{ "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", "from sklearn.metrics import confusion_matrix\n", "import matplotlib.pyplot as plt\n", "\n", "from utils import draw_in_row\n", "from utils import NormalDistribution\n", "from utils import plot_confusion_matrix\n", "from utils import MixtureGaussians\n", "\n", "plt.rcParams['figure.figsize'] = (10,6)\n", "\n", "np.random.seed(42)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Cautious classification\n", "\n", "Performing cautious classification is a method to predict the classes considering\n", "the option of abstaining to predict any instance, given that the instance seems\n", "ambiguous. In that case, the missclassification could be worst than abstaining\n", "giving the possibility of performing a further analysis of the instance.\n", "\n", "For example, lets assume that we have two classes with the following description" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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84xq/O4uGkDANljzpGx94QdvwWwgRkaTwEroy0ry6StVtvimwvJTTFUZiMOWr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\ncOQYG9RXN8GOv6ljzQJnL1YrXgsRgZrdlby66TJ8ehsAc/J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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=0.25)\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": "markdown", "metadata": {}, "source": [ "Then we can compute the posterior probabilities for both classes using Bayes' theorem." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ePFlAvauKLQVz+fbwe5TW7D3meFx4Cqd1m0F6wsV0CUsyIcLAVVqzl+2F89lW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\nHgIZd8LF2ZA0xttfstlYWPPL66HqgHn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h3IfdMH4pUAN8xBcbxmcB7wLfBD4c5HXUMC4i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\ncLzaP4fjN4yWiamE+BrGdfFcgaHzRWuL9DKAF4DHhjhH64t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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": [ "# Chow's rule\n", "\n", "Chow's rule states that it is possible to make cautious classifications by \n", "rejecting the predictions for which the posterior probabilites for the instance\n", "$x$ are\n", "\n", "$$ \\forall_i,p(y=i|x) < \\theta $$\n", "\n", "We can visualize this with the posterior probabilities and we can see that this\n", "corresponds to reject the regions of the input space where the posterior probabilites\n", "are really similar." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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bb1NeXs59993X4H5FRUU899xzjBw5kqqqKuLi4ujRowePPvookydPJjU1lfj4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\ni2Y0RJmYN458g33NTwNgGh42LP9P8tNX2ByViCQ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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", "theta = 0.6\n", "\n", "def plot_predictions(x, f1, f2, reject):\n", " plt.plot(x, f1, color='yellowgreen', label=r'$p(f_1|x)$', linewidth=3)\n", " plt.plot(x, f2, color='orange', label=r'$p(f_2|x)$', linewidth=3)\n", " plt.plot(x, reject, color='red', label=r'$reject$', linewidth=3)\n", " plt.legend()\n", " plt.xlim([x.min(), x.max()])\n", " plt.grid(True)\n", " plt.title(\"Prediction is the argmax of the next three\")\n", "\n", "reject = np.ones_like(x_lin)*theta\n", "plot_predictions(x_lin, p_f1_g_f_x, p_f2_g_f_x, reject)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# C. Ferri and J. Hernández Orallo\n", "\n", "Another option is to have one thershold $\\theta$ per class. Then, if the posterior probability\n", "of one class is lower than its corresponding threshold then the models abstains." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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7C55nVPA5TIq4krEhF3jOE3sttaRFfA4fLoHWuo7jOiNM/AmkrgRzuPvKJzyO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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "theta_f1 = 0.6\n", "theta_f2 = 0.9\n", "thetas = np.array([theta_f1, theta_f2])\n", "\n", "def plot_original_thresholds(x, f1, f2, theta1, theta2):\n", " plt.plot(x, f1, color='yellowgreen', label=r'$p(f_1|x)$', linewidth=3)\n", " plt.plot(x, f2, color='orange', label=r'$p(f_2|x)$', linewidth=3)\n", " plt.plot(x, np.ones_like(x)*theta1, '--', color='yellowgreen', label=r\"$\\theta_1 = {}$\".format(theta1), linewidth=3)\n", " plt.plot(x, np.ones_like(x)*theta2, '--', color='orange', label=r\"$\\theta_2 = {}$\".format(theta2), linewidth=3)\n", "\n", " plt.legend()\n", " plt.xlim([x.min(), x.max()])\n", " plt.grid(True)\n", "\n", "plt.subplot(2,1,1)\n", "plot_original_thresholds(x_lin, p_f1_g_f_x, p_f2_g_f_x, theta_f1, theta_f2)\n", "\n", "c = np.argmax(np.vstack((p_f1_g_f_x, p_f2_g_f_x)), axis=0)\n", "reject = thetas[c]\n", "\n", "plt.subplot(2,1,2)\n", "plot_predictions(x_lin, p_f1_g_f_x, p_f2_g_f_x, reject)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However with imbalanced classes this method can be problematic as some of the classes could have really low probabilities. For that reason the same authors proposed the use of scaled probabilities with respect to their corresponding thresholds.