{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "[](https://colab.research.google.com/github/ksachdeva/rethinking-tensorflow-probability/blob/master/notebooks/12_monsters_and_mixtures.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 12. Monsters and Mixtures" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# Install packages that are not installed in colab\n", "try:\n", " import google.colab\n", " %pip install -q watermark\n", " %pip install git+https://github.com/ksachdeva/rethinking-tensorflow-probability.git\n", "except:\n", " pass" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%load_ext watermark" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# Core\n", "import numpy as np\n", "import arviz as az\n", "import tensorflow as tf\n", "import tensorflow_probability as tfp\n", "\n", "# visualization\n", "import matplotlib.pyplot as plt\n", "\n", "from rethinking.data import RethinkingDataset\n", "from rethinking.data import dataframe_to_tensors\n", "from rethinking.mcmc import sample_posterior\n", "\n", "\n", "# aliases\n", "tfd = tfp.distributions\n", "tfb = tfp.bijectors\n", "Root = tfd.JointDistributionCoroutine.Root\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "numpy : 1.21.5\n", "tensorflow : 2.7.0\n", "tensorflow_probability: 0.15.0\n", "arviz : 0.11.4\n", "scipy : 1.7.3\n", "pandas : 1.3.5\n", "rethinking : 0.1.0\n", "\n" ] } ], "source": [ "%watermark -p numpy,tensorflow,tensorflow_probability,arviz,scipy,pandas,rethinking" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# config of various plotting libraries\n", "%config InlineBackend.figure_format = 'retina'" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 12.1 Over-dispersed counts" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 12.1.1 Beta-binomial" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Code 12.1\n", "\n", "\n", "A beta distribution is a probability distribution for probabilities !" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "WARNING:tensorflow:@custom_gradient grad_fn has 'variables' in signature, but no ResourceVariables were used on the forward pass.\n" ] }, { "data": { "image/png": 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", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "image/png": { "height": 261, "width": 392 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pbar = 0.5 # mean\n", "theta = 5 # total concentration\n", "\n", "alpha = pbar * theta\n", "beta = (1 - pbar) * theta\n", "\n", "x = np.linspace(0, 1, 101)\n", "\n", "plt.plot(x, tf.exp(tfd.Beta(alpha, beta).log_prob(x)))\n", "plt.gca().set(xlabel=\"probability\", ylabel=\"Density\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Code 12.2" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "d = RethinkingDataset.UCBadmit.get_dataset()\n", "d[\"gid\"] = (d[\"applicant.gender\"] != \"male\").astype(int)\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "tdf = dataframe_to_tensors(\n", " \"UCBAdmit\",\n", " d,\n", " {\n", " \"gid\": tf.int32,\n", " \"applications\": tf.float32,\n", " \"admit\": tf.float32,\n", " \"reject\": tf.float32,\n", " },\n", ")\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "def model_12_1(gid, N):\n", " def _generator():\n", " alpha = yield Root(tfd.Sample(tfd.Normal(loc=0.0, scale=1.5), sample_shape=2))\n", " phi = yield Root(tfd.Sample(tfd.Exponential(rate=1.0), sample_shape=1))\n", " theta = phi + 2\n", " pbar = tf.sigmoid(tf.squeeze(tf.gather(alpha, gid, axis=-1)))\n", "\n", " # prepare the concentration vector\n", " concentration1 = pbar * theta[..., tf.newaxis]\n", " concentration0 = (1 - pbar) * theta[..., tf.newaxis]\n", "\n", " concentration = tf.stack([concentration1, concentration0], axis=-1)\n", "\n", " # outcome A i.e. admit\n", " # since it is a multinomial we will have K = 2\n", " # note - this does not really behave like Binomial in terms of the sample shape\n", " A = yield tfd.Independent(\n", " tfd.DirichletMultinomial(total_count=N, concentration=concentration),\n", " reinterpreted_batch_ndims=1,\n", " )\n", "\n", " return tfd.JointDistributionCoroutine(_generator, validate_args=False)\n", "\n", "\n", "jdc_12_1 = model_12_1(tdf.gid, tdf.applications)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Code 12.3" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "# Prepare the expected shape by the DirichletMultinomial\n", "obs_values = tf.stack([tdf.admit, tdf.reject], axis=-1)\n" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "WARNING:tensorflow:@custom_gradient grad_fn has 'variables' in signature, but no ResourceVariables were used on the forward pass.