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@petermchale
Last active August 2, 2021 21:34
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hidden markov model (trained in an unsupervised manner) to infer genomic regions under natural selection
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Preliminaries\n",
"\n",
"The code in this notebook is based upon: https://www.tensorflow.org/probability/examples/Multiple_changepoint_detection_and_Bayesian_model_selection\n",
"\n",
"The time-series analysis performed there is sometimes called \"change point detection\" or \"regime switching\".\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import tensorflow.compat.v2 as tf\n",
"tf.enable_v2_behavior()\n",
"import tensorflow_probability as tfp\n",
"from tensorflow_probability import distributions as tfd\n",
"from matplotlib import pylab as plt\n",
"import scipy.stats\n",
"\n",
"%matplotlib inline\n",
"\n",
"font_size = 25 "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Simulating genomic mutations \n",
"\n",
"Given an average number of mutations in a given genomic interval, one can generate a realization of those mutations along the interval by drawing inter-mutation distances from an exponential distribution and stacking those distances along the interval. Consequently, the number of mutations in the given interval is Poisson distributed. \n",
"\n",
"In the model below, I define sub-intervals (\"regimes\"), each with their own expected number of mutations, and generate mutations accordingly. \n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"def compute_mutation_positions_core(offset, duration, rate):\n",
" inter_arrival_times = np.random.exponential(scale=1/rate, size=10*rate*duration)\n",
" mutation_positions = np.cumsum(inter_arrival_times) \n",
" return offset + mutation_positions[mutation_positions < duration]\n",
"\n",
"def compute_mutation_positions(durations, rates): \n",
" offsets = np.insert(np.cumsum(durations[:-1]), 0, 0)\n",
" return np.concatenate([\n",
" compute_mutation_positions_core(offset, duration, rate) \n",
" for offset, duration, rate in zip(offsets, durations, rates)\n",
" ]).astype(np.float32)\n",
"\n",
"def compute_observed_counts(durations, rates): \n",
" bins = np.linspace(start=0, stop=np.sum(durations), num=np.sum(durations)+1)\n",
" mutation_positions = compute_mutation_positions(durations, rates)\n",
" mutation_counts, _ = np.histogram(mutation_positions, bins)\n",
" bin_centers = 0.5*(bins[:-1] + bins[1:])\n",
" return bin_centers, mutation_counts, mutation_positions\n",
"\n",
"def plot_mutations_rates_counts(): \n",
" unit_interval = 100 # bps\n",
" true_durations = [5, 2, 5, 5, 5] # \"time\" spent in each hidden state (measured in multiples of \"unit_interval\")\n",
" true_rates = 1*np.array([10, 1, 10, 1, 10]) # average number of mutations per duration per unit_interval\n",
" \n",
" bin_centers, mutation_counts, mutation_positions = compute_observed_counts(true_durations, true_rates)\n",
"\n",
" bin_centers *= unit_interval\n",
" mutation_positions *= unit_interval\n",
" y_label_ = 'number of mutations per {} bps'.format(unit_interval) \n",
" \n",
" true_rates_concatenated_ = np.concatenate([\n",
" true_rate*np.ones(true_duration)\n",
" for true_rate, true_duration in zip(true_rates, true_durations)\n",
" ]).astype(np.float32)\n",
"\n",
" plt.figure(figsize=[12, 8])\n",
" plt.rcParams.update({'font.size': font_size}) \n",
" plt.plot(bin_centers, mutation_counts)\n",
" plt.plot(bin_centers, true_rates_concatenated_)\n",
" plt.stem(mutation_positions, 0.1*np.max(true_rates_concatenated_)*np.ones(len(mutation_positions)))\n",
" plt.xlabel('genomic coordinate (bps)')\n",
" plt.ylabel(y_label_)\n",
" \n",
" return mutation_counts.astype(np.float32), bin_centers, mutation_positions, y_label_, true_rates_concatenated_\n",
" \n",
"observed_counts, observed_bin_centers, observed_mutation_positions, y_label, true_rates_concatenated = plot_mutations_rates_counts()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Inferring selection by fitting a Hidden Markov Model to the mutation-count data in an unsupervised fashion"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Initial logits of hidden (evolutionary) states:\n",
"[0. 0.]\n",
"Transition probabilities between hidden states:\n",
"[[0.95 0.05]\n",
" [0.05 0.95]]\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/anaconda2/envs/tf_tfp/lib/python3.7/site-packages/tensorflow_probability/python/distributions/hidden_markov_model.py:498: UserWarning: HiddenMarkovModel.log_prob in TFP versions < 0.12.0 had a bug in which the transition model was applied prior to the initial step. This bug has been fixed. You may observe a slight change in behavior.\n",
