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tensorflow_probability.ipynb
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| { | |
| "nbformat": 4, | |
| "nbformat_minor": 0, | |
| "metadata": { | |
| "colab": { | |
| "name": "tensorflow_probability.ipynb", | |
| "provenance": [], | |
| "collapsed_sections": [], | |
| "include_colab_link": true | |
| }, | |
| "kernelspec": { | |
| "name": "python3", | |
| "display_name": "Python 3" | |
| } | |
| }, | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "view-in-github", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "<a href=\"https://colab.research.google.com/gist/CihanSoylu/48f1be6038291cf446b3c3e4420922ed/tensorflow_probability.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "RqLHXJ7FhiFT", | |
| "colab_type": "code", | |
| "outputId": "8452311e-bdcb-43ce-b3f4-ca0b83018f98", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "%tensorflow_version 2.x" | |
| ], | |
| "execution_count": 1, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": [ | |
| "TensorFlow 2.x selected.\n" | |
| ], | |
| "name": "stdout" | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "bYU2iEhGh0Q4", | |
| "colab_type": "code", | |
| "outputId": "7eb0fb68-fa2f-4680-a805-9b5db247ea7b", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "import numpy as np\n", | |
| "import tensorflow as tf\n", | |
| "import tensorflow_probability as tfp\n", | |
| "print(tf.__version__)\n", | |
| "\n", | |
| "tfd = tfp.distributions" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": [ | |
| "2.0.0-beta1\n" | |
| ], | |
| "name": "stdout" | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "aPqN8COsG3TS", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "# Distributions" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "E0mmSQ7pHce-", | |
| "colab_type": "code", | |
| "outputId": "9ea0130d-6181-4c5d-ca65-4e64e1e2ac0c", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "# Create a normal distribution\n", | |
| "n = tfd.Normal(loc=0., scale=1.)\n", | |
| "n" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tfp.distributions.Normal 'Normal/' batch_shape=[] event_shape=[] dtype=float32>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 3 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "EbSxp2NoJoNn", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "Event shape = ( ) means it is a scalar distribution. " | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "W12A0REIIKU7", | |
| "colab_type": "code", | |
| "outputId": "a8c572aa-b7dc-4970-ea80-d952e20e80d8", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "# Draw a sample from it\n", | |
| "n.sample()" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tf.Tensor: id=22, shape=(), dtype=float32, numpy=0.95941013>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 4 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "lWms-qtRINqW", | |
| "colab_type": "code", | |
| "outputId": "7388d2d3-4135-4188-a8fb-e3a5dbeef9ab", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "# Draw three samples from it\n", | |
| "n.sample(3)" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tf.Tensor: id=47, shape=(3,), dtype=float32, numpy=array([-1.2171098, 1.2464374, -1.3972762], dtype=float32)>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 5 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "gAeua0UVIZlv", | |
| "colab_type": "code", | |
| "outputId": "522885d3-9d13-4402-9e78-1ed023e761b0", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "# Evaluate the log prob\n", | |
| "n.log_prob(0.)" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tf.Tensor: id=59, shape=(), dtype=float32, numpy=-0.9189385>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 6 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "LJCEvsfGI4iU", | |
| "colab_type": "code", | |
| "outputId": "d472e034-c4bc-49f2-a477-77077083b544", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "b = tfd.Bernoulli(probs=0.7)\n", | |
| "b" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tfp.distributions.Bernoulli 'Bernoulli/' batch_shape=[] event_shape=[] dtype=int32>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 7 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "6OYr77IFI-G9", | |
| "colab_type": "code", | |
| "outputId": "a2f80ceb-3f8c-4fe7-e357-8610de143560", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "b.sample(8)" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tf.Tensor: id=90, shape=(8,), dtype=int32, numpy=array([0, 1, 1, 1, 1, 1, 1, 1], dtype=int32)>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 8 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "Qn95ZtCnJFt7", | |
| "colab_type": "code", | |
| "outputId": "7a48c8a5-2d22-486c-b63e-0edb3012c9b5", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 122 | |
| } | |
| }, | |