\n", "WARNING:tensorflow:@custom_gradient grad_fn has 'variables' in signature, but no ResourceVariables were used on the forward pass.\n", "WARNING:tensorflow:@custom_gradient grad_fn has 'variables' in signature, but no ResourceVariables were used on the forward pass.\n" ] } ], "source": [ "NUMBER_OF_CHAINS_12_1 = 2\n", "\n", "init_state = [tf.zeros([NUMBER_OF_CHAINS_12_1, 2]), tf.ones([NUMBER_OF_CHAINS_12_1])]\n", "\n", "bijectors = [tfb.Identity(), tfb.Identity()]\n", "\n", "\n", "posterior_12_1, trace_12_1 = sample_posterior(\n", " jdc_12_1,\n", " num_samples=1000,\n", " observed_data=(obs_values,),\n", " init_state=init_state,\n", " bijectors=bijectors,\n", " params=[\"alpha\", \"phi\"],\n", ")\n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "# compute the difference between alphas\n", "trace_12_1.posterior[\"da\"] = (\n", " trace_12_1.posterior[\"alpha\"][:, :, 0] - trace_12_1.posterior[\"alpha\"][:, :, 1]\n", ")\n", "\n", "# compute theta\n", "trace_12_1.posterior[\"theta\"] = trace_12_1.posterior[\"phi\"] + 2\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "<div>\n", "<style scoped>\n", " .dataframe tbody tr th:only-of-type {\n", " vertical-align: middle;\n", " }\n", "\n", " .dataframe tbody tr th {\n", " vertical-align: top;\n", " }\n", "\n", " .dataframe thead th {\n", " text-align: right;\n", " }\n", "</style>\n", "<table border=\"1\" class=\"dataframe\">\n", " <thead>\n", " <tr style=\"text-align: right;\">\n", " <th></th>\n", " <th>mean</th>\n", " <th>sd</th>\n", " <th>hdi_5.5%</th>\n", " <th>hdi_94.5%</th>\n", " <th>mcse_mean</th>\n", " <th>mcse_sd</th>\n", " <th>ess_bulk</th>\n", " <th>ess_tail</th>\n", " <th>r_hat</th>\n", " </tr>\n", " </thead>\n", " <tbody>\n", " <tr>\n", " <th>alpha[0]</th>\n", " <td>-0.407</td>\n", " <td>0.418</td>\n", " <td>-1.108</td>\n", " <td>0.188</td>\n", " <td>0.016</td>\n", " <td>0.012</td>\n", " <td>697.0</td>\n", " <td>607.0</td>\n", " <td>1.01</td>\n", " </tr>\n", " <tr>\n", " <th>alpha[1]</th>\n", " <td>-0.282</td>\n", " <td>0.424</td>\n", " <td>-0.949</td>\n", " <td>0.357</td>\n", " <td>0.018</td>\n", " <td>0.013</td>\n", " <td>552.0</td>\n", " <td>679.0</td>\n", " <td>1.00</td>\n", " </tr>\n", " <tr>\n", " <th>phi</th>\n", " <td>0.668</td>\n", " <td>0.874</td>\n", " <td>-0.653</td>\n", " <td>1.968</td>\n", " <td>0.078</td>\n", " <td>0.057</td>\n", " <td>142.0</td>\n", " <td>153.0</td>\n", " <td>1.02</td>\n", " </tr>\n", " <tr>\n", " <th>da</th>\n", " <td>-0.125</td>\n", " <td>0.601</td>\n", " <td>-0.949</td>\n", " <td>1.017</td>\n", " <td>0.025</td>\n", " <td>0.019</td>\n", " <td>604.0</td>\n", " <td>472.0</td>\n", " <td>1.01</td>\n", " </tr>\n", " <tr>\n", " <th>theta</th>\n", " <td>2.668</td>\n", " <td>0.874</td>\n", " <td>1.347</td>\n", " <td>3.968</td>\n", " <td>0.078</td>\n", " <td>0.057</td>\n", " <td>142.0</td>\n", " <td>153.0</td>\n", " <td>1.02</td>\n", " </tr>\n", " </tbody>\n", "</table>\n", "</div>" ], "text/plain": [ " mean sd hdi_5.5% hdi_94.5% mcse_mean mcse_sd ess_bulk \\\n", "alpha[0] -0.407 0.418 -1.108 0.188 0.016 0.012 697.0 \n", "alpha[1] -0.282 0.424 -0.949 0.357 0.018 0.013 552.0 \n", "phi 0.668 0.874 -0.653 1.968 0.078 0.057 142.0 \n", "da -0.125 0.601 -0.949 1.017 0.025 0.019 604.0 \n", "theta 2.668 0.874 1.347 3.968 0.078 0.057 142.0 \n", "\n", " ess_tail r_hat \n", "alpha[0] 607.0 1.01 \n", "alpha[1] 679.0 1.00 \n", "phi 153.0 1.02 \n", "da 472.0 1.01 \n", "theta 153.0 1.02 " ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "az.summary(trace_12_1, hdi_prob=0.89)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Code 