" 'HiddenMarkovModel.log_prob in TFP versions < 0.12.0 had a bug in '\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"step 0: loss: 97.93757629394531 rates_of_hidden_states: [6.607831 2.7444327]\n",
"step 20: loss: 69.55445098876953 rates_of_hidden_states: [10.154117 0.78994167]\n",
"step 40: loss: 69.31456756591797 rates_of_hidden_states: [11.3082075 1.0876744]\n",
"step 60: loss: 69.18182373046875 rates_of_hidden_states: [11.136429 1.0230861]\n",
"step 80: loss: 69.15613555908203 rates_of_hidden_states: [11.009809 1.0438827]\n",
"step 100: loss: 69.15339660644531 rates_of_hidden_states: [10.963743 1.033458]\n",
"step 120: loss: 69.1529541015625 rates_of_hidden_states: [10.945956 1.0394473]\n",
"step 140: loss: 69.15289306640625 rates_of_hidden_states: [10.938612 1.0368782]\n",
"step 160: loss: 69.15290832519531 rates_of_hidden_states: [10.9371805 1.0375652]\n",
"step 180: loss: 69.15287780761719 rates_of_hidden_states: [10.937856 1.0375793]\n",
"step 200: loss: 69.15289306640625 rates_of_hidden_states: [10.938255 1.0374829]\n",
"Inferred rates_of_hidden_states: [10.938255 1.0374829]\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"def log_probability_of_model_rates(trainable_log_rates, hmm):\n",
" rate_prior = tfd.LogNormal(5, 5) # weakly-informative LogNormal prior on a single model rate\n",
" return (\n",
" hmm.log_prob(observed_counts) # likelihood of the observed count data under the model\n",
" + tf.reduce_sum(rate_prior.log_prob(tf.math.exp(trainable_log_rates))) # assumes that model rates are independent\n",
" )\n",
"\n",
"# shift the model rates to increase their probability, conditioned upon the observed count data \n",
"@tf.function(autograph=False)\n",
"def shift_model_rates(optimizer, trainable_log_rates, hmm):\n",
" with tf.GradientTape() as tape:\n",
" negative_log_probability_of_model_rates = -log_probability_of_model_rates(trainable_log_rates, hmm)\n",
" gradients = tape.gradient(negative_log_probability_of_model_rates, [trainable_log_rates])[0]\n",
" optimizer.apply_gradients([(gradients, trainable_log_rates)])\n",
" return negative_log_probability_of_model_rates, tf.math.exp(trainable_log_rates)\n",
"\n",
"def create_and_train_HMM(): \n",
" number_evolutionary_states = 2 # a neutral state and a negative-selection state\n",
" inter_state_transition_probability = 0.05\n",
" initial_evolutionary_state_logits = np.zeros([number_evolutionary_states], dtype=np.float32) # distribution of initial states is uniform\n",
"\n",
" transition_probabilites = inter_state_transition_probability/(number_evolutionary_states-1)*np.ones(\n",
" [number_evolutionary_states, number_evolutionary_states], \n",
" dtype=np.float32\n",
" )\n",
"\n",
" np.fill_diagonal(transition_probabilites, 1-inter_state_transition_probability)\n",
"\n",
" print(\"Initial logits of hidden (evolutionary) states:\\n{}\".format(initial_evolutionary_state_logits))\n",
" print(\"Transition probabilities between hidden states:\\n{}\".format(transition_probabilites))\n",
" \n",
" trainable_log_rates = tf.Variable(\n",
" np.log(np.mean(observed_counts)) + tf.random.normal([number_evolutionary_states]),\n",
" name='log_rates'\n",
" )\n",
"\n",
" hmm = tfd.HiddenMarkovModel(\n",
" initial_distribution = tfd.Categorical(logits=initial_evolutionary_state_logits),\n",
" transition_distribution = tfd.Categorical(probs=transition_probabilites),\n",
" observation_distribution = tfd.Poisson(log_rate=trainable_log_rates),\n",
" num_steps = len(observed_counts)\n",
" )\n",
"\n",
" optimizer = tf.keras.optimizers.Adam(learning_rate=0.1)\n",
" \n",
" for step in range(201):\n",
" loss, rates_of_hidden_states = [\n",
" element.numpy() for element in shift_model_rates(optimizer, trainable_log_rates, hmm)\n",
" ]\n",
" if step % 20 == 0:\n",
" print(\"step {}: loss: {} rates_of_hidden_states: {}\".format(step, loss, rates_of_hidden_states))\n",
"\n",
" print(\"Inferred rates_of_hidden_states: {}\".format(rates_of_hidden_states))\n",
" \n",
" return hmm, rates_of_hidden_states\n",
"\n",
"def compare_inferred_and_true_rate(): \n",
" hmm, rates_of_hidden_states = create_and_train_HMM()\n",
" \n",
" # Compute probability distribution over the evolutionary states, conditioned on observed count data.\n",
" # This is done for each time point by marginalizing over the other time points \n",
" # (forward-backward algorithm):\n",
" # https://en.wikipedia.org/wiki/Hidden_Markov_model#Smoothing\n",
" probability_distribution_over_hidden_states_at_each_time_point = hmm.posterior_marginals(observed_counts).probs_parameter().numpy()\n",
"\n",
" # ideal solution is to use the Viterbi algorithm to compute the hidden-state \n",
" # path with the largest probability, given the observed count data:\n",
" # https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/HiddenMarkovModel#posterior_mode\n",