| "source": [ | |
| "b.log_prob([1,0])" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": [ | |
| "WARNING: Logging before flag parsing goes to stderr.\n", | |
| "W0904 13:10:26.867488 140202921670528 deprecation.py:323] From /usr/local/lib/python3.6/dist-packages/tensorflow/python/ops/nn_impl.py:182: add_dispatch_support.<locals>.wrapper (from tensorflow.python.ops.array_ops) is deprecated and will be removed in a future version.\n", | |
| "Instructions for updating:\n", | |
| "Use tf.where in 2.0, which has the same broadcast rule as np.where\n" | |
| ], | |
| "name": "stderr" | |
| }, | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tf.Tensor: id=113, shape=(2,), dtype=float32, numpy=array([-0.35667494, -1.2039728 ], dtype=float32)>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 9 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "NC7M7LbcJSz2", | |
| "colab_type": "code", | |
| "outputId": "78aa4804-52f4-4ac1-f2a8-578941657def", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "# Multivariate normal with diagonal covariance\n", | |
| "nd = tfd.MultivariateNormalDiag(loc=[0., 10.], scale_diag=[1., 4.])\n", | |
| "nd" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tfp.distributions.MultivariateNormalDiag 'MultivariateNormalDiag/' batch_shape=[] event_shape=[2] dtype=float32>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 10 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "xSchAFkSJv2a", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "Event shape = (2) means the sample space is 2 dimensional." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "3_8nsDkjJh0E", | |
| "colab_type": "code", | |
| "outputId": "889ef915-5520-49cd-8949-2de70262fdfc", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "nd.sample()" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tf.Tensor: id=194, shape=(2,), dtype=float32, numpy=array([-0.7479573, 16.969402 ], dtype=float32)>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 11 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "6aIWET43KGzK", | |
| "colab_type": "code", | |
| "outputId": "5e576817-a61f-4ffd-89b2-7a8156554043", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 102 | |
| } | |
| }, | |
| "source": [ | |
| "nd.sample(4)" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tf.Tensor: id=246, shape=(4, 2), dtype=float32, numpy=\n", | |
| "array([[ 0.33959457, 14.147322 ],\n", | |
| " [ 0.05219507, 17.290096 ],\n", | |
| " [-0.2815908 , 6.8896832 ],\n", | |
| " [-0.32239607, 10.473448 ]], dtype=float32)>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 12 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "iK6Qm0NCKavr", | |
| "colab_type": "code", | |
| "outputId": "d5ffe56c-2f42-4ac2-a678-a03b80c42955", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "nd.log_prob([0., 10])" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tf.Tensor: id=306, shape=(), dtype=float32, numpy=-3.2241714>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 13 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "mV1JiAp7KkfG", | |
| "colab_type": "code", | |
| "outputId": "c6651cb9-f1b4-48bf-eec6-da71a3d7c584", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 281 | |
| } | |
| }, | |
| "source": [ | |
| "import matplotlib.pyplot as plt\n", | |
| "nd = tfd.MultivariateNormalFullCovariance(\n", | |
| " loc = [0., 5], covariance_matrix = [[1., .7], [.7, 1.]])\n", | |
| "data = nd.sample(200)\n", | |
| "plt.scatter(data[:, 0], data[:, 1], color='blue', alpha=0.4)\n", | |
| "plt.axis([-5, 5, 0, 10])\n", | |
| "plt.title(\"Data set\")\n", | |
| "plt.show()" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "image/png": 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hco0EXUwZ4UU+v5PPqVOMjgcGuMB42WW0aACKYUsLRXh4mHbLRz4SCGC8mHd0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\nIkjQhRAiIkjQhRAiIkjQhRA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| |
| "text/plain": [ | |
| "<Figure size 432x288 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| } | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "gOOfu2-qKvPH", | |
| "colab_type": "code", | |
| "outputId": "730d03dc-d860-4b29-93b5-533fa940d506", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "# Batch of independent Bernouilli distributions\n", | |
| "b3 = tfd.Bernoulli(probs=[.3, .5, .7])\n", | |
| "b3" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tfp.distributions.Bernoulli 'Bernoulli/' batch_shape=[3] event_shape=[] dtype=int32>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 15 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "TzcwgjIVLNUA", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "Batch shape [3] means the distribution object is a batch of three distributions and event shape [ ] means each distribution is scalar. " | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "2oeUmnCoL66L", | |
| "colab_type": "code", | |
| "outputId": "f29ca200-0335-430e-f3d9-9f24a123879a", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "b3.sample()" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tf.Tensor: id=460, shape=(3,), dtype=int32, numpy=array([0, 0, 1], dtype=int32)>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 16 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "SBXCpSsCMyWP", | |
| "colab_type": "code", | |
| "outputId": "2c5b3750-bd54-4d06-f3c0-c3f810ff7cae", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "b3.prob([1, 1, 0])" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tf.Tensor: id=476, shape=(3,), dtype=float32, numpy=array([0.29999998, 0.5 , 0.29999998], dtype=float32)>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 17 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "kvs823cVNaXW", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "The function prob(v) returns a vector where the ith entry is the probability of the ith coin being v[i]. " | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "MPfAVkh4p5YK", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "## tfp.distributions.Independent\n", | |
| "\n", | |
| "In order to create a joint distribution you can use Independent function. The prob function applied to a vector for such a distribution will be a number unlike the b3 example above. The Independent function convert a batch of distributions into a single joint distribution of independent distributions. The batch shape becomes the event shape. " | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "LOqWcHT0OuoB", | |
| "colab_type": "code", | |
| "outputId": "26edee47-ee76-41d3-df20-cb96801da604", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "b3_joint = tfd.Independent(b3, reinterpreted_batch_ndims=1)\n", | |
| "b3_joint" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tfp.distributions.Independent 'IndependentBernoulli/' batch_shape=[] event_shape=[3] dtype=int32>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 20 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "0gnU4S5OP9NH", | |
| "colab_type": "code", | |
| "outputId": "a77e60fd-7dd9-4a18-9266-e9183f611157", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "# Prob(1,1,1) = 0.3 x 0.5 x 0.7\n", | |
| "b3_joint.prob([1,1,1])" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tf.Tensor: id=516, shape=(), dtype=float32, numpy=0.105000004>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 21 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "n0ppRSAUKDgm", | |
| "colab_type": "code", | |
| "outputId": "b54d3cec-7c0f-4e50-c20f-d0ed95bcf734", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "# Make independent distribution from a 2-batch Normal.\n", | |
| "n = tfd.Normal(loc=[-1., 1], scale=[0.1, 0.5])\n", | |
| "ind = tfd.Independent(\n", | |
| " distribution=tfd.Normal(loc=[-1., 1], scale=[0.1, 0.5]),\n", | |
| " reinterpreted_batch_ndims=1)\n", | |
| "ind" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tfp.distributions.Independent 'IndependentNormal/' batch_shape=[] event_shape=[2] dtype=float32>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 22 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "25jav7oUKfE9", | |
| "colab_type": "code", | |
| "outputId": "120dc37a-9955-48ef-87de-2e3df4f847f6", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "n" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tfp.distributions.Normal 'Normal/' batch_shape=[2] event_shape=[] dtype=float32>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 23 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "hn3bOgaZKgff", | |
| "colab_type": "code", | |
| "outputId": "3b256463-a20e-47aa-a45b-9d00838bc047", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "n.sample()" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tf.Tensor: id=545, shape=(2,), dtype=float32, numpy=array([-0.9780394, 0.8697878], dtype=float32)>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 24 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "B2stBhNFKR8F", | |
| "colab_type": "code", | |
| "outputId": "8a0577c3-886a-455c-a0df-99d9bd9e5b8c", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "ind.sample()" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tf.Tensor: id=581, shape=(2,), dtype=float32, numpy=array([-0.9398609, 1.255456 ], dtype=float32)>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 25 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "Nl9EteMfKR4a", | |
| "colab_type": "code", | |
| "outputId": "941feb40-d33e-4c21-a090-240364e84012", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "# Make independent distribution from a 2-batch bivariate Normal.\n", | |
| "ind = tfd.Independent(\n", | |
| " distribution=tfd.MultivariateNormalDiag(\n", | |