12.4" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "# Since we have two chains and data is stored in InferenceData format\n", "# we have to manually extract it\n", "#\n", "# Here I am using the data from chain 0\n", "sample_alpha = trace_12_1.posterior[\"alpha\"][0, :].values\n", "sample_theta = trace_12_1.posterior[\"theta\"][0, :].values\n" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "image/png": { "height": 277, "width": 385 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "gid = 1\n", "# draw posterior mean beta distribution\n", "x = np.linspace(0, 1, 101)\n", "pbar = tf.reduce_mean(tf.sigmoid(sample_alpha[:, gid]))\n", "theta = tf.reduce_mean(sample_theta)\n", "plt.plot(x, tf.exp(tfd.Beta(pbar * theta, (1 - pbar) * theta).log_prob(x)))\n", "plt.gca().set(ylabel=\"Density\", xlabel=\"probability admit\", ylim=(0, 3))\n", "\n", "# draw 50 beta distributions sampled from posterior\n", "for i in range(50):\n", " p = tf.sigmoid(sample_alpha[i, gid])\n", " theta = sample_theta[i]\n", " plt.plot(\n", " x, tf.exp(tfd.Beta(p * theta, (1 - p) * theta).log_prob(x)), \"k\", alpha=0.2\n", " )\n", "plt.title(\"distribution of female admission rates\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Code 12.5" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "# get samples given the posterior distribution\n", "N = tf.cast(d.applications.values, dtype=tf.float32)\n", "gid = d.gid.values\n", "\n", "sample_pbar = tf.sigmoid(tf.squeeze(tf.gather(sample_alpha, gid, axis=-1)))\n", "\n", "# need to reshape it to make it happy\n", "st = tf.reshape(sample_theta, shape=(1000, 1))\n", "\n", "# prepare the concentration vector\n", "concentration1 = sample_pbar * st\n", "concentration0 = (1 - sample_pbar) * st\n", "\n", "concentration = tf.stack([concentration1, concentration0], axis=-1)\n", "\n", "dist = tfd.DirichletMultinomial(total_count=N, concentration=concentration)\n", "\n", "predictive_samples = dist.sample()\n" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "# numpy style indexing magic ! .. hate it !\n", "admit_rate = predictive_samples[::, ::, 0] / N\n" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "image/png": { "height": 248, "width": 372 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.scatter(range(1, 13), d.admit.values / N)\n", "plt.errorbar(\n", " range(1, 13),\n", " np.mean(admit_rate, 0),\n", " np.std(admit_rate, 0) / 2,\n", " fmt=\"o\",\n", " c=\"k\",\n", " mfc=\"none\",\n", " ms=7,\n", " elinewidth=1,\n", ")\n", "plt.plot(range(1, 13), np.percentile(admit_rate, 5.5, 0), \"k+\")\n", "plt.plot(range(1, 13), np.percentile(admit_rate, 94.5, 0), \"k+\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the above plot, the vertifical axis shows the predicted proportion admitted, for each case on the horizontal.\n", "\n", "Blue points show the empirical proportion admitted on each row of data\n", "\n", "Open circles are the posterior mean pbar and + symbols mark the 89% interval of predicted counts of admission" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 12.1.2 Negative-binomial or gamma-Poisson" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Code 12.6 (Not working !)\n", "\n", "Start to use **Gamma-Poisson** (also known as **Negative Binomial**) models.\n", "\n", "Essentially Gamm-Poisson is about associating a rate to each Posisson count observation. Estimates the shape of gamma distribution to describe the Poisson rates across cases.\n", "\n", "Gamma-Poisson also expects more variation around the mean rate.\n", "\n", "The negative binomial distribution arises naturally from a probability experiment of performing a series of independent Bernoulli trials until the occurrence of the rth success where r is a positive integer." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/html": [ "<div>\n", "<style scoped>\n", " .dataframe tbody tr th:only-of-type {\n", " vertical-align: middle;\n", " }\n", "\n", " .dataframe tbody tr th {\n", " vertical-align: top;\n", " }\n", "\n", " .dataframe thead th {\n", " text-align: right;\n", " }\n", "</style>\n", "<table border=\"1\" class=\"dataframe\">\n", " <thead>\n", " <tr style=\"text-align: right;\">\n", " <th></th>\n", " <th>culture</th>\n", " <th>population</th>\n", " <th>contact</th>\n", " <th>total_tools</th>\n", " <th>mean_TU</th>\n", " <th>P</th>\n", " <th>cid</th>\n", " </tr>\n", " </thead>\n", " <tbody>\n", " <tr>\n", " <th>0</th>\n", " <td>Malekula</td>\n", " <td>1100</td>\n", " <td>low</td>\n", " <td>13</td>\n", " <td>3.2</td>\n", " <td>-1.291473</td>\n", " <td>0</td>\n", " </tr>\n", " <tr>\n", " <th>1</th>\n", " <td>Tikopia</td>\n", " <td>1500</td>\n", " <td>low</td>\n", " <td>22</td>\n", " <td>4.7</td>\n", " <td>-1.088551</td>\n", " <td>0</td>\n", " </tr>\n", " <tr>\n", " <th>2</th>\n", " <td>Santa Cruz</td>\n", " <td>3600</td>\n", " <td>low</td>\n", " <td>24</td>\n", " <td>4.0</td>\n", " <td>-0.515765</td>\n", " <td>0</td>\n", " </tr>\n", " <tr>\n", " <th>3</th>\n", " <td>Yap</td>\n", " <td>4791</td>\n", " <td>high</td>\n", " <td>43</td>\n", " <td>5.0</td>\n", " <td>-0.328773</td>\n", " <td>1</td>\n", " </tr>\n", " <tr>\n", " <th>4</th>\n", " <td>Lau Fiji</td>\n", " <td>7400</td>\n", " <td>high</td>\n", " <td>33</td>\n", " <td>5.0</td>\n", " <td>-0.044339</td>\n", " <td>1</td>\n", " </tr>\n", " </tbody>\n", "</table>\n", "</div>" ], "text/plain": [ " culture population contact total_tools mean_TU P cid\n", "0 Malekula 1100 low 13 3.2 -1.291473 0\n", "1 Tikopia 1500 low 22 4.7 -1.088551 0\n", "2 Santa Cruz 3600 low 24 4.0 -0.515765 0\n", "3 Yap 4791 high 43 5.0 -0.328773 1\n", "4 Lau Fiji 7400 high 33 5.0 -0.044339 1" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "d = RethinkingDataset.Kline.get_dataset()\n", "d[\"P\"] = d.population.pipe(np.log).pipe(lambda x: (x - x.mean()) / x.std())\n", "d[\"cid\"] = (d.contact == \"high\").astype(int)\n", "\n", "d.head()\n" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "def model_12_2(cid, P):\n", " def _generator():\n", " alpha = yield Root(tfd.Sample(tfd.Normal(loc=1.0, scale=1.0), sample_shape=2))\n", " beta = yield Root(tfd.Sample(tfd.Exponential(rate=1.0), sample_shape=2))\n", " gamma = yield Root(tfd.Sample(tfd.Exponential(rate=1.0), sample_shape=1))\n", " phi = yield Root(tfd.Sample(tfd.Exponential(rate=1.0), sample_shape=1))\n", "\n", " lambda_ = (\n", " tf.exp(tf.squeeze(tf.gather(alpha, cid, axis=-1)))\n", " * tf.math.pow(P, tf.squeeze(tf.gather(beta, cid, axis=-1)))\n", " / gamma\n", " )\n", "\n", " g_concentration = lambda_ / phi\n", " g_rate = 1 / phi\n", "\n", " t1 = yield tfd.Independent(\n", " tfd.Gamma(concentration=g_concentration, rate=g_rate),\n", " reinterpreted_batch_ndims=1,\n", " )\n", "\n", " T = yield tfd.Independent(tfd.Poisson(rate=t1), reinterpreted_batch_ndims=1)\n", "\n", " return tfd.JointDistributionCoroutine(_generator, validate_args=True)\n", "\n", "\n", "jdc_12_2 = model_12_2(d.cid.values, tf.cast(d.P.values, dtype=tf.float32))\n", "\n", "# Issue -\n", "# Even prior sampling is not coming back !\n", "# jdc_12_2.sample()\n" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "# NUMBER_OF_CHAINS_12_2 = 1\n", "\n", "# alpha_init, beta_init, gamma_init, phi_init, t1_init, _ = jdc_12_2.sample(2)\n", "\n", "# init_state = [\n", "# alpha_init,\n", "# beta_init,\n", "# gamma_init,\n", "# phi_init,\n", "# t1_init\n", "# ]\n", "\n", "# bijectors = [\n", "# tfb.Identity(),\n", "# tfb.Exp(),\n", "# tfb.Exp(),\n", "# tfb.Exp(),\n", "# tfb.Identity(),\n", "# ]\n", "\n", "# posterior_12_2, trace_12_2 = sample_posterior(jdc_12_2,\n", "# observed_data=(d.total_tools.values,),\n", "# init_state=init_state,\n", "# bijectors=bijectors,\n", "# params=['alpha', 'beta', 'gamma' 'phi', 't1'])\n" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "# az.summary(trace_12_2, credible_interval=0.89)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 12.2 Zero-inflated outcomes (TODO)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 12.3 Ordered categorical outcomes (TODO)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 12.4 Ordered categorical predictors (TODO)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.7.12" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }