{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "### DS4420: Estimation via sampling and LDA\n", "\n", "Some inspiration here from Iain Murray. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider the simple regression example below. We will assume we observe ($x, y$) data from this and want to recover the parameters. Obviously, we could use MLE here, but we will use this to introduce sampling methods." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "b0_true = 0.40\n", "b1_true = 1.25\n", "\n", "f = lambda x : b0_true + b1_true * x\n", "X = [-1, 0, 1.5, 2.0]\n", "y = [f(x_i) for x_i in X]" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from matplotlib.pyplot import plot\n", "import seaborn as sns\n", "\n", "plot(X, y, 'bo--')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Of course, we wouldn't *know* the true line in practice; the idea is to estimate $b_0$ and $b_1$. Obviously for simple linear regression we can do this via least-squares, but for illustration let's think about using MCMC. Specifically we'll take a Bayesian view and use importance sampling to find parameters.\n", "\n", "We might assume the following conditional distribution, given true parameters $\\beta$:\n", "\n", "$p(y|\\beta, x) \\sim \\mathcal{N}(\\beta_0 + \\beta_1 \\cdot x, \\sigma^2)$\n", "\n", "And then \n", "\n", "$p(\\beta) \\sim \\mathcal{N}([0, 0], I\\cdot[\\sigma^2_{\\text{prior}}, \\sigma^2_{\\text{prior}}])$\n" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.15915494309189535" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "import scipy\n", "\n", "# pick a prior over our coefficients.\n", "# Note: Is this a good choice? Why or why not?\n", "mu_prior, std_prior = [0]*2, [1]*2\n", "prior = scipy.stats.multivariate_normal(mu_prior, std_prior)\n", "prior.pdf([0, 0])" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "def candidate_beta():\n", " return np.random.normal(mu_prior, std_prior)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What's the probability of a given $\\beta$? " ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.0009526407323445032" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "beta = candidate_beta()\n", "y_hat = beta[0] + beta[1] * X[0]\n", "scipy.stats.norm(y[0], 0.1).pdf(y_hat) * prior.pdf(beta)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "def data_likelihood(beta, X, y, error_var=.5):\n", " d_prob = 1\n", " # note: am being verbose and inefficient; much better\n", " # to take a matrix vector product\n", " for x_i, y_i in zip(X, y):\n", " y_hat = beta[0] + beta[1] * x_i\n", " d_prob *= scipy.stats.norm(y_i, error_var).pdf(y_hat)\n", " return d_prob\n", " " ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3.970204507689646e-37" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data_likelihood(beta, X, y)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "def importance_sample_betas(n_samples):\n", " # sample betas from our prior\n", " samples = [candidate_beta() for _ in range(n_samples)]\n", " \n", " # calculate data likelihood -- p(y|X,\\beta) and multiply by prior for\n", " # all betas\n", " likelihoods = [data_likelihood(beta, X, y) * prior.pdf(beta) for beta in samples]\n", " \n", " # normalize the probabilities \n", " z = sum(likelihoods)\n", " weights = [l/z for l in likelihoods]\n", " \n", " # take a weighted average over samples\n", " #import pdb; pdb.set_trace()\n", " return (np.dot(np.array(samples).T, np.array(weights)), samples, weights)\n" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0.40619106 1.19020783]\n" ] }, { "data": { "text/plain": [ "[]" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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o4YskmdxcePZZaNoUpk/3a5EM6vmtn5JzwQV+AB+gRQs46KBQY5VgKeGLJJkhQ/4oYrlw9nZu2DCIlFbN4auv4Jln4Kqrwg5RionG8EWSQHY2rF/vx+mvuQbq1/dDOfa3y/2KJd27wxNP+LurJGGpHr5Igps3D664AsqU8VUQSmX+6Mfoq1XzO3/8Ef7yl7DDlICoHr5IEtq+He65xy8vuGYN3HZrLqVGPAcNG/pJ9uBXoVKyTxqBJHwze8nMfjKzBYXsP9XMNuZZAnFgEMcVkYJ99x0cc4wfr+/ZE5a+MY/zHz8Rrr3Wl7u87bawQ5QQBDWGPwoYDryyhzafOue6BHQ8EdmD2rWhXj148kk4M/Pf0KG3n2D/6qv+L4CmWSalQHr4zrnpwIYg3ktE9s8HH0CHDn8UO/vgnS2ceSZw2mm+Z790KVxyiZJ9EivJMfy2ZjbPzN41s6YFNTCzvmaWbmbpmZmZJRiaSPzasMGvOHXmmbB2Lfz01Uro1g26dPmj2NnTT0OVKmGHKiErqYQ/B6jvnGsJPA2ML6iRc26Ecy7NOZdWo0aNEgpNJH699ZYvdvbqq3DPHTuZf9k/OfzsJr6WcZcu/i4rkYgSmYfvnNuU5/kUM3vWzKo759aXxPFFEpFz8NRTfrz+kxHLaXLPeTB/PnTt6nv0hx0WdogSY0ok4ZtZTeBH55wzs9b4/1n8XBLHFkkkzvne/Bln+Hukxr3pqFLVKLOjJlSqBOPH++EckQIEkvDNbCxwKlDdzFYD9wFlAJxzzwEXANeaWTawDejuYvWOL5EY9f33cPXV/uLsvfc4Hjj63xwyYoQfvqlYEWbMCDtEiXGBJHznXI+97B+On7YpIvsoN9eXuLnzTj/B5t/3LOFvM66FB6dBmza+ZkKdOmGHKXFAd9qKxLgHH4Qbb4RTT8xi1RUD6flIC2zuXHj+efjsMyV7KTIVTxOJQTt3+o57rVp+Cv0RR0DP7inYie/BxRf7pakOPTTsMCXOqIcvEmPmzIHjj4e//hVy12RQ466ruKTTeqx0Ckyb5q/aKtnLflDCF4kR27bBgAHQujVkrsthRMtnKNWkkU/wM2f6RhUqhBukxDUlfJEYsHw5tGoFjzwCA7vMYWWdtrQc2c9n/9/n1otESQlfJAbUrevH6T/8EAaWfZjSa36A//zHz8Fs0CDs8CRB6KKtSEjeew8efhj+O8lR8YO3eXdoU2jUCFoMh7JloXLlsEOUBKMevkgJ+/ln6NULzjoLyqz+H3ZOF794+FNP+QaHHKJkL8VCPXyREuIcjBsH/frBbz9n8cFpj9Pxi8HYulJ+Pdkbbgg7RElw6uGLlKDhw/3CJMv7DeWMqXdhZ50FixdD//5+nVmRYqTfMJFi5ByMGuVr1dcuu553HsigUrvmlN5+PZzZwo/riJQQ9fBFismKFb6q5RVXOGZd8zI0akTV63tQulSuL3amZC8lTAlfJGA5OX4t2ebNYdPnC1lzVHvOnXSFn4Hz2mtQSv/sJBz6zRMJ2IMP+iH5a1p9waysVtTesBBeeAGmT4dmzcIOT5KYxvBFApCV5Yud1a4N/S5Yx9FH16T7hcdjQ+6B664DLdkpMUAJXyRK6enQpw/UtTX896ibqTZtKj2WLIHS1eG++8IOT2QXDemI7Kdt2+D22+HE1tl0+/4pJixthE3+rx/POeigsMMT2U1QSxy+BHQBfnLO7TZIaWYGPAV0BrYCvZ1zc4I4tkgYli2Dzp1h3fLfWFb9VOqvn+PnXj7zDBx5ZNjhiRQoqB7+KKDTHvafBTSIPPoC/wrouCKhqFcrm6OPhgkfH0T9i9rA66/Du+8q2UtMCyThO+emAxv20KQb8IrzvgAqm1mtII4tUlImT4aTT3JsH/065ZsdxeTHl9ChA75Xf9FFfsFZkRhWUmP4dYBVeV6vjmz7EzPra2bpZpaemZlZQqGJ7Nn69XDJJXBjl+94eG4nyvfuDtWqQXZ22KGJ7JOSSvgFdX3cbhucG+GcS3POpdXQNDYJmXP+PqnGjaH+2IdZUroZJ5b6HIYNgy+/1Jx6iTslNS1zNVAvz+u6wNoSOrbIfnv+eb8wSf/OmZTZ3hWGDvWT7UXiUEkl/IlAPzN7DTgB2OicyyihY4sUmXPw4ovQ5YRMaj5+G+NvvIyKXTuQwqOQkhJ2eCJRCWpa5ljgVKC6ma0G7gPKADjnngOm4KdkLsdPy7w8iOOKBOm776DvlbkcPu0lepa/HXI2c3BaGqR0AJTsJf4FkvCdcz32st8B1wdxLJGg5eT4xabG3jWfp7OvoQ0zca1PgX/9C5o0CTs8kcDoTltJeg8+CLfeClc2+D+Or7QURo3Cpk1TspeEo1o6kpSysiAzE+rMmcQt9bNo9Nr5XHT+tdjGHn7KpUgCUg9fks6XX0Ln5qv4ttm50LUrB416mosvcljpFCV7SWjq4UvS2LoV7rs7m9ynhjGBgZQvmwsPP+yLnekuWUkCSviSFJYtg06d4PAV0/iIW9l55tmkPDccUlPDDk2kxCjhS0JzDmzjr9SfP4OmTbtw60sdocxnlGnbVr16STpK+JKwJk10zP77WAb+2p+ym39j4qpVkTH6E8MOTSQUumgrCSczE/qf/S0HdDuD+5f1JKt2Knz2mS7IStJTD18ShnMwdizc1+9nvv7lWEqXL032o89S/rq+KosgghK+JJJFixg5sgnVG1bj13NHUPeyDlCzZthRicQMJXyJa7m58O/Hf+SCmbdQYfx/GD/x/6jY+RRSUv4WdmgiMUcJX+LWsqW5TOwygj7LB1A2ZRsMHMjBHY9XnTORQijhS9zJzoYnHncce1cnbs39kLWNOnDwO89Co4ZhhyYS0zRLR+LLli0MfsBxxwBjccse/DLsVWov+ghTshfZKyV8iQs7tjvWj3wHGjXitkNGM24c9Jt9OVVuuEQ3UIkUkRK+xLzZb6/ksxrdqN73PFyVKlRMa8T55yvPi+wrJXyJWVu2wNiOL9Lo/Ca02fIxi698DJs9G9q0CTs0kbiki7YSk75d6jizk9Hs+0NomtqRIyY/TeMmh4UdlkhcC6SHb2adzGypmS03swEF7O9tZplmNjfyuDKI40ricT9vgKuu4oh/P0DLlnD79HNo8b8JVFSyF4la1AnfzFKAZ4CzgCZADzMraG24151zrSKPF6I9riQY50i/8RV+rdkQ9/LLlHY7GT8eTj457MBEEkcQQzqtgeXOuRUAZvYa0A1YFMB7SxJY//ky1nXrS1rmNOZVaMuWN5+jbucWYYclknCCGNKpA6zK83p1ZFt+55vZN2Y2zszqFfRGZtbXzNLNLD0zMzOA0CSWOQevvALnnbmFQzMXMKXb8zTZMEPJXqSYBJHwC5oc5/K9ngSkOudaAB8Bowt6I+fcCOdcmnMurUaNGgGEJjHr/ffhnnsYPRpymrdiw9c/0Hl8X8qU08QxkeISxL+u1UDeHntdYG3eBs65n51zOyIvRwLHBXBciRNjxsDxdTP4P2tPp1rzmHV4d+jUCXtrHG++9BvTp0PDVgeEHaZIwgsi4X8FNDCzw82sLNAdmJi3gZnVyvOyK7A4gONKHBgzBvr2hSvWDOJkPmXCuuNp+f14Xms8CObNo2r9g1SqXqSERH3R1jmXbWb9gPfxdQpfcs4tNLMHgHTn3ETgRjPrCmQDG4De0R5X4sPdd0OlrRn0ZjSlcJQmh5OYxtotJ9K9XNjRiSSXQG68cs5NAabk2zYwz/M7gTuDOJbEkU2b6LZyFA1ZjJELwE5KcwljuGGV1pUVKWm6QibBc46s/4wj++jGDOUmruAlypMFQHmyuJyXOa7OupCDFEk+SvgSrP/9jw3tulC254Us33QIq9LO261JKXL4d8PBIQQnktyU8CUwmzflsu64synz+XQeqDKUH8Z9Rf3sFbt6978rTxYNf54ZUpQiyUvF0yR6M2fybcVjOeOc8tT65WX+cnkdbh9Wl4oVgc5fhx2diESohy/7b/163OVXQLt2HDFlOMcdB4/POIEHXookexGJKerhy77LzYVRo9hx022kbNlETv87KHfDtbx9YNiBicieqIcv+2zLlTdBnz58tbkxPRp+zZp+D8OByvYisU49fCmarVtxO7IYPaEyL77Zh6alW3H4A5cz9rZSlNZvkUhc0D9V2bspU+D666F9e175YRS0akX/F1rRsGHYgYnIvlDCl8KtWYO76WbsrXHsbNCYMpdfzlst4OCDoZQGA0XijhK+FOzdd8m54CKyt2dzPw9Rscet3N2+LFXCjktE9pv6afJn2dns3AlPTWvJ+G2daHvQQpq8cid33V827MhEJErq4Yu3caMvbbl4MYNP/IjBj9bmoove5N1hcOihYQcnIkFQwk92zsEbb+Buuhkyf8Kuv56br8si7fhydO0adnAiEiQN6SSzjAzo1Am6d2fhr3W4tMEscp8cRtVaSvYiiUg9/CS2iUr8lp7BP3ia92pdy/PPpGj2jUgC0z/vZDN1KpxzDkvnbafZCQdy2Ia5lLm5H/MWpHD66WEHJyLFKZCEb2adzGypmS03swEF7C9nZq9H9s8ys9Qgjiv74KefoFcv6NABFi7k8FIrad0aZswsxdChqowgkgyiTvhmlgI8A5wFNAF6mFmTfM36AL84544ChgKPRHtcKaLcXBg5EteoEbljxvJirbvZ9PlCyjZvyLhx0LZt2AGKSEkJooffGljunFvhnMsCXgO65WvTDRgdeT4OON3MLIBjy944R9azI1lYqgVNc+bxr9oP8vPWA8KOSkRCEETCrwOsyvN6dWRbgW2cc9nARqBa/jcys75mlm5m6ZmZmQGElqS2bIF778VlrufFUSk0/O5djt88lT7/bMwXX8Dhh4cdoIiEIYhZOgX11N1+tME5NwIYAZCWlrbbfimCSZOgXz/44Qc44kjGju1N/WOr8eELcNRRYQcnImEKIuGvBurleV0XWFtIm9VmVho4GNgQwLHld6tWwY03wvjxrK/VjJy3ZnDoee0Ydy5UqqRiZyISzJDOV0ADMzvczMoC3YGJ+dpMBHpFnl8AfOKcUw8+SHfdRe577/NMvYeplTGHkYvaAVC5spK9iHhR9/Cdc9lm1g94H0gBXnLOLTSzB4B059xE4EXgVTNbju/Zd4/2uAJ88QVUrUpW6tE8U+tRns0ezC9bUxk9Bnr0CDs4EYk1gdxp65ybAkzJt21gnufbgQuDOJYAv/wCd94JI0bAxRfzYIOxDP5nLbp3h2HDoEaNsAMUkVik0grxxDn4z3/glltw69fz2xU3U2noIPpnQ+vW0KVL2AGKSCzT6G48ef55uOQSNlVL5a910jl1zhPkHngQVaoo2YvI3inhx7rt22H5cgA2nnMJr7R/gSqLZ7KgzDE89pguyIpI0SldxLKPPoIWLeDss1myIJumJ1Tk8k/70P/WFObP92VxRESKSgk/Fq1bBz17whln4JyD4cM54ujStGsHn38Ojz0GFSqEHaSIxBtdtI01CxdCu3a4bdtYeN5ArlpxJ++fUJ5KZeH118MOTkTimXr4seK33/zXRo3YfN5lXNfuG5q/PYjcsuXZoHuSRSQASvhh++03uOUWaNAAl7mekS+lUOetYYz+oiFPPAEzZ0JqathBikgi0JBOWJyD8eN9/ZvVq+Hqq6F0ad54A447DkaOhCOPDDtIEUkkSvhh2L4dLrwQ/vtfXPPmvH7eG7T7e1vqVYFx43yxM60WICJB05BOSfq9Xlz58lCtGhl/f4wTy86mx7C2vPqq33XwwUr2IlI8lPBLymefQVoaLFnCjh1wf+oo6j91K8tXlmHsWF8aR0SkOCnhF7eff4arroKTToLMTMjM5MEHYdAgP6qzeDF0765evYgUP43hF6cxY+Dmm+GXX8i6+TYyrhxI/aYVuaWZXzy8c+ewAxSRZKIefnH6+mto0IBZ/5pD44mPcu6lFcnNhSpVlOxFpOQp4Qdp2za4916YOhWAX28bQt8mM2jTtwWlSsHQoSp2JiLh0ZBOUN5/H667DlasAGBxzdPo2LEc69bB7bfD/ffDAQeEG6KIJLeoEr6ZVQVeB1KB74GLnHO/FNAuB5gfefmDc65rNMeNKWvXQv/+8MYbcPTRuI8+xk7vwJFZcO20JSwAAAliSURBVMopcOutfnKOiEjYoh1gGAB87JxrAHwceV2Qbc65VpFH4iR78HfLTpiAG/QAY+/8hmP/3oFNm6BsWRg7VsleRGJHtAm/GzA68nw08Nco3y8+zJ4Nkyb551dfzdqPF3POl/fyt8vLUb68X3JWRCTWRJvwD3XOZQBEvh5SSLvyZpZuZl+YWaF/FMysb6RdemZmZpShFYNNm+Cmm/wCsnfdhcvJ5bmRKTQ663CmToUnn4QZM6B+/bADFRHZ3V7H8M3sI6BmAbvu3ofjHOacW2tmRwCfmNl859x3+Rs550YAIwDS0tLcPrx/8XIO3nrLJ/uMDH9x9sEHoVQp3n7b5/8RI+CII8IOVESkcHtN+M65joXtM7MfzayWcy7DzGoBPxXyHmsjX1eY2TTgGGC3hB+zZs3yt8UecwzZ48bz5GfHc9EmOKyyL3Z20EG6U1ZEYl+0QzoTgV6R572ACfkbmFkVMysXeV4daAcsivK4xS8rCz791D9v0wYmTGDeyC85od/x3Habv4kWVNlSROJHtAn/YeAMM1sGnBF5jZmlmdkLkTaNgXQzmwdMBR52zsV2wp8+HVq1go4dYc0aduyAe7/qSlqb0qxeDW++CQMKm48kIhKjopqH75z7GTi9gO3pwJWR5zOB5tEcp8SsX+/vknr5Zb/M1NtvQ506PHivH7K/7DJ44gmoVi3sQEVE9p3utP3d5s3QrJmvbjlgAFtuuZefNlfgcPzNUyedBGeeGXaQIiL7Twl/7VqoXRsqVvQ1i9u146N1zbiqNVSu7KfcV66sZC8i8S95S3lt3epXHUlN3VXs7JeLrqbP0GaccYa/U3bYMBU7E5HEkZw9/MmToV8/+P576N0bmjdn0SI4/XS/RsmAAXDffX4lQhGRRJF8Cf+KK/xF2caNYdo0ck9uT6lScFQl6NDBj9cfe2zYQYqIBC85Biyys/9YQLxNGxgyBPf1XF5Z2Z5WrWDjRj+EM2aMkr2IJK7ETPgZGdC+PaxbB19+6WsfjI7UeOvbl5U97+KsbmXp1cvfJbtxY7jhioiUhMRM+IMH+ypmZ5zhe/Q//ghVq5KbC88842dfzpgBTz/tb6Y97LCwAxYRKX6JN4afkQEvvgi5ubBgAVx5JTz+OFSqhDmYOBHatYPnn1dVSxFJLomX8AcP9skeoEwZclLK8vhzlbj4Yp/gx43zU+5V/0ZEkk1iDelkZJD9wsv+Ii3Azp1kjXiZJ+5Yx9ixfpMqW4pIskqohP/tpYPJ3pn7p23mcniz+WAVOxORpJdQCX/n9M8pT9aftpUni6pLZoYUkYhI7EioMfzm2V9T0DJZlg25BWwXEUkmCdXDL2x6paZdiogkWMIfMgQqVPjztgoV/HYRkWSXUAm/Z0+/mHj9+n4mTv36/nXPnmFHJiISvoQawwef3JXgRUR2F1UP38wuNLOFZpZrZml7aNfJzJaa2XIz0wRJEZEQRDukswA4D5heWAMzSwGeAc4CmgA9zKxJlMcVEZF9FO0i5osBbM+3rrYGljvnVkTavgZ0AxZFc2wREdk3JXHRtg6wKs/r1ZFtuzGzvmaWbmbpmZmZJRCaiEjy2GsP38w+AmoWsOtu59yEIhyjoO5/QfdH4ZwbAYwASEtLK7CNiIjsn70mfOdcxyiPsRqol+d1XWDt3r5p9uzZ681sZRTHrQ6sj+L7Y0WinAfoXGJVopxLopwHRHcuhRZ+L4lpmV8