{ "cells": [ { "cell_type": "markdown", "metadata": { "id": "EheA5_j_cEwc" }, "source": [ "##### Copyright 2019 The TensorFlow Probability Authors.\n", "\n", "Licensed under the Apache License, Version 2.0 (the \"License\");" ] }, { "cell_type": "code", "execution_count": 0, "metadata": { "id": "YCriMWd-pRTP" }, "outputs": [], "source": [ "#@title Licensed under the Apache License, Version 2.0 (the \"License\"); { display-mode: \"form\" }\n", "# you may not use this file except in compliance with the License.\n", "# You may obtain a copy of the License at\n", "#\n", "# https://www.apache.org/licenses/LICENSE-2.0\n", "#\n", "# Unless required by applicable law or agreed to in writing, software\n", "# distributed under the License is distributed on an \"AS IS\" BASIS,\n", "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n", "# See the License for the specific language governing permissions and\n", "# limitations under the License." ] }, { "cell_type": "markdown", "metadata": { "id": "73ztBH5yK_bS" }, "source": [ "# Multiple changepoint detection and Bayesian model selection\n" ] }, { "cell_type": "markdown", "metadata": { "id": "Qianaf6u_7G_" }, "source": [ "# Bayesian model selection\n", "\n", " \n", " \n", " \n", " \n", "
\n", " View on TensorFlow.org\n", " \n", " Run in Google Colab\n", " \n", " View source on GitHub\n", " \n", " Download notebook\n", "
" ] }, { "cell_type": "markdown", "metadata": { "id": "-o9zA5TO_-hx" }, "source": [ "## Imports" ] }, { "cell_type": "code", "execution_count": 0, "metadata": { "id": "No2QPkJ1_9z9" }, "outputs": [], "source": [ "import numpy as np\n", "import tensorflow as tf\n", "import tf_keras\n", "import tensorflow_probability as tfp\n", "from tensorflow_probability import distributions as tfd\n", "\n", "from matplotlib import pylab as plt\n", "%matplotlib inline\n", "import scipy.stats" ] }, { "cell_type": "markdown", "metadata": { "id": "UoIGcwDcLK8s" }, "source": [ "## Task: changepoint detection with multiple changepoints" ] }, { "cell_type": "markdown", "metadata": { "id": "MkPCuGGp464l" }, "source": [ "Consider a changepoint detection task: events happen at a rate that changes over time, driven by sudden shifts in the (unobserved) state of some system or process generating the data.\n", "\n", "For example, we might observe a series of counts like the following:" ] }, { "cell_type": "code", "execution_count": 0, "metadata": { "colab": { "height": 282 }, "id": "kmk8w7-vuKSm", "outputId": "50ce2d12-dbdd-480c-c78e-b6186a80e21d" }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 0, "metadata": { "tags": [] }, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": { "tags": [] }, "output_type": "display_data" } ], "source": [ "true_rates = [40, 3, 20, 50]\n", "true_durations = [10, 20, 5, 35]\n", "\n", "observed_counts = tf.concat(\n", " [tfd.Poisson(rate).sample(num_steps)\n", " for (rate, num_steps) in zip(true_rates, true_durations)], axis=0)\n", "\n", "plt.plot(observed_counts)" ] }, { "cell_type": "markdown", "metadata": { "id": "TWx9cuas0EcE" }, "source": [ "These could represent the number of failures in a datacenter, number of visitors to a webpage, number of packets on a network link, etc.\n", "\n", "Note it's not entirely apparent how many distinct system regimes there are just from looking at the data. Can you tell where each of the three switchpoints occurs?" ] }, { "cell_type": "markdown", "metadata": { "id": "09nB0iTzky85" }, "source": [ "## Known number of states\n", "\n", "We'll first consider the (perhaps unrealistic) case where the number of unobserved states is known a priori. Here, we'd assume we know there are four latent states.\n", "\n", "We model this problem as a switching (inhomogeneous) Poisson process: at each point in time, the number of events that occur is Poisson distributed, and the *rate* of events is determined by the unobserved system state $z_t$:\n", "\n", "$$x_t \\sim \\text{Poisson}(\\lambda_{z_t})$$\n", "\n", "The latent states are discrete: $z_t \\in \\{1, 2, 3, 4\\}$, so $\\lambda = [\\lambda_1, \\lambda_2, \\lambda_3, \\lambda_4]$ is a simple vector containing a Poisson rate for each state. To model the evolution of states over time, we'll define a simple transition model $p(z_t | z_{t-1})$: let's say that at each step we stay in the previous state with some probability $p$, and with probability $1-p$ we transition to a different state uniformly at random. The initial state is also chosen uniformly at random, so we have:\n", "\n", "$$\n", "\\begin{align*}\n", "z_1 &\\sim \\text{Categorical}\\left(\\left\\{\\frac{1}{4}, \\frac{1}{4}, \\frac{1}{4}, \\frac{1}{4}\\right\\}\\right)\\\\\n", "z_t | z_{t-1} &\\sim \\text{Categorical}\\left(\\left\\{\\begin{array}{cc}p & \\text{if } z_t = z_{t-1} \\\\ \\frac{1-p}{4-1} & \\text{otherwise}\\end{array}\\right\\}\\right)\n", "\\end{align*}$$\n", "\n", "These assumptions correspond to a [hidden Markov model](http://mlg.eng.cam.ac.uk/zoubin/papers/ijprai.pdf) with Poisson emissions. We can encode them in TFP using `tfd.HiddenMarkovModel`. First, we define the transition matrix and the uniform prior on the initial state:" ] }, { "cell_type": "code", "execution_count": 0, "metadata": { "id": "0qs_l4p4nygq", "outputId": "20d4892e-a92a-4234-ffa0-e8373ff0c22c" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Initial state logits:\n", "[0. 0. 0. 0.]\n", "Transition matrix:\n", "[[0.95 0.01666667 0.01666667 0.01666667]\n", " [0.01666667 0.95 0.01666667 0.01666667]\n", " [0.01666667 0.01666667 0.95 0.01666667]\n", " [0.01666667 0.01666667 0.01666667 0.95 ]]\n" ] } ], "source": [ "num_states = 4\n", "initial_state_logits = tf.zeros([num_states]) # uniform distribution\n", "\n", "daily_change_prob = 0.05\n", "transition_probs = tf.fill([num_states, num_states],\n", " daily_change_prob / (num_states - 1))\n", "transition_probs = tf.linalg.set_diag(transition_probs,\n", " tf.fill([num_states],\n", " 1 - daily_change_prob))\n", "\n", "print(\"Initial state logits:\\n{}\".format(initial_state_logits))\n", "print(\"Transition matrix:\\n{}\".format(transition_probs))" ] }, { "cell_type": "markdown", "metadata": { "id": "vWshnDRepxaT" }, "source": [ "Next, we build a `tfd.HiddenMarkovModel` distribution, using a trainable variable to represent the rates associated with each system state. We parameterize the rates in log-space to ensure they are positive-valued." ] }, { "cell_type": "code", "execution_count": 0, "metadata": { "id": "bvEpqBxvoleY" }, "outputs": [], "source": [ "# Define variable to represent the unknown log rates.\n", "trainable_log_rates = tf.Variable(\n", " tf.math.log(tf.reduce_mean(observed_counts)) +\n", " tf.random.stateless_normal([num_states], seed=(42, 42)),\n", " name='log_rates')\n", "\n", "hmm = tfd.HiddenMarkovModel(\n", " initial_distribution=tfd.Categorical(\n", " logits=initial_state_logits),\n", " transition_distribution=tfd.Categorical(probs=transition_probs),\n", " observation_distribution=tfd.Poisson(log_rate=trainable_log_rates),\n", " num_steps=len(observed_counts))" ] }, { "cell_type": "markdown", "metadata": { "id": "4JA6D9EsqNTe" }, "source": [ "Finally, we define the model's total log density, including a weakly-informative LogNormal prior on the rates, and run an optimizer to compute the [maximum a posteriori](https://en.wikipedia.org/wiki/Maximum_a_posteriori_estimation) (MAP) fit to the observed count data." ] }, { "cell_type": "code", "execution_count": 0, "metadata": { "colab": { "height": 282 }, "id": "6mirKxnNqJSu", "outputId": "42b48655-27d9-4445-a91b-9dc0f81dd8f8" }, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Negative log marginal likelihood')" ] }, "execution_count": 0, "metadata": { "tags": [] }, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": { "tags": [] }, "output_type": "display_data" } ], "source": [ "rate_prior = tfd.LogNormal(5, 5)\n", "\n", "def log_prob():\n", " return (tf.reduce_sum(rate_prior.log_prob(tf.math.exp(trainable_log_rates))) +\n", " hmm.log_prob(observed_counts))\n", "\n", "losses = tfp.math.minimize(\n", " lambda: -log_prob(),\n", " optimizer=tf_keras.optimizers.Adam(learning_rate=0.1),\n", " num_steps=100)\n", "plt.plot(losses)\n", "plt.ylabel('Negative log marginal likelihood')" ] }, { "cell_type": "code", "execution_count": 0, "metadata": { "id": "gSjyTtkDrOHu", "outputId": "037ee965-2895-4b0c-afd0-16606284e558" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Inferred rates: [ 2.8302798 49.58499 41.928307 17.35112 ]\n", "True rates: [40, 3, 20, 50]\n" ] } ], "source": [ "rates = tf.exp(trainable_log_rates)\n", "print(\"Inferred rates: {}\".format(rates))\n", "print(\"True rates: {}\".format(true_rates))" ] }, { "cell_type": "markdown", "metadata": { "id": "9kGRv8gwrtP5" }, "source": [ "It worked! Note that the latent states in this model are identifiable only up to permutation, so the rates we recovered are in a different order, and there's a bit of noise, but generally they match pretty well." ] }, { "cell_type": "markdown", "metadata": { "id": "43AfcMTjvs7a" }, "source": [ "### Recovering the state trajectory\n", "\n", "Now that we've fit the model, we might want to reconstruct *which* state the model believes the system was in at each timestep.\n", "\n", "This is a *posterior inference* task: given the observed counts $x_{1:T}$ and model parameters (rates) $\\lambda$, we want to infer the sequence of discrete latent variables, following the posterior distribution $p(z_{1:T} | x_{1:T}, \\lambda)$. In a hidden Markov model, we can efficiently compute marginals and other properties of this distribution using standard message-passing algorithms. In particular, the `posterior_marginals` method will efficiently compute (using the [forward-backward algorithm](https://en.wikipedia.org/wiki/Forward%E2%80%93backward_algorithm)) the marginal probability distribution $p(Z_t = z_t | x_{1:T})$ over the discrete latent state $Z_t$ at each timestep $t$." ] }, { "cell_type": "code", "execution_count": 0, "metadata": { "id": "IpTbdyah-IyX" }, "outputs": [], "source": [ "# Runs forward-backward algorithm to compute marginal posteriors.\n", "posterior_dists = hmm.posterior_marginals(observed_counts)\n", "posterior_probs = posterior_dists.probs_parameter().numpy()" ] }, { "cell_type": "markdown", "metadata": { "id": "cOYMlvssFDwx" }, "source": [ "Plotting the posterior probabilities, we recover the model's \"explanation\" of the data: at which points in time is each state active?" ] }, { "cell_type": "code", "execution_count": 0, "metadata": { "colab": { "height": 731 }, "id": "oZ7C937t-Xh3", "outputId": "a6de00cc-ffd2-4709-bd9f-8502020d3230" }, "outputs": [ { "data": { "image/png": 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vp59+OieddBLnnHMOEp801dPTw9GjR6t+FT81yB5TKWfOflPLE/Vs0Wlubva0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"text/plain": [ "
" ] }, "metadata": { "tags": [] }, "output_type": "display_data" } ], "source": [ "def plot_state_posterior(ax, state_posterior_probs, title):\n", " ln1 = ax.plot(state_posterior_probs, c='blue', lw=3, label='p(state | counts)')\n", " ax.set_ylim(0., 1.1)\n", " ax.set_ylabel('posterior probability')\n", " ax2 = ax.twinx()\n", " ln2 = ax2.plot(observed_counts, c='black', alpha=0.3, label='observed counts')\n", " ax2.set_title(title)\n", " ax2.set_xlabel(\"time\")\n", " lns = ln1+ln2\n", " labs = [l.get_label() for l in lns]\n", " ax.legend(lns, labs, loc=4)\n", " ax.grid(True, color='white')\n", " ax2.grid(False)\n", "\n", "fig = plt.figure(figsize=(10, 10))\n", "plot_state_posterior(fig.add_subplot(2, 2, 1),\n", " posterior_probs[:, 0],\n", " title=\"state 0 (rate {:.2f})\".format(rates[0]))\n", "plot_state_posterior(fig.add_subplot(2, 2, 2),\n", " posterior_probs[:, 1],\n", " title=\"state 1 (rate {:.2f})\".format(rates[1]))\n", "plot_state_posterior(fig.add_subplot(2, 2, 3),\n", " posterior_probs[:, 2],\n", " title=\"state 2 (rate {:.2f})\".format(rates[2]))\n", "plot_state_posterior(fig.add_subplot(2, 2, 4),\n", " posterior_probs[:, 3],\n", " title=\"state 3 (rate {:.2f})\".format(rates[3]))\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": { "id": "_QhFHJ01NPVj" }, "source": [ "In this (simple) case, we see that the model is usually quite confident: at most timesteps it assigns essentially all probability mass to a single one of the four states. Luckily, the explanations look reasonable!" ] }, { "cell_type": "markdown", "metadata": { "id": "92psCOwMGiQp" }, "source": [ "We can also visualize this posterior in terms of the rate associated with the *most likely* latent state at each timestep, condensing the probabilistic posterior into a single explanation:" ] }, { "cell_type": "code", "execution_count": 0, "metadata": { "id": "PsXpBrH3DKbl" }, "outputs": [], "source": [ "most_probable_states = hmm.posterior_mode(observed_counts)\n", "most_probable_rates = tf.gather(rates, most_probable_states)" ] }, { "cell_type": "code", "execution_count": 0, "metadata": { "colab": { "height": 312 }, "id": "CCIwVTnyOcsW", "outputId": "95a3e23b-6fff-454e-f547-fb78b7c18870" }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 0, "metadata": { "tags": [] }, "output_type": "execute_result" }, { "data": { "image/png": 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JiXJycsjPz+fy5cuh9zvdjEaAtLQ0LBbLtDMbg59FT0/PrGZ1Bq/VfCmcOp1g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\n2rIQtIvIEoDAbUeS25N0ImLFH3Q9ZYz5z8BmvU4RBIY7foM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" ] }, "metadata": { "tags": [] }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(10, 4))\n", "ax = fig.add_subplot(1, 1, 1)\n", "ax.plot(most_probable_rates, c='green', lw=3, label='inferred rate')\n", "ax.plot(observed_counts, c='black', alpha=0.3, label='observed counts')\n", "ax.set_ylabel(\"latent rate\")\n", "ax.set_xlabel(\"time\")\n", "ax.set_title(\"Inferred latent rate over time\")\n", "ax.legend(loc=4)" ] }, { "cell_type": "markdown", "metadata": { "id": "7ytq0tN7tteU" }, "source": [ "## Unknown number of states\n", "\n", "In real problems, we may not know the 'true' number of states in the system we're modeling. This may not always be a concern: if you don't particularly care about the identities of the unknown states, you could just run a model with more states than you know the model will need, and learn (something like) a bunch of duplicate copies of the actual states. But let's assume you do care about inferring the 'true' number of latent states.\n", "\n", "We can view this as a case of [Bayesian model selection](http://alumni.media.mit.edu/~tpminka/statlearn/demo/): we have a set of candidate models, each with a different number of latent states, and we want to choose the one that is most likely to have generated the observed data. To do this, we compute the marginal likelihood of the data under each model (we could also add a prior on the models themselves, but that won't be necessary in this analysis; the [Bayesian Occam's razor](https://www.cs.princeton.edu/courses/archive/fall09/cos597A/papers/MacKay2003-Ch28.pdf) turns out to be sufficient to encode a preference towards simpler models).\n", "\n", "Unfortunately, the true marginal likelihood, which integrates over both the discrete states $z_{1:T}$ and the (vector of) rate parameters $\\lambda$, $$p(x_{1:T}) = \\int p(x_{1:T}, z_{1:T}, \\lambda) dz d\\lambda,$$ is not tractable for this model. For convenience, we'll approximate it using a so-called \"[empirical Bayes](https://www.cs.ubc.ca/~schmidtm/Courses/540-W16/L19.pdf)\" or \"type II maximum likelihood\" estimate: instead of fully integrating out the (unknown) rate parameters $\\lambda$ associated with each system state, we'll optimize over their values:\n", "\n", "$$\\tilde{p}(x_{1:T}) = \\max_\\lambda \\int p(x_{1:T}, z_{1:T}, \\lambda) dz$$\n", "\n", "This approximation may overfit, i.e., it will prefer more complex models than the true marginal likelihood would. We could consider more faithful approximations, e.g., optimizing a variational lower bound, or using a Monte Carlo estimator such as [annealed importance sampling](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/sample_annealed_importance_chain); these are (sadly) beyond the scope of this notebook. (For more on Bayesian model selection and approximations, chapter 7 of the excellent [Machine Learning: a Probabilistic Perspective\n", "](https://www.cs.ubc.ca/~murphyk/MLbook/) is a good reference.)