| " loc=[[-1., 1], [1, -1]],\n", | |
| " scale_identity_multiplier=[1., 0.5]),\n", | |
| " reinterpreted_batch_ndims=1)\n", | |
| "\n", | |
| "ind" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tfp.distributions.Independent 'IndependentMultivariateNormalDiag/' batch_shape=[] event_shape=[2, 2] dtype=float32>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 26 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "OrMkbXdyKRxM", | |
| "colab_type": "code", | |
| "outputId": "001c382a-d5c4-46c0-a68a-279aa9f7b9cb", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 68 | |
| } | |
| }, | |
| "source": [ | |
| "ind.sample()" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tf.Tensor: id=700, shape=(2, 2), dtype=float32, numpy=\n", | |
| "array([[-2.382836 , -0.77324414],\n", | |
| " [ 1.5233893 , -1.3743069 ]], dtype=float32)>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 27 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "E76sKBRhUqfJ", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "## Batches of multivariate distributions" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "hVImLaBjQI9C", | |
| "colab_type": "code", | |
| "outputId": "a8cb9a06-40a6-4012-9cff-95372e4e071f", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "nd_batch = tfd.MultivariateNormalFullCovariance(\n", | |
| " loc = [[0., 0.], [1., 1.], [2., 2.]],\n", | |
| " covariance_matrix = [[[1., .1], [.1, 1.]], \n", | |
| " [[1., .3], [.3, 1.]],\n", | |
| " [[1., .5], [.5, 1.]]])\n", | |
| "nd_batch" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tfp.distributions.MultivariateNormalFullCovariance 'MultivariateNormalFullCovariance/' batch_shape=[3] event_shape=[2] dtype=float32>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 28 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "wttOT_o0U7Ps", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "nd_batch is a batch of 3 independent normal distributions where each distribution is 2 dimensional and the elements of the individual distributions are not independent. " | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "eLoUi6KNVRiq", | |
| "colab_type": "code", | |
| "outputId": "ee0d5a03-efcd-408c-b6f4-c4312d99f50b", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 289 | |
| } | |
| }, | |
| "source": [ | |
| "nd_batch.sample(4)" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tf.Tensor: id=800, shape=(4, 3, 2), dtype=float32, numpy=\n", | |
| "array([[[-4.9703220e-01, 1.1425320e+00],\n", | |
| " [ 2.5317080e+00, 1.3575239e+00],\n", | |
| " [ 2.6210568e+00, 2.3021798e+00]],\n", | |
| "\n", | |
| " [[-1.1117331e+00, 9.0224606e-01],\n", | |
| " [ 1.2685717e+00, 2.8281617e-01],\n", | |
| " [ 3.5086212e+00, 1.8443767e+00]],\n", | |
| "\n", | |
| " [[ 8.9322239e-01, -7.6503921e-01],\n", | |
| " [ 9.1081977e-01, 1.4396188e+00],\n", | |
| " [ 1.3879120e-01, 6.2994027e-01]],\n", | |
| "\n", | |
| " [[ 6.8450880e-01, 8.3123893e-04],\n", | |
| " [ 1.4884772e+00, 1.5386418e+00],\n", | |
| " [ 1.6536089e+00, 1.0512571e+00]]], dtype=float32)>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 29 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "BryrnlWMIhlt", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "## Broadcasting" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "iERqIocoIEkX", | |
| "colab_type": "code", | |
| "outputId": "45b99ddc-62ac-41b2-ca06-6d1b53ba0fb8", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "n = tfd.Normal(loc=0., scale=1.)\n", | |
| "n" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tfp.distributions.Normal 'Normal/' batch_shape=[] event_shape=[] dtype=float32>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 30 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "oTSzey2BImS3", | |
| "colab_type": "code", | |
| "outputId": "0afddd24-cd6f-476c-b5fd-22375a59cf1a", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "n.log_prob(0.)" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tf.Tensor: id=818, shape=(), dtype=float32, numpy=-0.9189385>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 31 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "EGhcrNiVInMD", | |
| "colab_type": "code", | |
| "outputId": "f05d10ba-5db6-41d2-c487-2277fb569dfe", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "n.log_prob([0.])" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tf.Tensor: id=829, shape=(1,), dtype=float32, numpy=array([-0.9189385], dtype=float32)>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 32 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "Z1fUyS3rInUB", | |
| "colab_type": "code", | |
| "outputId": "d6f3f4a1-d45e-4f29-e909-b0c4d5e074ff", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 68 | |
| } | |
| }, | |
| "source": [ | |
| "n.log_prob([[0., 1.], [-1., 2.]])" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tf.Tensor: id=840, shape=(2, 2), dtype=float32, numpy=\n", | |
| "array([[-0.9189385, -1.4189385],\n", | |
| " [-1.4189385, -2.9189386]], dtype=float32)>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 33 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "b8Dphj03InXX", | |
| "colab_type": "code", | |
| "outputId": "d87823f1-7638-4bd3-9c79-0faf8dcf6348", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "nd = tfd.MultivariateNormalDiag(loc=[0., 1.], scale_diag=[1., 1.])\n", | |
| "nd" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tfp.distributions.MultivariateNormalDiag 'MultivariateNormalDiag/' batch_shape=[] event_shape=[2] dtype=float32>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 34 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "BSzqUiKLIndC", | |
| "colab_type": "code", | |
| "outputId": "c0d0bad3-3226-4781-be3e-aa6727bb7db6", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "nd.log_prob([0., 0.])" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tf.Tensor: id=931, shape=(), dtype=float32, numpy=-2.337877>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 35 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "GGeQwQkLIna4", | |
| "colab_type": "code", | |
| "outputId": "5a651846-5522-4b88-a177-9bb52e8fdced", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "nd.log_prob([[0., 0.],\n", | |
| " [1., 1.],\n", | |
| " [2., 2.]])" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tf.Tensor: id=982, shape=(3,), dtype=float32, numpy=array([-2.337877 , -2.337877 , -4.3378773], dtype=float32)>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 36 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "DCh8mkk2iUIj", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "# Distribution Lambda\n", | |
| "\n", | |
| "This creates a distribution from the output of the previous layer. " | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "G-LSLeUuoLuT", | |
| "colab_type": "code", | |
| "outputId": "cfd6e53c-8ecd-4feb-d442-4ad0aa19d561", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "layer = tfp.layers.DistributionLambda(lambda t: tfd.Normal(t, 1.))\n", | |
| "distribution = layer(2.)\n", | |
| "assert isinstance(distribution, tfd.Normal)\n", | |
| "distribution.loc\n", | |
| "# ==> 2.\n", | |
| "distribution.stddev()" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tf.Tensor: id=1013, shape=(), dtype=float32, numpy=1.0>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 37 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "JU5GnItuiK1C", | |
| "colab_type": "code", | |
| "colab": {} | |
| }, | |
| "source": [ | |
| "model = tf.keras.Sequential([\n", | |
| " tf.keras.layers.Dense(2, input_dim=2),\n", | |
| " tfp.layers.DistributionLambda(\n", | |
| " make_distribution_fn=lambda t: tfp.distributions.Normal(\n", | |
| " loc=t[..., 0], scale=tf.exp(t[..., 1]))\n", | |
| " )\n", | |
| "])" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "-897JKTvifhX", | |
| "colab_type": "code", | |
| "outputId": "cc97598f-87e0-4016-f3d2-f2cfbdd6bb73", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "x = np.array([[0,1], [2,3]])\n", | |
| "model(x)" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tfp.distributions.Normal 'sequential/distribution_lambda_1/Normal/' batch_shape=[2] event_shape=[] dtype=float32>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 39 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "ODOkx1N_iiWR", | |
| "colab_type": "code", | |
| "outputId": "89f2b4e7-27d3-4b88-aba0-dbfd12837876", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 119 | |
| } | |
| }, | |
| "source": [ | |
| "model(x).sample(5)" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tf.Tensor: id=1176, shape=(5, 2), dtype=float32, numpy=\n", | |
| "array([[ 1.2495792 , -7.5877295 ],\n", | |
| " [ 2.3519795 , -26.219402 ],\n", | |
| " [ 1.673234 , -7.4577127 ],\n", | |
| " [ -5.0821986 , 17.405872 ],\n", | |
| " [ 0.36446828, -9.862875 ]], dtype=float32)>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 40 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "y1xFwwxZjlyO", | |
| "colab_type": "code", | |
| "outputId": "d272d62c-9752-4a04-a53a-592e4616e130", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 221 | |
| } | |
| }, | |
| "source": [ | |
| "model.summary()" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": [ | |
| "Model: \"sequential\"\n", | |
| "_________________________________________________________________\n", | |
| "Layer (type) Output Shape Param # \n", | |
| "=================================================================\n", | |
| "dense (Dense) (None, 2) 6 \n", | |
| "_________________________________________________________________\n", | |
| "distribution_lambda_1 (Distr ((None,), (None,)) 0 \n", | |
| "=================================================================\n", | |
| "Total params: 6\n", | |
| "Trainable params: 6\n", | |
| "Non-trainable params: 0\n", | |
| "_________________________________________________________________\n" | |
| ], | |
| "name": "stdout" | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "CzeZ_QXrnbZF", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "# Variable Layer\n", | |
| "\n", | |
| "This is basically a layer with a trainable output independent of the inputs. Think of it as a usual Dense layer with weights forced to be zero and the bias is the output no matter what the input is. " | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "YUVzDmDZo2rh", | |
| "colab_type": "code", | |
| "colab": {} | |
| }, | |
| "source": [ | |
| "vl = tfp.layers.VariableLayer(\n", | |
| " shape=[3, 4, 2],\n", | |
| " dtype=tf.float64\n", | |
| " )" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "BOe4KNn5o-eb", | |
| "colab_type": "code", | |
| "outputId": "3d60b1b6-9cdd-414b-f48d-8cad2085a4b2", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 272 | |
| } | |
| }, | |
| "source": [ | |
| "vl(4)" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tf.Tensor: id=1189, shape=(3, 4, 2), dtype=float64, numpy=\n", | |
| "array([[[0., 0.],\n", | |
| " [0., 0.],\n", | |
| " [0., 0.],\n", | |
| " [0., 0.]],\n", | |
| "\n", | |
| " [[0., 0.],\n", | |
| " [0., 0.],\n", | |
| " [0., 0.],\n", | |
| " [0., 0.]],\n", | |
| "\n", | |
| " [[0., 0.],\n", | |
| " [0., 0.],\n", | |
| " [0., 0.],\n", | |
| " [0., 0.]]])>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 43 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "G-hOFPvdpEbk", | |
| "colab_type": "code", | |
| "outputId": "ac1baf84-29f6-44fe-f854-f070d8c74c49", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "vl = tfp.layers.VariableLayer(\n", | |
| " shape=[3, 4, 4],\n", | |
| " dtype=tf.float64,\n", | |
| " initializer=tfp.layers.BlockwiseInitializer([\n", | |
| " 'zeros',\n", | |
| " tf.keras.initializers.Constant(np.log(np.expm1(1.))),\n", | |
| " 'ones'\n", | |
| " ], sizes=[1, 2, 1])\n", | |
| " )\n", | |
| "vl" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tensorflow_probability.python.layers.variable_input.VariableLayer at 0x7f8347c6c710>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 44 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "hvgag8vRpO4b", | |
| "colab_type": "code", | |
| "outputId": "551fcce0-33b8-47e4-dfb4-784f41856615", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 272 | |
| } | |
| }, | |
| "source": [ | |
| "vl(1)" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tf.Tensor: id=1211, shape=(3, 4, 4), dtype=float64, numpy=\n", | |
| "array([[[0. , 0.54132485, 0.54132485, 1. ],\n", | |
| " [0. , 0.54132485, 0.54132485, 1. ],\n", | |
| " [0. , 0.54132485, 0.54132485, 1. ],\n", | |
| " [0. , 0.54132485, 0.54132485, 1. ]],\n", | |
| "\n", | |
| " [[0. , 0.54132485, 0.54132485, 1. ],\n", | |
| " [0. , 0.54132485, 0.54132485, 1. ],\n", | |
| " [0. , 0.54132485, 0.54132485, 1. ],\n", | |
| " [0. , 0.54132485, 0.54132485, 1. ]],\n", | |
| "\n", | |
| " [[0. , 0.54132485, 0.54132485, 1. ],\n", | |
| " [0. , 0.54132485, 0.54132485, 1. ],\n", | |
| " [0. , 0.54132485, 0.54132485, 1. ],\n", | |
| " [0. , 0.54132485, 0.54132485, 1. ]]])>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 45 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "IHPYpyKIle8q", | |
| "colab_type": "code", | |
| "colab": {} | |
| }, | |
| "source": [ | |
| "trainable_normal = tf.keras.models.Sequential([\n", | |
| " tfp.layers.VariableLayer(\n", | |
| " shape=[3, 4, 2],\n", | |
| " dtype=tf.float64,\n", | |
| " initializer=tfp.layers.BlockwiseInitializer([\n", | |
| " 'zeros',\n", | |
| " tf.keras.initializers.Constant(np.log(np.expm1(1.))),\n", | |
| " ], sizes=[1, 1])),\n", | |
| " tfp.layers.DistributionLambda(lambda t: tfp.distributions.Independent(\n", | |
| " tfp.distributions.Normal(loc=t[..., 0], scale=tf.math.softplus(t[..., 1])),\n", | |
| " reinterpreted_batch_ndims=1)),\n", | |
| "])\n", | |
| "\n", | |
| "# The output of the model is a distribution and so rv_x below will be a distribution\n", | |
| "# and rv_x.log_prob(x) makes sense.\n", | |
| "\n", | |
| "negloglik = lambda x, rv_x: -rv_x.log_prob(x)\n", | |
| "trainable_normal.compile(optimizer='adam', loss=negloglik)" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "3kLrnFr_RHcw", | |
| "colab_type": "code", | |
| "outputId": "ab7a72d2-4033-4c3f-bcd3-acd427fb02a9", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "x = trainable_normal(0.) # `0.` ignored; like conditioning on emptyset.\n", | |
| "x" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tfp.distributions.Independent 'Independentsequential_3/distribution_lambda_4/Normal/' batch_shape=[3] event_shape=[4] dtype=float64>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 54 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "ObcWuDmYRObs", | |
| "colab_type": "code", | |
| "outputId": "8011f7dc-349b-49d6-941f-23b6c28d1dbe", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "x.dtype" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "tf.float64" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 48 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "31T3hz40RUQ3", | |
| "colab_type": "code", | |
| "outputId": "ba35b397-2613-4da1-de62-810fdb4c0d76", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "x.batch_shape" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "TensorShape([3])" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 50 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "cYK7TH5NRWhh", | |
| "colab_type": "code", | |
| "outputId": "362b10d6-e0c6-47b6-a4a4-e0bfdfc2b687", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 34 | |
| } | |
| }, | |
| "source": [ | |
| "x.event_shape" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "TensorShape([4])" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 105 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "O71JWgrtRfBy", | |
| "colab_type": "code", | |
| "outputId": "897427cb-df68-47e2-c996-3746c84a1144", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 85 | |
| } | |
| }, | |
| "source": [ | |
| "x.mean()" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tf.Tensor: id=1420, shape=(3, 4), dtype=float64, numpy=\n", | |
| "array([[0., 0., 0., 0.],\n", | |
| " [0., 0., 0., 0.],\n", | |
| " [0., 0., 0., 0.]])>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 55 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "2PUq0_FKRhKj", | |
| "colab_type": "code", | |
| "outputId": "f71d2a6b-b0ed-4678-cb85-33bbadd6b903", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 85 | |
| } | |
| }, | |
| "source": [ | |
| "x.variance()" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tf.Tensor: id=1426, shape=(3, 4), dtype=float64, numpy=\n", | |
| "array([[1., 1., 1., 1.],\n", | |
| " [1., 1., 1., 1.],\n", | |
| " [1., 1., 1., 1.]])>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 56 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "QbwBr_G3RoPK", | |
| "colab_type": "code", | |
| "colab": {} | |
| }, | |
| "source": [ | |
| "m = np.zeros((3,4)) + 2\n", | |
| "s = np.zeros((3,4)) + 0.5" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "WuGa6GF_S4R0", | |
| "colab_type": "code", | |
| "colab": {} | |
| }, | |
| "source": [ | |
| "gen = tfp.distributions.Independent(\n", | |
| " tfp.distributions.Normal(loc=m, scale=s),\n", | |
| " reinterpreted_batch_ndims=1)" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "EVWrrMPsTGwc", | |
| "colab_type": "code", | |
| "colab": {} | |
| }, | |
| "source": [ | |
| "x = gen.sample(100).numpy()\n", | |
| "dataset = tf.data.Dataset.from_tensor_slices((x,x))" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "jfLnMXBNTJXL", | |
| "colab_type": "code", | |
| "colab": {} | |
| }, | |
| "source": [ | |
| "dataset = dataset.shuffle(50)" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "j5CyzevpTkYh", | |
| "colab_type": "code", | |
| "outputId": "e3d0e99e-6ed9-4a67-c14d-e4fdc9adaca5", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 1000 | |
| } | |
| }, | |
| "source": [ | |
| "trainable_normal.fit(dataset, epochs = 50)" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": [ | |
| "Epoch 1/50\n", | |
| "100/100 [==============================] - 1s 5ms/step - loss: 11.3457\n", | |
| "Epoch 2/50\n", | |
| "100/100 [==============================] - 0s 2ms/step - loss: 10.2659\n", | |
| "Epoch 3/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 9.4590\n", | |
| "Epoch 4/50\n", | |
| "100/100 [==============================] - 0s 2ms/step - loss: 8.8378\n", | |
| "Epoch 5/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 8.3467\n", | |
| "Epoch 6/50\n", | |
| "100/100 [==============================] - 0s 2ms/step - loss: 7.9486\n", | |
| "Epoch 7/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 7.6181\n", | |
| "Epoch 8/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 7.3374\n", | |
| "Epoch 9/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 7.0935\n", | |
| "Epoch 10/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 6.8768\n", | |
| "Epoch 11/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 6.6801\n", | |
| "Epoch 12/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 6.4977\n", | |
| "Epoch 13/50\n", | |
| "100/100 [==============================] - 0s 2ms/step - loss: 6.3252\n", | |
| "Epoch 14/50\n", | |
| "100/100 [==============================] - 0s 2ms/step - loss: 6.1592\n", | |
| "Epoch 15/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 5.9967\n", | |
| "Epoch 16/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 5.8353\n", | |
| "Epoch 17/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 5.6733\n", | |
| "Epoch 18/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 5.5091\n", | |
| "Epoch 19/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 5.3416\n", | |
| "Epoch 20/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 5.1701\n", | |
| "Epoch 21/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 4.9943\n", | |
| "Epoch 22/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 4.8144\n", | |
| "Epoch 23/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 4.6312\n", | |
| "Epoch 24/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 4.4461\n", | |
| "Epoch 25/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 4.2611\n", | |
| "Epoch 26/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 4.0788\n", | |
| "Epoch 27/50\n", | |
| "100/100 [==============================] - 0s 2ms/step - loss: 3.9024\n", | |
| "Epoch 28/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 3.7351\n", | |
| "Epoch 29/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 3.5803\n", | |
| "Epoch 30/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 3.4405\n", | |
| "Epoch 31/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 3.3177\n", | |
| "Epoch 32/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 3.2126\n", | |
| "Epoch 33/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 3.1252\n", | |
| "Epoch 34/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 3.0542\n", | |
| "Epoch 35/50\n", | |
| "100/100 [==============================] - 0s 2ms/step - loss: 2.9980\n", | |
| "Epoch 36/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 2.9543\n", | |
| "Epoch 37/50\n", | |
| "100/100 [==============================] - 0s 2ms/step - loss: 2.9210\n", | |
| "Epoch 38/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 2.8960\n", | |
| "Epoch 39/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 2.8774\n", | |
| "Epoch 40/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 2.8636\n", | |
| "Epoch 41/50\n", | |
| "100/100 [==============================] - 0s 2ms/step - loss: 2.8535\n", | |
| "Epoch 42/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 2.8461\n", | |
| "Epoch 43/50\n", | |
| "100/100 [==============================] - 0s 2ms/step - loss: 2.8407\n", | |
| "Epoch 44/50\n", | |
| "100/100 [==============================] - 0s 2ms/step - loss: 2.8367\n", | |
| "Epoch 45/50\n", | |
| "100/100 [==============================] - 0s 2ms/step - loss: 2.8337\n", | |
| "Epoch 46/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 2.8315\n", | |
| "Epoch 47/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 2.8298\n", | |
| "Epoch 48/50\n", | |
| "100/100 [==============================] - 0s 2ms/step - loss: 2.8286\n", | |
| "Epoch 49/50\n", | |
| "100/100 [==============================] - 0s 1ms/step - loss: 2.8277\n", | |
| "Epoch 50/50\n", | |
| "100/100 [==============================] - 0s 2ms/step - loss: 2.8270\n" | |
| ], | |
| "name": "stdout" | |
| }, | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tensorflow.python.keras.callbacks.History at 0x7f834749c5c0>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 61 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "3mBUt-55Tvsf", | |
| "colab_type": "code", | |
| "outputId": "40de7c6c-e22f-4a08-a2a0-abe4861a1de7", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 85 | |
| } | |
| }, | |
| "source": [ | |
| "trainable_normal(0.).mean()" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tf.Tensor: id=32211, shape=(3, 4), dtype=float64, numpy=\n", | |
| "array([[2.01612234, 1.93767194, 1.97366429, 1.97893472],\n", | |
| " [1.93390999, 1.97119836, 2.02611989, 1.95313365],\n", | |
| " [2.06840718, 1.92072485, 1.99626747, 1.97700717]])>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 62 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "6ZZFrFHsUqrh", | |
| "colab_type": "code", | |
| "outputId": "250a6a2a-2d5e-4fdd-8ee2-b694c384eccd", | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 85 | |
| } | |
| }, | |
| "source": [ | |
| "trainable_normal(0.).stddev()" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<tf.Tensor: id=32265, shape=(3, 4), dtype=float64, numpy=\n", | |
| "array([[0.48401529, 0.5119396 , 0.51694257, 0.40709828],\n", | |
| " [0.45146548, 0.49992078, 0.51552555, 0.56620307],\n", | |
| " [0.51147882, 0.51625875, 0.51407853, 0.53042485]])>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 63 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "NL5_9zm955DP", | |
| "colab_type": "code", | |
| "colab": {} | |
| }, | |
| "source": [ | |
| "" | |
| ], | |
| "execution_count": 0, | |
| "outputs": [] | |
| } | |
| ] | |
| } |
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