{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Implementation of Infinite Mixture Models using Dirichlet Process taken from http://blog.echen.me/2012/03/20/infinite-mixture-models-with-nonparametric-bayes-and-the-dirichlet-process/" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.stats import norm\n", "import seaborn as sns\n", "sns.set(color_codes=True)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Generate table assignments for `num_customers` customers, according to\n", "# a Chinese Restaurant Process with dispersion parameter `alpha`.\n", "# returns an array of integer table assignments\n", "def chinese_restaurant_process(num_customers, alpha):\n", " if num_customers <= 0:\n", " return []\n", " table_assignments = [1] # first customer sits at table 1\n", " next_open_table = 2 # index of the next empty table\n", " # Now generate table assignments for the rest of the customers.\n", " for i in range(1,num_customers):\n", " rand_p = np.random.rand()\n", " if (rand_p < alpha*1.0/(alpha + i)):\n", " # Customer sits at new table\n", " table_assignments.append(next_open_table)\n", " next_open_table += 1\n", " else:\n", " # Customer sites at an exiting table\n", " # He chooses which table to sit at by giving equal weight to each\n", " # customer already sitting at a table\n", " rand_index = np.random.random_integers(0,i-1)\n", " #print i, len(table_assignments), rand_index, rand_p, alpha*1.0/(alpha + i), table_assignments\n", " which_table = table_assignments[rand_index]\n", " table_assignments.append(which_table)\n", " return table_assignments" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def get_points(N=10, alpha_max=1000, runs_per_alpha=10):\n", " points = []\n", " for alpha in range(1,alpha_max):\n", " #print \"Alpha: \", alpha\n", " max_groups = []\n", " for i in range(runs_per_alpha):\n", " distribution = chinese_restaurant_process(num_customers = N, alpha = alpha)\n", " max_groups.append(max(distribution))\n", " #print \"Run[%s]:\\t%s\" %(i, distribution)\n", " mean_groups = np.mean(max_groups)\n", " #print \"Alpha: %s, Mean: %s\" % (alpha, mean_groups)\n", " points.append([alpha, mean_groups])\n", " return np.array(points)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAm0AAAJiCAYAAACVXfVrAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3XeAVOW5+PHv9D7bG9vZXVh6V6QoqCAooMRoNBFJ9HJt\n", "id7ITa6/FEvCNeXea7xX7IklRmNMJHbUqChdgaV3lu29T9up5/z+GHdgZSnCUoY8n784Z8458555\n", "hzPPvuV5NaqqqgghhBBCiHOa9mwXQAghhBBCHJ8EbUIIIYQQcUCCNiGEEEKIOCBBmxBCCCFEHJCg\n", 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"plt.show()" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Poyla Urn Process\n", "# Draw `num_balls` colored balls according to a Polya Urn Model\n", "# with a specified base color distribution and dispersion parameter\n", "# `alpha`.\n", "#\n", "# returns an array of ball colors\n", "def polya_urn_model(base_color_distribution, num_balls, alpha):\n", " if num_balls <= 0:\n", " return []\n", " balls_in_urn = []\n", " for i in range(num_balls):\n", " urn_size = len(balls_in_urn)\n", " if np.random.rand() < alpha*1.0 / (alpha + urn_size):\n", " # Draw a new color, put a ball of this color in the urn.\n", " new_color = base_color_distribution()\n", " balls_in_urn.append(new_color)\n", " else:\n", " # Draw a ball from the urn, add another ball of the same color.\n", " ball = balls_in_urn[np.random.random_integers(0,urn_size-1)]\n", " balls_in_urn.append(ball)\n", " return np.array(balls_in_urn)\n" ] }, { "cell_type": 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"s/8DRgYsX4/2lvwAAAAASUVORK5CYII=\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "unit_uniform = lambda: int(np.random.rand()*100)/100.0\n", "plt.figure(figsize=[10,10])\n", "for i in range(3):\n", " X = polya_urn_model(unit_uniform, num_balls = 1000, alpha = 1)\n", " #print X\n", " sns.kdeplot(X, shade=True);" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "'0.6.0'" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sns.__version__" ] }, { "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": "2.7.9" } }, "nbformat": 4, "nbformat_minor": 0 }