" most_probable_hidden_state_at_each_time_point = np.argmax(probability_distribution_over_hidden_states_at_each_time_point, axis=1)\n",
" most_probable_rate_at_each_time_point = rates_of_hidden_states[most_probable_hidden_state_at_each_time_point]\n",
"\n",
" plt.figure(figsize=[12, 8])\n",
" plt.rcParams.update({'font.size': font_size}) \n",
" plt.step(observed_bin_centers, true_rates_concatenated, where='mid', c='black', lw=3, label='true rate', alpha=0.3)\n",
" plt.step(observed_bin_centers, most_probable_rate_at_each_time_point, where='mid', c='green', lw=3, label='inferred rate')\n",
" plt.xlabel('genomic coordinate (bps)')\n",
" plt.ylabel(y_label)\n",
" plt.legend(loc=4) \n",
" \n",
"compare_inferred_and_true_rate()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Inferring selection from largest inter-mutation distances "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"def compare_intermutation_intervals_and_true_rate(): \n",
" interval_starts = observed_mutation_positions[:-1]\n",
" interval_ends = observed_mutation_positions[1:]\n",
" interval_lengths = interval_ends - interval_starts\n",
" sorted_interval_indices = np.argsort(-interval_lengths)\n",
"\n",
" for number_of_intervals in np.arange(2,10,2):\n",
" plt.figure(figsize=[12, 8])\n",
" plt.rcParams.update({'font.size': font_size}) \n",
" plt.step(observed_bin_centers, true_rates_concatenated, where='mid', c='black', lw=3, label='true rate', alpha=1)\n",
" for index in np.arange(number_of_intervals): \n",
" start = interval_starts[sorted_interval_indices][index]\n",
" end = interval_ends[sorted_interval_indices][index]\n",
" plt.axvspan(start, end, alpha=0.5, color='red')\n",
" plt.xlabel('genomic coordinate (bps)')\n",
" plt.ylabel(y_label)\n",
" plt.title('largest {} inter-mutation intervals'.format(number_of_intervals))\n",
" plt.legend(loc=4) \n",
" plt.show()\n",
"\n",
"compare_intermutation_intervals_and_true_rate()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## TODO: call regions under negative selection\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"# 1. compute a p-value for a given region inferred to be in a hidden negative-selection state. Here are some approaches: \n",
"# 1.1 likelihood ratio test using a null model where only the neutral state is allowed\n",
"# 1.2 the \"peakiness\" of the probability distribution over the hidden states, conditioned upon the observed count data, \n",
"# c.f. EQ. (11) of Kern and Haussler: https://academic.oup.com/mbe/article/27/7/1673/967167 \n",
"# 2. use p-values to set a p-value threshold for calling that controls the FDR at given level\n",
"# 3. call regions using that p-value threshold\n",
"# 4. assess power/recall as a function of: \n",
"# a. effect size (difference between rates of hidden states and/or size of region under negative selection)\n",
"# b. genome-wide mutation density\n",
"# c. window size "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## TODO: infer negative selection specific to a given cancer type \n",
"\n",
"One approach is to infer selection independently for each cancer type, and then find inferred regions under \n",
"selection that are unique to one cancer type. One may assess significance in a variety of ways, e.g., test if two mutation counts are drawn from same Poisson, c.f.,\n",
"https://quinlangroup.slack.com/archives/C449KJT3J/p1615413323114400?thread_ts=1615344636.106300&cid=C449KJT3J\n",
"\n",
"A more powerful approach is to form a HMM that models both cancer types simultaneously. \n",
"Let $n$ be a matrix representing the observed mutation counts both as a function of genomic coordinate and \n",
"cancer type. Let $\\lambda$ be a similar matrix representing the model mutation rates. \n",
"Then the HMM would be defined by stipulating an $n^2$ X $n^2$\n",
"transition matrix $p(\\lambda_t | \\lambda_{t-1})$, where $n$ is the number of hidden states, \n",
"and a multivariate Poisson distribution $p(n_t | \\lambda_t)$. This would enable us to model\n",
"correlations between cancer types, e.g., one may allow the observed mutation counts to be correlated\n",
"when the cancer types are in the \"neutral\" evolutionary state, but not when one of them is in a \n",
"\"negative-selection\" state. \n",
"\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## TODO: other generalizations\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"# generalize model to include sequence context \n",
"\n",
"# generalize model from discrete to continuous hidden states (could be difficult)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"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": "3.8.2"
},
"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": 5
}
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