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@petermchale
Last active May 14, 2023 15:11
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Training a neural network model of a Poisson Mixture Distribution on bimodal data
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This notebook lives [here](https://github.com/petermchale/denoising_coverage_profiles/blob/master/poisson_mixture_distribution_basic.ipynb).\n",
"\n",
"## Multi-modal data\n",
"\n",
"Generate synthetic data such that there are regions of the $x$-axis that map to multiple y-values: "
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline \n",
"\n",
"def prior_vector(x_): \n",
" if x_ < 0.5: \n",
" return np.array([1, 0])\n",
" elif x_ < 1.5: \n",
" return np.array([0.5, 0.5])\n",
" else: \n",
" return np.array([0, 1])\n",
"\n",
"def lmbda(component_, x_): \n",
" return 10**(0.8*(component_+1)) * x_ \n",
" \n",
"def mean_vector(x_): \n",
" return np.array([lmbda(component_=0, x_=x_), lmbda(component_=1, x_=x_)])\n",
" \n",
"def sample_lambdas(x_, number_of_lambdas=100): \n",
" components = np.random.choice(a=2, size=number_of_lambdas, p=prior_vector(x_))\n",
" return lmbda(components, x_)\n",
" \n",
"def sample_from_mixture_distribution(x_): \n",
" lambdas = sample_lambdas(x_)\n",
" # https://github.com/numpy/numpy/issues/7843 ...\n",
" return np.random.poisson(lam=lambdas[:, np.newaxis], size=(len(lambdas), 1)) \n",
"\n",
"def generate_data():\n",
" xs = []\n",
" ys = []\n",
" for x_ in np.random.uniform(0, 2, 100): \n",
" ys_temp = sample_from_mixture_distribution(x_)\n",
" xs.extend(x_*np.ones_like(ys_temp)) \n",
" ys.extend(ys_temp)\n",
" return np.array(xs), np.array(ys)\n",
" \n",
"x, y = generate_data() \n",
"\n",
"plt.figure(figsize=(8, 8))\n",
"plt.plot(x, y, 'ro', alpha=0.3)\n",
"plt.yscale('log')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Mixture-network model\n",
"Following [Bishop](http://publications.aston.ac.uk/373/1/NCRG_94_004.pdf), we create a neural network that, when given a single value of $x$, outputs `number_mixture_components` tuples that together parametrize a mixture of elementary distributions: "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Using TensorFlow backend.\n"
]
}
],
"source": [
"import tensorflow as tf\n",
"from keras.layers import Input, Dense\n",
"from tensorflow.keras import regularizers\n",
"\n",
"x_tensor = Input(shape=(1,))\n",
"hidden = Dense(20, activation=tf.nn.tanh, kernel_regularizer=regularizers.l2(0.01))(x_tensor)\n",
"number_mixture_components = 10\n",
"priors = Dense(number_mixture_components, activation=tf.nn.softmax)(hidden)\n",
"means = Dense(number_mixture_components, activation=tf.nn.softplus)(hidden)\n",
"\n",
"import tensorflow_probability as tfp\n",
"tfd = tfp.distributions\n",
"\n",
"# https://en.wikipedia.org/wiki/Mixture_distribution\n",
"# https://en.wikipedia.org/wiki/Compound_probability_distribution\n",
"mixture_distribution = tfd.MixtureSameFamily(\n",
" mixture_distribution=tfd.Categorical(probs=priors),\n",
" components_distribution=tfd.Poisson(rate=means))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Use the so-computed probability distribution of $y$ to compute the loss function:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"y_tensor = tf.placeholder(tf.float32, shape=[None, 1])\n",
"loss = -tf.reduce_sum(mixture_distribution.log_prob(tf.reshape(y_tensor, [-1])))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notice that we flattened `y_tensor` before passing it off to `mixture_distribution.log_prob()`. Here's why: "
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"mixture_distribution.log_prob(y_tensor) computes each of the 3 x-dependent likelihood functions on each of the 3 y values:\n",
"[[-1.1112616 -1.1655859 -1.1964211]\n",
" [-2.224642 -2.2371073 -2.194483 ]\n",
" [-3.6964872 -3.6043622 -3.4506855]]\n",
"the above leads to inappropriately summing over all elements in a 3x3 matrix in tf.reduce_sum(), which is NOT the log likelihood of the data\n",
"\n",
"mixture_distribution.log_prob(tf.reshape(y_tensor, [-1])) computes each of the 3 likelihood functions on the corresponding 3 y-values:\n",
"[-1.1112616 -2.2371073 -3.4506855]\n",
"the above leads to the expected sum of 3 numbers in tf.reduce_sum(), which IS the correct log likelihood of the data\n"
]
}
],
"source": [
"with tf.Session() as debug_session: \n",
" debug_session.run(tf.global_variables_initializer())\n",