\n", "\n", "In principle, we could do this model comparison simply by rerunning the optimization above many times with different values of `num_states`, but that would be a lot of work. Here we'll show how to consider multiple models in parallel, using TFP's `batch_shape` mechanism for vectorization." ] }, { "cell_type": "markdown", "metadata": { "id": "dtClNe6fyZAD" }, "source": [ "**Transition matrix and initial state prior**: rather than building a single model description, now we'll build a *batch* of transition matrices and prior logits, one for each candidate model up to `max_num_states`. For easy batching we'll need to ensure that all computations have the same 'shape': this must correspond to the dimensions of the largest model we'll fit. To handle smaller models, we can 'embed' their descriptions in the topmost dimensions of the state space, effectively treating the remaining dimensions as dummy states that are never used." ] }, { "cell_type": "code", "execution_count": 0, "metadata": { "id": "vqyTuY5hrmdR", "outputId": "44d1da51-e674-43c3-f696-770188678bcd" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Shape of initial_state_logits: (10, 10)\n", "Shape of transition probs: (10, 10, 10)\n", "Example initial state logits for num_states==3:\n", "[ -0. -0. -0. -100. -100. -100. -100. -100. -100. -100.]\n", "Example transition_probs for num_states==3:\n", "[[0.95 0.025 0.025 0. 0. 0. 0. 0. 0. 0. ]\n", " [0.025 0.95 0.025 0. 0. 0. 0. 0. 0. 0. ]\n", " [0.025 0.025 0.95 0. 0. 0. 0. 0. 0. 0. ]\n", " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0. ]\n", " [0. 0. 0. 0. 1. 0. 0. 0. 0. 0. ]\n", " [0. 0. 0. 0. 0. 1. 0. 0. 0. 0. ]\n", " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0. ]\n", " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0. ]\n", " [0. 0. 0. 0. 0. 0. 0. 0. 1. 0. ]\n", " [0. 0. 0. 0. 0. 0. 0. 0. 0. 1. ]]\n" ] } ], "source": [ "max_num_states = 10\n", "\n", "def build_latent_state(num_states, max_num_states, daily_change_prob=0.05):\n", "\n", " # Give probability exp(-100) ~= 0 to states outside of the current model.\n", " active_states_mask = tf.concat([tf.ones([num_states]),\n", " tf.zeros([max_num_states - num_states])],\n", " axis=0)\n", " initial_state_logits = -100. * (1 - active_states_mask)\n", "\n", " # Build a transition matrix that transitions only within the current\n", " # `num_states` states.\n", " transition_probs = tf.fill([num_states, num_states],\n", " 0. if num_states == 1\n", " else daily_change_prob / (num_states - 1)) \n", " padded_transition_probs = tf.eye(max_num_states) + tf.pad(\n", " tf.linalg.set_diag(transition_probs,\n", " tf.fill([num_states], - daily_change_prob)),\n", " paddings=[(0, max_num_states - num_states),\n", " (0, max_num_states - num_states)])\n", "\n", " return initial_state_logits, padded_transition_probs\n", "\n", "# For each candidate model, build the initial state prior and transition matrix.\n", "batch_initial_state_logits = []\n", "batch_transition_probs = []\n", "for num_states in range(1, max_num_states+1):\n", " initial_state_logits, transition_probs = build_latent_state(\n", " num_states=num_states,\n", " max_num_states=max_num_states)\n", " batch_initial_state_logits.append(initial_state_logits)\n", " batch_transition_probs.append(transition_probs)\n", "\n", "batch_initial_state_logits = tf.stack(batch_initial_state_logits)\n", "batch_transition_probs = tf.stack(batch_transition_probs)\n", "print(\"Shape of initial_state_logits: {}\".format(batch_initial_state_logits.shape))\n", "print(\"Shape of transition probs: {}\".format(batch_transition_probs.shape))\n", "print(\"Example initial state logits for num_states==3:\\n{}\".format(batch_initial_state_logits[2, :]))\n", "print(\"Example transition_probs for