familiarity ratio\n", "\n", "$$r(x)=\\frac{p(x,f)}{p(x,b)} = \\frac{q_f(x) \\max_x p(x,f)}{q_b(x) \\max_x p(x,f)} = \\frac{q_f(x)}{q_b(x)}$$\n", "\n", "Furthermore, it is possible to estimate the relative _foreground_ density estimation from the likelihood $p(x|f)$ and in the other way around as:\n", "\n", "$$\n", "q_f(x) = \\frac{p(x|f)}{\\max_xp(x|f)}, \\\\\n", "p(x|f) = \\frac{q_f(x)}{\\int_x q_f(x) \\,dx}\n", "$$\n", "\n", "## Estimating the Relative _Foreground_/_Background_ Densities\n", "\n", "For that reason, we will need to infer the density of the background given the only information available from the _foreground_. In the absense of knowledge we will argue four different _inductive biases_ each one stronger than the previous one.\n", "\n", "### 1st Inductive bias:\n", "\n", "The _background_ density has any function $\\mu$ with rescpect to the _foreground_ density\n", "\n", "$$q_b(x) = \\mu(q_f(x))$$ " ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Xff7002H4cJu0+/LLUx5W0vk1n+Xq3Bm++QZyctyOJCl8m89ly2zsqWVLtyNJ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\nRCSteWkaBPVYiTht8mS4887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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "norm_f = NormalDistribution(mu=1, sigma=0.3)\n", "\n", "q_f = norm_f.pdf(x_lin)\n", "q_f /= q_f.max()\n", "q_b = np.sin(np.cos(np.tan(q_f*1.35)))\n", "\n", "plt.plot(x_lin, q_f, '-.', color='blue', label='$q_f$', linewidth=1)\n", "plt.plot(x_lin, q_b, '-', color='red', label='$q_b$', linewidth=1)\n", "plt.xlim([x_min, x_max])\n", "plt.grid(True)\n", "plt.title(\"$\\sigma = {}$\".format(sigma))\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2nd Inductive bias: monotonic background bias\n", "\n", "The _backgrond_ denstiy is monotonically increasing or decreasing with respect to the _foreground_" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "norm_f = NormalDistribution(mu=1, sigma=0.3)\n", "\n", "q_f = norm_f.pdf(x_lin)\n", "q_f /= q_f.max()\n", "q_b = -np.log(q_f)\n", "\n", "plt.plot(x_lin, q_f, '-.', color='blue', label='$q_f$', linewidth=1)\n", "plt.plot(x_lin, q_b, '-', color='red', label='$q_b$', linewidth=1)\n", "plt.xlim([x_min, x_max])\n", "plt.grid(True)\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3rd Inductive bias: affine background bias\n", "\n", "The _backgrond_ denstiy is monotonically incresing or decreasing within fixed bounds $\\mu(0)$ and $\\mu(1)$.\n", "\n", "$$ q_b(x) = (1-q_f(x))\\mu(0) + q_f(x)\\mu(1)$$" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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tWqkSqHKkeZuhaFHn5G7z5lJJ0bK0u3BKMAsQTyIrGGOBUzMUY4Fgl8e2ANYD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\nfl6txPFlRuM4LhxdRN4Os4DUI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vg63zYrkQkHIBMJTgPWuRSfUTNmyKB/5Umau0UYMkQ+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\nRMUKRd7a6dxz4cUX4cILTUdypPnz4dZbQ3W7T3M3TuefDwMHy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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "norm_f = NormalDistribution(mu=1, sigma=0.3)\n", "\n", "q_f = norm_f.pdf(x_lin)\n", "max_p_x_f = q_f.max()\n", "q_f /= max_p_x_f\n", "\n", "fig = plt.figure(figsize=(12,12))\n", "\n", "n_values = 4\n", "values = np.linspace(0,1,n_values)\n", "for i, mu1 in enumerate(reversed(values)):\n", " for j, mu0 in enumerate(values):\n", " plt.subplot(n_values, n_values, i*n_values+j+1)\n", " q_b = (1-q_f)*mu0 + q_f*mu1\n", "\n", " plt.plot(x_lin, q_f, '-.', color='blue', label='$q_f$', linewidth=1)\n", " plt.plot(x_lin, q_b, '-', color='red', label='$q_b$', linewidth=1)\n", " \n", " plt.xlim([x_min, x_max])\n", " plt.ylim([-0.01,1.01])\n", " \n", " if i==0 and j==0:\n", " plt.legend()\n", " \n", " if i == n_values-1:\n", " plt.xlabel('$\\mu(0) = {:.2f}$'.format(mu0))\n", " if j == 0:\n", " plt.ylabel('$\\mu(1) = {:.2f}$'.format(mu1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 4th nductive bias: constant background bias\n", "\n", "The _background_ density is constant in all the feature space. This is a particualr case in which $\\mu(0) = \\mu(1) = 0.5$\n", "\n", "$$ q_b(x) = (1-q_f(x))0.5 + q_f(x)0.5 = 0.5 $$" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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0FKp2zjypKJYvh/vvDx2FpJjNnQuHHJJ8Gk+qVFEUT/Zry2PJEvjf/4VSn0A0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\nRkYAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "norm_f = NormalDistribution(mu=1, sigma=0.3)\n", "\n", "q_f = norm_f.pdf(x_lin)\n", "q_f /= q_f.max()\n", "q_b = (1-q_f)*0.5 + q_f*0.5\n", "\n", "plt.plot(x_lin, q_f, '-.', color='blue', label='$q_f$', linewidth=1)\n", "plt.plot(x_lin, q_b, '-', color='red', label='$q_b$', linewidth=1)\n", "plt.xlim([x_min, x_max])\n", "plt.grid(True)\n", "plt.title(\"$\\mu(0) = \\mu(1) = 0.5$\")\n", "plt.legend()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.6" } }, "nbformat": 4, "nbformat_minor": 0 }