BDczscGAN0B34296+yTlXI5qDmlm6c67QmUPxIlHOA3QusSpRziVRzgOK71yinZZ5rpmtBtoCk83s/cj22mY2BcA5lw30A94HFgNvOOcWRhe2iIjsq2hn6bwDvFPA9rVA5zyvpwBTojmWiIhEJ6FKK+QzIuwAApIo5wE6l1iVKOeSKOcBxXQu5pwmw4iIJINE7uGLiEgeSvgiIkkiYRJ+ohRyM7OqZvahmS2LfK1SSLscM5sbeUws6Tj3ZG8/YzMrZ2avR/bPMrPUko+yaIpwLr3NLDPPZ3FlGHHujZm9ZGY/mdmCQvabmQ2LnOc3ZnZsScdYFEU4j1PNbGOez2NgScdYVGZWz8ymmtniSO66qYA2wX4uzrmEeACNgYbANCCtkDYpwHfAEUBZYB7QJOzY88X4KDAg8nwA8Egh7TaHHev+/oyB64DnIs+7A6+HHXcU59IbGB52rEU4l1OAY4EFhezvDLyLvzO+DTAr7Jj38zxOBf4bdpxFPJdawLGR5wcB3xbw+xXo55IwPXzn3GLn3NK9NNtVyM05lwX8XsgtlnQDRkeejwb+GmIs+6MoP+O85zgOON32UoEvJPHw+1IkzrnpwIY9NOkGvOK8L4DKZlarZKIruiKcR9xwzmU45+ZEnv+Gv08pf52xQD+XhEn4RVTkQm4hOtQ5lwH+FwI4pJB25SOF5r4ws1j6o1CUn/GuNs7fmLcRqFYi0e2bov6+nB/57/Y4M6tXwP54EA//NoqqrZnNM7N3zaxp2MEURWRY8xhgVr5dgX4ucbXiVUkWcitOezqPfXibw5xza83sCOATM5vvnPsumAijUpSfcUx8DkVQlDgnAWOdczvM7Br8/1w6FHtkwYuXz2Rv5gD1nXObzawzMB5oEHJMe2RmFYG3gJudc5vy7y7gW/b7c4mrhO9CKuQWtD2dh5n9aGa1nHMZkf+6/VTIe6yNfF1hZtPwvYNYSPhF+Rn/3ma1mZUGDiY2/5u+13Nxzv2c5+VI4JESiKs4xMS/jWjlTZjOuSlm9qyZVXfOxWRRNTMrg0/2Y5xzbxfQJNDPJdmGdHYVcjOzsvgLhjE1wwUfT6/I817Abv9zMbMqZlYu8rw60I7YWVCmKD/jvOd4AfCJi1yhijF7PZd846ld8eOw8WgicFlkVkgbYOPvQ4vxxMxq/n49yMxa43Pcz3v+rnBE4nwRWOyce6KQZsF+LmFfqQ7wive5+L+GO4Afgfcj22sDU/Jd9f4W3xu+O+y4CziPasDHwLLI16qR7WnAC5HnJwLz8bNG5gN9wo473zns9jMGHgC6Rp6XB94ElgNfAkeEHXMU5/IPYGHks5gKNAo75kLOYyyQAeyM/DvpA1wDXBPZb/ilSL+L/E4VONMt7EcRzqNfns/jC+DEsGPew7mchB+e+QaYG3l0Ls7PRaUVRESSRLIN6YiIJC0lfBGRJKGELyKSJJTwRUSShBK+iEiSUMIXEUkSSvgiIkni/wEb+G2/Hnb2/QAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# [0.4, 1.25]\n", "beta_est, betas, weights = importance_sample_betas(500)\n", "print(beta_est)\n", "plot(X, y, 'bo--')\n", "y_hat = [beta_est[0] + x_i * beta_est[1] for x_i in X]\n", "plot(X, y_hat, 'r^--')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's look at the samples we drew. " ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:8: UserWarning: Matplotlib is currently using module://ipykernel.pylab.backend_inline, which is a non-GUI backend, so cannot show the figure.\n", " \n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "f, ax = plt.subplots()\n", "for beta_hat, w in (zip(betas, weights)):\n", " y_hat = [beta_hat[0] + x_i * beta_hat[1] for x_i in X]\n", " ax.plot(X, y_hat, 'r-', alpha=0.2)\n", "ax.set_ylim((-1,3))\n", "f.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And now let's factor in their weights. What's happening here is that most of the lines are so unlikely that they don't appear at all!" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:6: UserWarning: Matplotlib is currently using module://ipykernel.pylab.backend_inline, which is a non-GUI backend, so cannot show the figure.\n", " \n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "\n", "f, ax = plt.subplots()\n", "for beta_hat, w in (zip(betas, weights)):\n", " y_hat = [beta_hat[0] + x_i * beta_hat[1] for x_i in X]\n", " ax.plot(X, y_hat, 'r-', alpha=w)\n", "ax.set_ylim((-1,3))\n", "f.