num_states==3:\\n{}\".format(batch_transition_probs[2, :, :]))" ] }, { "cell_type": "markdown", "metadata": { "id": "k9NMBMBq2UQw" }, "source": [ "Now we proceed similarly as above. This time we'll use an extra batch dimension in `trainable_rates` to separately fit the rates for each model under consideration." ] }, { "cell_type": "code", "execution_count": 0, "metadata": { "id": "Ok-3Nzt1suyw", "outputId": "fd06f84f-ad86-4009-be1c-3799a6cc9de5" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Defined HMM with batch shape: (10,)\n" ] } ], "source": [ "trainable_log_rates = tf.Variable(\n", " tf.fill([batch_initial_state_logits.shape[0], max_num_states],\n", " tf.math.log(tf.reduce_mean(observed_counts))) + \n", " tf.random.stateless_normal([1, max_num_states], seed=(42, 42)),\n", " name='log_rates')\n", " \n", "hmm = tfd.HiddenMarkovModel(\n", " initial_distribution=tfd.Categorical(\n", " logits=batch_initial_state_logits),\n", " transition_distribution=tfd.Categorical(probs=batch_transition_probs),\n", " observation_distribution=tfd.Poisson(log_rate=trainable_log_rates),\n", " num_steps=len(observed_counts))\n", "print(\"Defined HMM with batch shape: {}\".format(hmm.batch_shape))" ] }, { "cell_type": "markdown", "metadata": { "id": "eC5vFBX12PvA" }, "source": [ "In computing the total log prob, we are careful to sum over only the priors for the rates actually used by each model component:\n" ] }, { "cell_type": "code", "execution_count": 0, "metadata": { "id": "ly0mT_mqdubx" }, "outputs": [], "source": [ "rate_prior = tfd.LogNormal(5, 5)\n", "\n", "def log_prob():\n", " prior_lps = rate_prior.log_prob(tf.math.exp(trainable_log_rates))\n", " prior_lp = tf.stack(\n", " [tf.reduce_sum(prior_lps[i, :i+1]) for i in range(max_num_states)])\n", " return prior_lp + hmm.log_prob(observed_counts)" ] }, { "cell_type": "markdown", "metadata": { "id": "yPqvJ9TS5F98" }, "source": [ "Now we optimize the *batch* objective we've constructed, fitting all candidate models simultaneously:" ] }, { "cell_type": "code", "execution_count": 0, "metadata": { "colab": { "height": 282 }, "id": "gSeUg44-0aiE", "outputId": "18d340bb-7064-4d9b-85f9-358f0d9318d6" }, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Negative log marginal likelihood')" ] }, "execution_count": 0, "metadata": { "tags": [] }, "output_type": "execute_result" }, { "data": { "image/png": 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lYGMZAL37jp5wGzfsMOuMapo2DbNuxQwWLKsCYN8DPxzPUI0xZkLlkhSc4H0I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\nY8ClqnqOqn5MVVtVNaGqOyY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"text/plain": [ "
" ] }, "metadata": { "tags": [] }, "output_type": "display_data" } ], "source": [ "losses = tfp.math.minimize(\n", " lambda: -log_prob(),\n", " optimizer=tf_keras.optimizers.Adam(0.1),\n", " num_steps=100)\n", "plt.plot(losses)\n", "plt.ylabel('Negative log marginal likelihood')" ] }, { "cell_type": "code", "execution_count": 0, "metadata": { "colab": { "height": 312 }, "id": "_Jsthql_IxhW", "outputId": "2b892a77-c675-436b-8786-eb9b52fd2d7a" }, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Model selection on latent states')" ] }, "execution_count": 0, "metadata": { "tags": [] }, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": { "tags": [] }, "output_type": "display_data" } ], "source": [ "num_states = np.arange(1, max_num_states+1)\n", "plt.plot(num_states, -losses[-1])\n", "plt.ylim([-400, -200])\n", "plt.ylabel(\"marginal likelihood $\\\\tilde{p}(x)$\")\n", "plt.xlabel(\"number of latent states\")\n", "plt.title(\"Model selection on latent states\")" ] }, { "cell_type": "markdown", "metadata": { "id": "Kq7SKiR-6c1l" }, "source": [ "Examining the likelihoods, we see that the (approximate) marginal likelihood tends to prefer a three-state model. This seems quite plausible -- the 'true' model had four states, but from just looking at the data it's hard to rule out a three-state explanation.