" print('mixture_distribution.log_prob(y_tensor) computes each of the 3 x-dependent likelihood functions on each of the 3 y values:')\n",
" print(debug_session.run(mixture_distribution.log_prob([[1], [2], [3]]), \n",
" feed_dict={x_tensor: [[1], [2], [3]]}))\n",
" print('the above leads to inappropriately summing over all elements in a 3x3 matrix in tf.reduce_sum(), which is NOT the log likelihood of the data')\n",
" print('')\n",
" print('mixture_distribution.log_prob(tf.reshape(y_tensor, [-1])) computes each of the 3 likelihood functions on the corresponding 3 y-values:')\n",
" print(debug_session.run(mixture_distribution.log_prob([1, 2, 3]), \n",
" feed_dict={x_tensor: [[1], [2], [3]]}))\n",
" print('the above leads to the expected sum of 3 numbers in tf.reduce_sum(), which IS the correct log likelihood of the data')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For more on this, see: \n",
"* \"Broadcasting, aka Why Is This So Confusing?\" at: \n",
"https://github.com/tensorflow/probability/blob/master/tensorflow_probability/examples/jupyter_notebooks/TensorFlow_Distributions_Tutorial.ipynb\n",
"* the graphical depiction of broadcasting rules at: \n",
"https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Complete the specification of the tensorflow graph: "
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"train_ops = tf.train.AdamOptimizer().minimize(loss)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Training the mixture-network model"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1000 : 242013.81\n",
"2000 : 130268.875\n",
"3000 : 83270.53\n",
"4000 : 60792.89\n",
"5000 : 45989.156\n",
"6000 : 37753.273\n",
"7000 : 33431.508\n",
"8000 : 31500.98\n",
"9000 : 30861.914\n",
"10000 : 30521.883\n"
]
}
],
"source": [
"with tf.Session() as session:\n",
" session.run(tf.global_variables_initializer())\n",
" for epoch in range(10000):\n",
" _, loss_ = session.run([train_ops, loss], feed_dict={x_tensor: x, y_tensor: y})\n",
" if (epoch + 1) % 1000 == 0:\n",
" print(str(epoch + 1) + \" : \" + str(loss_))\n",
"\n",
" x_test = np.linspace(0, 2, 100).reshape((-1, 1))\n",
" y_test_predicted = session.run(mixture_distribution.sample(), feed_dict={x_tensor: x_test})\n",
"\n",
" priors_predicted, means_predicted = session.run([priors, means], feed_dict={x_tensor: x}) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Evaluating the fit\n",
"\n",
"Let's see how samples from the model compare with the original data: "
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(8, 8))\n",
"plt.plot(x, y, 'ro', alpha=0.3, label='sample from truth')\n",
"plt.plot(x_test, y_test_predicted, 'go', alpha=0.3, label='sample from model')\n",
"plt.yscale('log')\n",
"_ = plt.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Looks pretty good. \n",
"\n",
"Let's compare the predicted means of each of the mixture components with the true means: "
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"means_true = []\n",
"for x_ in x: \n",
" means_true.append(mean_vector(float(x_))) \n",
"means_true = np.array(means_true)\n",
"\n",
"plt.figure(figsize=(8, 8))\n",
"for mixture_component in range(number_mixture_components): \n",
" plt.scatter(x, means_predicted[:, mixture_component], s=500*priors_predicted[:, mixture_component], facecolors='g', edgecolors='none', alpha=0.3, label=('predicted means' if mixture_component==0 else ''))\n",
"for mixture_component in range(2): \n",
" plt.scatter(x, means_true[:, mixture_component], s=10, facecolors='r', edgecolors='none', alpha=0.3, label=('true means' if mixture_component==0 else ''))\n",
"plt.yscale('log')\n",
"_ = plt.ylim(ymin=1e-1)\n",
"_ = plt.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
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"Here, I've made the marker size of each component proportional to the predicted probability of that component. You can see that that those components with large predicted probabilities have predicted means that coincide with the true means. "
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@FarhaU
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FarhaU commented May 14, 2023

Do you use Poisson-Poisson mixture models in your above working code?

@petermchale
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No, I use a bilinear combination of Poisson distributions to generate the data (e.g. see prior_vector and the graphs), and a linear combination of 10 Poisson distributions to model the data (see number_mixture_components).

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