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Coming back to LDA\n", "\n", "OK, so as we said, this is overkill for regression -- there are (much) better ways for estimating these parameters. We started out motivated by estimating parameters in LDA. \n", " \n", " $\\beta_k \\sim {\\text{Dirichlet}}(\\eta)$\n", " \n", " $\\theta_d \\sim {\\text{Dirichlet}}(\\alpha)$\n", " \n", " $z_{dn} \\sim \\text{Discrete}(\\theta_d)$\n", "\n", " $x_{dn}|z_{dn} \\sim \\text{Discrete}(\\beta_k)$\n", " \n", "Unfortunately, this is a much more complicated model, and naive importance weighting will not work. However, similar ideas will! In particular, we can use MCMC methods -- namely Gibbs, which we will next review." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Implementation (credit to Mathieu Blondel)\n", "\n", "Below is a nice implementation of the collapsed Gibbs model we reviewed from Mathieu Blondel (original at https://gist.github.com/mblondel/542786#file-lda_gibbs-py-L8)." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "\"\"\"\n", "(C) Mathieu Blondel - 2010\n", "License: BSD 3 clause\n", "\n", "Implementation of the collapsed Gibbs sampler for\n", "Latent Dirichlet Allocation, as described in\n", "\n", "Finding scientifc topics (Griffiths and Steyvers)\n", "\"\"\"\n", "\n", "import numpy as np\n", "import scipy as sp\n", "from scipy.special import gammaln\n", "\n", "def sample_index(p):\n", " \"\"\"\n", " Sample from the Multinomial distribution and return the sample index.\n", " \"\"\"\n", " return np.random.multinomial(1,p).argmax()\n", "\n", "def word_indices(vec):\n", " \"\"\"\n", " Turn a document vector of size vocab_size to a sequence\n", " of word indices. The word indices are between 0 and\n", " vocab_size-1. The sequence length is equal to the document length.\n", " \"\"\"\n", " for idx in vec.nonzero()[0]:\n", " for i in xrange(int(vec[idx])):\n", " yield idx\n", "\n", "def log_multi_beta(alpha, K=None):\n", " \"\"\"\n", " Logarithm of the multinomial beta function.\n", " \"\"\"\n", " if K is None:\n", " # alpha is assumed to be a vector\n", " return np.sum(gammaln(alpha)) - gammaln(np.sum(alpha))\n", " else:\n", " # alpha is assumed to be a scalar\n", " return K * gammaln(alpha) - gammaln(K*alpha)\n", "\n", " \n", "class LdaSampler(object):\n", "\n", " def __init__(self, n_topics, alpha=0.1, beta=0.1):\n", " \"\"\"\n", " n_topics: desired number of topics\n", " alpha: a scalar (FIXME: accept vector of size n_topics)\n", " beta: a scalar (FIME: accept vector of size vocab_size)\n", " \"\"\"\n", " self.n_topics = n_topics\n", " self.alpha = alpha\n", " self.beta = beta\n", "\n", " def _initialize(self, matrix):\n", " n_docs, vocab_size = matrix.shape\n", "\n", " # number of times document m and topic z co-occur\n", " self.nmz = np.zeros((n_docs, self.n_topics))\n", " # number of times topic z and word w co-occur\n", " self.nzw = np.zeros((self.n_topics, vocab_size))\n", " self.nm = np.zeros(n_docs)\n", " self.nz = np.zeros(self.n_topics)\n", " self.topics = {}\n", "\n", " for m in xrange(n_docs):\n", " # i is a number between 0 and doc_length-1\n", " # w is a number between 0 and vocab_size-1\n", " for i, w in enumerate(word_indices(matrix[m, :])):\n", " # choose an arbitrary topic as first topic for word i\n", " z = np.random.randint(self.n_topics)\n", " self.nmz[m,z] += 1\n", " self.nm[m] += 1\n", " self.nzw[z,w] += 1\n", " self.nz[z] += 1\n", " self.topics[(m,i)] = z\n", "\n", " def _conditional_distribution(self, m, w):\n", " \"\"\"\n", " Conditional distribution (vector of size n_topics).\n", " \"\"\"\n", " vocab_size = self.nzw.shape[1]\n", " left = (self.nzw[:,w] + self.beta) / \\\n", " (self.nz + self.beta * vocab_size)\n", " right = (self.nmz[m,:] + self.alpha) / \\\n", " (self.nm[m] + self.alpha * self.n_topics)\n", " p_z = left * right\n", " # normalize to obtain probabilities\n", " p_z /= np.sum(p_z)\n", " return p_z\n", "\n", " def loglikelihood(self):\n", " \"\"\"\n", " Compute the likelihood that the model generated the data.\n", " \"\"\"\n", " vocab_size = self.nzw.shape[1]\n", " n_docs = self.nmz.shape[0]\n", " lik = 0\n", "\n", " for z in xrange(self.n_topics):\n", " lik += log_multi_beta(self.nzw[z,:]+self.beta)\n", " lik -= log_multi_beta(self.beta, vocab_size)\n", "\n", " for m in xrange(n_docs):\n", " lik += log_multi_beta(self.nmz[m,:]+self.alpha)\n", " lik -= log_multi_beta(self.alpha, self.n_topics)\n", "\n", " return lik\n", "\n", " def phi(self):\n", " \"\"\"\n", " Compute phi = p(w|z).\n", " \"\"\"\n", " V = self.nzw.shape[1]\n", " num = self.nzw + self.beta\n", " num /= np.sum(num, axis=1)[:, np.newaxis]\n", " return num\n", "\n", " def run(self, matrix, maxiter=30):\n", " \"\"\"\n", " Run the Gibbs sampler.\n", " \"\"\"\n", " n_docs, vocab_size = matrix.shape\n", " self._initialize(matrix)\n", "\n", " for it in xrange(maxiter):\n", " for m in xrange(n_docs):\n", " for i, w in enumerate(word_indices(matrix[m, :])):\n", " z = self.topics[(m,i)]\n", " self.nmz[m,z] -= 1\n", " self.nm[m] -= 1\n", " self.nzw[z,w] -= 1\n", " self.nz[z] -= 1\n", "\n", " p_z = self._conditional_distribution(m, w)\n", " z = sample_index(p_z)\n", "\n", " self.nmz[m,z] += 1\n", " self.nm[m] += 1\n", " self.nzw[z,w] += 1\n", " self.nz[z] += 1\n", " self.topics[(m,i)] = z\n", "\n", " # FIXME: burn-in and lag!\n", " yield self.phi()\n", "\n", "if __name__ == \"__main__\":\n", " import os\n", " import shutil\n", "\n", " N_TOPICS = 10\n", " DOCUMENT_LENGTH = 100\n", " FOLDER = \"topicimg\"\n", "\n", " def vertical_topic(width, topic_index, document_length):\n", " \"\"\"\n", " Generate a topic whose words form a vertical bar.