\n", "\n", "If $\\exists p_i, p_i \\ge \\theta_i$ then class = argmax$_i(p_i / \\theta_i)$\n", "\n", "Else class = abstain\n", "\n", "## TODO modify this example" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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7C55nVPA5TIq4krEhF3jOE3sttaRFfA4fLoHWuo7jOiNM/AmkrgRzuPvKJzyO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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.subplot(2,1,1)\n", "plot_original_thresholds(x_lin, p_f1_g_f_x, p_f2_g_f_x, theta_f1, theta_f2)\n", "\n", "reject = np.ones_like(x_lin)\n", "\n", "plt.subplot(2,1,2)\n", "plot_predictions(x_lin, p_f1_g_f_x/theta_f1, p_f2_g_f_x/theta_f2, reject)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, the previous approach is merging two different aspects in the thresholds:\n", "\n", "1. The relevance of each class, given the differences between the thresholds\n", "2. The degree of abstention, given by the size of the thresholds\n", "\n", "Using the previous method, in order to decrease the abstention all the thresholds need to\n", "be decreased in the same proportion. In order to avoid that, it is possible to make the\n", "class biases to sum to one and then separate both aspects.\n", "\n", "Define the Class Bias $K = {k_i}$ for $i \\in {1,\\dots |C|}$, where $\\sum_i k_i = 1$ and a window\n", "size $w$, $0\\ge w \\ge 1$." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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7C55nVPA5TIq4krEhF3jOE3sttaRFfA4fLoHWuo7jOiNM/AmkrgRzuPvKJzyO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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "k_f1 = 0.2\n", "k_f2 = 0.8\n", "w = 0.5\n", "\n", "theta_f1 = (1-k_f1)*w + k_f1\n", "theta_f2 = (1-k_f2)*w + k_f2\n", "thetas = np.array([theta_f1, theta_f2])\n", "\n", "plt.subplot(2,1,1)\n", "plot_original_thresholds(x_lin, p_f1_g_f_x, p_f2_g_f_x, theta_f1, theta_f2)\n", "\n", "reject = np.ones_like(x_lin)\n", "\n", "plt.subplot(2,1,2)\n", "plot_predictions(x_lin, p_f1_g_f_x/theta_f1, p_f2_g_f_x/theta_f2, reject)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Background Check\n", "\n", "It is possible to solve the same task by assuming that there exist a _background_ class with the same distribution as the _foreground_ but with a different prior probability. In this case, regions where the probabilities for all the _foreground_ classes are lower than the _background_ probability is considered as an uncertain region and can be rejected.\n", "\n", "We achieve this behaviour by using the affine inductive bias\n", "\n", "$$ q_b(x) = (1-q_f(x))\\mu(0) + q_f(x)\\mu(1)$$\n", "\n", "were in this particular case $\\mu(0) = 0$ and $\\mu(1) = \\theta$.\n", "\n", "Then \n", "\n", "$$ q_b(x) = q_f(x)\\theta $$\n", "\n", "This means that the ratio between the two distributions is qual to the inverse of the threshold $\\theta$\n", "\n", "$$ \\frac{q_f(x)}{q_b(x)} = \\theta^{-1} = r(x) $$\n", "\n", "thus\n", "\n", "$$\n", "p(b|x) = \\frac{1}{1+\\theta^{-1}} \\\\\n", "p(f_c|x) = \\frac{p(f_c|f,x)\\theta^{-1}}{1+\\theta^{-1}}\n", "$$\n", "\n", "Because of this parametrization, the density of the _foreground_ and the _background_ are not important as they cancel each other and what it remains is their ratio. For that reason in the next examples we arebitrarly assigned to the _foreground_ a fixed constant distribution with the value 1." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(0, 1)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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H2Wy2oPTO9HStvY/uuahajJM0bCciIiISAPU8iYiIhCH1PAWHep5EREREOpmCJ/GLrj8l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\nUM+TiMgk6Io288bR+6nv3JmKZXqLWV/5AHOyVji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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "p_f_x = 1\n", "mu0 = 0\n", "mu1 = 0.6\n", "theta = mu1\n", "\n", "p_b_x = np.ones_like(x_lin)*1/(1 + theta**-1)\n", "\n", "p_f1_g_x = (p_f1_g_f_x*theta**-1)/(1+theta**-1)\n", "p_f2_g_x = (p_f2_g_f_x*theta**-1)/(1+theta**-1)\n", "\n", "plot_predictions(x_lin, p_f1_g_x, p_f2_g_x, p_b_x)\n", "plt.ylim([0,1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The same can be done with multiple thresholds as explained by C. Ferri and J. Hernàndez Orallo by setting a __background check__ per class.\n", "\n", "\n", "$$\n", "q_{bf_1}(x) = q_{f_1}(x)\\theta_1 \\\\\n", "q_{bf_2}(x) = q_{f_2}(x)\\theta_2\n", "$$\n", "\n", "## TODO create example with various thresholds (one per class)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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7C55nVPA5TIq4krEhF3jOE3sttaRFfA4fLoHWuo7jOiNM/AmkrgRzuPvKJzyO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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "k_f1 = 0.2\n", "k_f2 = 0.8\n", "w = 0.5\n", "\n", "theta_f1 = (1-k_f1)*w + k_f1\n", "theta_f2 = (1-k_f2)*w + k_f2\n", "thetas = np.array([theta_f1, theta_f2])\n", "\n", "p_f_x = 1\n", "mu0 = 0\n", "mu1 = theta_f1\n", "p_b_f1_x = np.ones_like(x_lin)*((1-p_f1_g_f_x)*mu0 + p_f1_g_f_x*mu1)\n", "\n", "mu1 = theta_f1\n", "p_b_f1_x = np.ones_like(x_lin)*((1-p_f1_g_f_x)*mu0 + p_f1_g_f_x*mu1)\n", "\n", "plt.subplot(2,1,1)\n", "plot_original_thresholds(x_lin, p_f1_g_f_x, p_f2_g_f_x, theta_f1, theta_f2)\n", "\n", "reject = np.ones_like(x_lin)\n", "\n", "plt.subplot(2,1,2)\n", "plot_predictions(x_lin, p_f1_g_f_x/theta_f1, p_f2_g_f_x/theta_f2, reject)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "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 }