\n" ] }, { "cell_type": "markdown", "metadata": { "id": "u0tqU6Lo6pFD" }, "source": [ "We can also extract the rates fit for each candidate model:" ] }, { "cell_type": "code", "execution_count": 0, "metadata": { "id": "lnXTiGX4d6e4", "outputId": "9b959f60-2e49-4d1d-cd5f-23dcb4d55ba1" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "rates for 1-state model: [32.968506]\n", "rates for 2-state model: [ 5.789209 47.948917]\n", "rates for 3-state model: [ 2.841977 48.057507 17.958897]\n", "rates for 4-state model: [ 2.8302798 49.585037 41.928406 17.351114 ]\n", "rates for 5-state model: [17.399694 77.83679 41.975216 49.62771 2.8256145]\n", "rates for 6-state model: [41.63677 77.20768 49.570934 49.557076 17.630419 2.8713436]\n", "rates for 7-state model: [41.711704 76.405945 49.581184 49.561283 17.451889 2.8722699\n", " 17.43608 ]\n", "rates for 8-state model: [41.771793 75.41323 49.568714 49.591846 17.2523 17.247969 17.231388\n", " 2.830598]\n", "rates for 9-state model: [41.83378 74.50916 49.619488 49.622494 2.8369408 17.254414\n", " 17.21532 2.5904858 17.252514 ]\n", "rates for 10-state model: [4.1886074e+01 7.3912338e+01 4.1940136e+01 4.9652588e+01 2.8485537e+00\n", " 1.7433832e+01 6.7564294e-02 1.9590002e+00 1.7430998e+01 7.8838937e-02]\n" ] } ], "source": [ "rates = tf.exp(trainable_log_rates)\n", "for i, learned_model_rates in enumerate(rates):\n", " print(\"rates for {}-state model: {}\".format(i+1, learned_model_rates[:i+1]))" ] }, { "cell_type": "markdown", "metadata": { "id": "8eArj7lke9Ei" }, "source": [ "And plot the explanations each model provides for the data:" ] }, { "cell_type": "code", "execution_count": 0, "metadata": { "id": "XEuhytSKcn4g" }, "outputs": [], "source": [ "most_probable_states = hmm.posterior_mode(observed_counts)" ] }, { "cell_type": "code", "execution_count": 0, "metadata": { "colab": { "height": 874 }, "id": "g3RiZCjzuL8o", "outputId": "2c5b3aa2-621e-4262-afe8-f00f43596f32" }, "outputs": [ { "data": { "image/png": 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7O+OeO38kcakE3djJs6qqivr6erTWC3ZgT2Sx0U2A+vp6zGYzw8PDcWs8Dcud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" ] }, "metadata": { "tags": [] }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(14, 12))\n", "for i, learned_model_rates in enumerate(rates):\n", " ax = fig.add_subplot(4, 3, i+1)\n", " ax.plot(tf.gather(learned_model_rates, most_probable_states[i]), c='green', lw=3, label='inferred rate')\n", " ax.plot(observed_counts, c='black', alpha=0.3, label='observed counts')\n", " ax.set_ylabel(\"latent rate\")\n", " ax.set_xlabel(\"time\")\n", " ax.set_title(\"{}-state model\".format(i+1))\n", " ax.legend(loc=4)\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": { "id": "sw25-htzfxLZ" }, "source": [ "It's easy to see how the one-, two-, and (more subtly) three-state models provide inadequate explanations. Interestingly, all models above four states provide essentially the same explanation! This is likely because our 'data' is relatively clean and leaves little room for alternative explanations; on messier real-world data we would expect the higher-capacity models to provide progressively better fits to the data, with some tradeoff point where the improved fit is outweighted by model complexity." ] }, { "cell_type": "markdown", "metadata": { "id": "fY5E0BaPI7lz" }, "source": [ "### Extensions\n", "\n", "The models in this notebook could be straightforwardly extended in many ways. For example:\n", "\n", "- allowing latent states to have different probabilities (some states may be common vs rare)\n", "- allowing nonuniform transitions between latent states (e.g., to learn that a machine crash is usually followed by a system reboot is usually followed by a period of good performance, etc.)\n", "- other emission models, e.g. `NegativeBinomial` to model varying dispersions in count data, or continous distributions such as `Normal` for real-valued data.\n" ] } ], "metadata": { "colab": { "collapsed_sections": [], "name": "Multiple changepoint detection and Bayesian model selection", "toc_visible": true }, "kernelspec": { "display_name": "Python 3", "name": "python3" } }, "nbformat": 4, "nbformat_minor": 0 }