\n", " \"\"\"\n", " m = np.zeros((width, width))\n", " m[:, topic_index] = int(document_length / width)\n", " return m.flatten()\n", "\n", " def horizontal_topic(width, topic_index, document_length):\n", " \"\"\"\n", " Generate a topic whose words form a horizontal bar.\n", " \"\"\"\n", " m = np.zeros((width, width))\n", " m[topic_index, :] = int(document_length / width)\n", " return m.flatten()\n", "\n", " def save_document_image(filename, doc, zoom=2):\n", " \"\"\"\n", " Save document as an image.\n", "\n", " doc must be a square matrix\n", " \"\"\"\n", " height, width = doc.shape\n", " zoom = np.ones((width*zoom, width*zoom))\n", " # imsave scales pixels between 0 and 255 automatically\n", " sp.misc.imsave(filename, np.kron(doc, zoom))\n", "\n", " def gen_word_distribution(n_topics, document_length):\n", " \"\"\"\n", " Generate a word distribution for each of the n_topics.\n", " \"\"\"\n", " width = n_topics / 2\n", " vocab_size = int(width ** 2)\n", " \n", " m = np.zeros((n_topics, vocab_size))\n", "\n", " for k in range(width):\n", " m[k,:] = vertical_topic(width, k, document_length)\n", "\n", " for k in range(width):\n", " m[k+width,:] = horizontal_topic(width, k, document_length)\n", "\n", " m /= m.sum(axis=1)[:, np.newaxis] # turn counts into probabilities\n", "\n", " return m\n", "\n", " def gen_document(word_dist, n_topics, vocab_size, length=DOCUMENT_LENGTH, alpha=0.1):\n", " \"\"\"\n", " Generate a document:\n", " 1) Sample topic proportions from the Dirichlet distribution.\n", " 2) Sample a topic index from the Multinomial with the topic\n", " proportions from 1).\n", " 3) Sample a word from the Multinomial corresponding to the topic\n", " index from 2).\n", " 4) Go to 2) if need another word.\n", " \"\"\"\n", " theta = np.random.mtrand.dirichlet([alpha] * n_topics)\n", " v = np.zeros(vocab_size)\n", " for n in range(length):\n", " z = sample_index(theta)\n", " w = sample_index(word_dist[z,:])\n", " v[w] += 1\n", " return v\n", "\n", " def gen_documents(word_dist, n_topics, vocab_size, n=500):\n", " \"\"\"\n", " Generate a document-term matrix.\n", " \"\"\"\n", " m = np.zeros((n, vocab_size))\n", " for i in xrange(n):\n", " m[i, :] = gen_document(word_dist, n_topics, vocab_size)\n", " return m\n", "\n", " if os.path.exists(FOLDER):\n", " shutil.rmtree(FOLDER)\n", " os.mkdir(FOLDER)\n", "\n", " \n", " width = N_TOPICS / 2\n", " vocab_size = width ** 2\n", " word_dist = gen_word_distribution(N_TOPICS, DOCUMENT_LENGTH)\n", " matrix = gen_documents(word_dist, N_TOPICS, vocab_size)\n", " sampler = LdaSampler(N_TOPICS)\n", "\n", " for it, phi in enumerate(sampler.run(matrix)):\n", " print (\"Iteration\", it)\n", " print (\"Likelihood\", sampler.loglikelihood())\n", "\n", " if it % 5 == 0:\n", " for z in range(N_TOPICS):\n", " save_document_image(\"topicimg/topic%d-%d.png\" % (it,z),\n", " phi[z,:].reshape(width,-1))\n", "\n" ] } ], "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }