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Documents/Github/Human_Learning/Miscellaneous/Barebone_Bayesian.ipynb
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{
"cells": [
{
"metadata": {
"id": "apY_J6IdBwhn",
"colab_type": "text"
},
"cell_type": "markdown",
"source": "# 1D Metropolis–Hastings with theano and tensorflow\nA small benchmark on speed etc, also an idea to use control flow to get full MH trace."
},
{
"metadata": {
"id": "I9UDOiP7q292",
"executionInfo": {
"status": "ok",
"elapsed": 1135,
"user": {
"userId": "105576906394621715471",
"photoUrl": "//lh6.googleusercontent.com/-tlKDbTjNSYQ/AAAAAAAAAAI/AAAAAAAAA-0/skVQo0Ji1Pw/s50-c-k-no/photo.jpg",
"displayName": "Charles Lao"
},
"timestamp": 1520330746290,
"user_tz": -60
},
"outputId": "f5844909-b55f-4ad1-8358-f36a6d5528ed",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"base_uri": "https://localhost:8080/",
"output_extras": [
{
"item_id": 1
},
{
"item_id": 2
}
],
"height": 54
},
"colab_type": "code",
"trusted": true
},
"cell_type": "code",
"source": "%pylab inline\nimport numpy as np\nimport pymc3 as pm\n\nimport theano.tensor as tt\nimport theano\n\npm.__version__",
"execution_count": 2,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "Populating the interactive namespace from numpy and matplotlib\n"
},
{
"output_type": "stream",
"name": "stderr",
"text": "/usr/local/lib/python3.5/dist-packages/h5py/__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n from ._conv import register_converters as _register_converters\n"
},
{
"metadata": {},
"output_type": "execute_result",
"data": {
"text/plain": "'3.3'"
},
"execution_count": 2
}
]
},
{
"metadata": {
"id": "2Bk1kUDlrOeO",
"colab_type": "text"
},
"cell_type": "markdown",
"source": "Record in the PyMC3 doc: [How PyMC3 uses Theano](http://docs.pymc.io/theano.html#how-pymc3-uses-theano), the most important side effect of a model construction is the model log-likelihood function and its gradient: it is the non-normalized posterior distribution, proportional to likelihood times prior."
},
{
"metadata": {
"trusted": true,
"id": "Ai_lRB4Rsl-0",
"colab_type": "code",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
}
}
},
"cell_type": "code",
"source": "data = 10.\n# prior for mu and sd\nprior = [0., 100.]",
"execution_count": 3,
"outputs": []
},
{
"metadata": {
"trusted": true,
"id": "NzWEJZx_qg-O",
"colab_type": "code",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
}
}
},
"cell_type": "code",
"source": "theano.config.compute_test_value='off'\nmu_th = tt.scalar('mu')\nlogp_th = pm.Normal.dist(mu=prior[0], sd=prior[1]).logp(mu_th)\nlogp_th += pm.Normal.dist(mu_th, 1.).logp(data)",
"execution_count": 4,
"outputs": []
},
{
"metadata": {
"id": "L6PUJQDzso4a",
"executionInfo": {
"status": "ok",
"elapsed": 404,
"user": {
"userId": "105576906394621715471",
"photoUrl": "//lh6.googleusercontent.com/-tlKDbTjNSYQ/AAAAAAAAAAI/AAAAAAAAA-0/skVQo0Ji1Pw/s50-c-k-no/photo.jpg",
"displayName": "Charles Lao"
},
"timestamp": 1520330748014,
"user_tz": -60
},
"outputId": "5acad640-81d8-4796-9076-479807dfa657",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"base_uri": "https://localhost:8080/",
"output_extras": [
{
"item_id": 1
}
],
"height": 35
},
"colab_type": "code",
"trusted": true
},
"cell_type": "code",
"source": "logp_th.eval({mu_th: 0.})",
"execution_count": 5,
"outputs": [
{
"metadata": {},
"output_type": "execute_result",
"data": {
"text/plain": "array(-56.44304725)"
},
"execution_count": 5
}
]
},
{
"metadata": {
"id": "BHBB0dW2C9u7",
"colab_type": "text"
},
"cell_type": "markdown",
"source": "Similarly, we can set up the logp in tensorflow as below:"
},
{
"metadata": {
"id": "7ScMd0lujTRT",
"executionInfo": {
"status": "ok",
"elapsed": 1844,
"user": {
"userId": "105576906394621715471",
"photoUrl": "//lh6.googleusercontent.com/-tlKDbTjNSYQ/AAAAAAAAAAI/AAAAAAAAA-0/skVQo0Ji1Pw/s50-c-k-no/photo.jpg",
"displayName": "Charles Lao"
},
"timestamp": 1520330750027,
"user_tz": -60
},
"outputId": "bbd7fa29-cf25-4339-a8af-7d8301375af4",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"base_uri": "https://localhost:8080/",
"output_extras": [
{
"item_id": 1
}
],
"height": 35
},
"colab_type": "code",
"trusted": true
},
"cell_type": "code",
"source": "import tensorflow as tf\nfrom tensorflow.contrib import distributions as tfd\nfrom tensorflow.contrib import bayesflow as bf\nfrom tensorflow.contrib.bayesflow.python.ops import \\\n metropolis_hastings_impl as mh\n\ntf.__version__",
"execution_count": 6,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "WARNING:tensorflow:From /usr/local/lib/python3.5/dist-packages/tensorflow/contrib/learn/python/learn/datasets/base.py:198: retry (from tensorflow.contrib.learn.python.learn.datasets.base) is deprecated and will be removed in a future version.\nInstructions for updating:\nUse the retry module or similar alternatives.\n"
},
{
"metadata": {},
"output_type": "execute_result",
"data": {
"text/plain": "'1.6.0-rc1'"
},
"execution_count": 6
}
]
},
{
"metadata": {
"trusted": true,
"id": "wcHG4KB3jauc",
"colab_type": "code",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
}
}
},
"cell_type": "code",
"source": "mu0 = tf.Variable(0., tf.float64)",
"execution_count": 7,
"outputs": []
},
{
"metadata": {
"trusted": true,
"id": "hPC9_zuwj_xz",
"colab_type": "code",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
}
}
},
"cell_type": "code",
"source": "mu_tf = tfd.Normal(loc=prior[0], scale=prior[1])",
"execution_count": 8,
"outputs": []
},
{
"metadata": {
"id": "2TnPQx0IkLhg",
"executionInfo": {
"status": "ok",
"elapsed": 408,
"user": {
"userId": "105576906394621715471",
"photoUrl": "//lh6.googleusercontent.com/-tlKDbTjNSYQ/AAAAAAAAAAI/AAAAAAAAA-0/skVQo0Ji1Pw/s50-c-k-no/photo.jpg",
"displayName": "Charles Lao"
},
"timestamp": 1520330751617,
"user_tz": -60
},
"outputId": "f28da80d-764a-493e-f8b3-df024146aab8",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"base_uri": "https://localhost:8080/",
"output_extras": [
{
"item_id": 1
}
],
"height": 35
},
"colab_type": "code",
"trusted": true
},
"cell_type": "code",
"source": "mu_tf.log_prob(mu0)",
"execution_count": 9,
"outputs": [
{
"metadata": {},
"output_type": "execute_result",
"data": {
"text/plain": "<tf.Tensor 'Normal_1/log_prob/sub:0' shape=() dtype=float32>"
},
"execution_count": 9
}
]
},
{
"metadata": {
"trusted": true,
"id": "5vE1M-wNjc8h",
"colab_type": "code",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
}
}
},
"cell_type": "code",
"source": "y_tf = tfd.Normal(loc=mu0, scale=1.)\nlogp_tf = y_tf.log_prob(data) + mu_tf.log_prob(mu0)",
"execution_count": 10,
"outputs": []
},
{
"metadata": {
"id": "HZaw17crjt62",
"executionInfo": {
"status": "ok",
"elapsed": 402,
"user": {
"userId": "105576906394621715471",
"photoUrl": "//lh6.googleusercontent.com/-tlKDbTjNSYQ/AAAAAAAAAAI/AAAAAAAAA-0/skVQo0Ji1Pw/s50-c-k-no/photo.jpg",
"displayName": "Charles Lao"
},
"timestamp": 1520330752861,
"user_tz": -60
},
"outputId": "acc62da8-b372-439e-f811-ea4fca984566",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"base_uri": "https://localhost:8080/",
"output_extras": [
{
"item_id": 1
}
],
"height": 35
},
"colab_type": "code",
"trusted": true
},
"cell_type": "code",
"source": "sess = tf.Session()\ninit = tf.global_variables_initializer()\nsess.run(init)\nprint(sess.run(logp_tf))",
"execution_count": 11,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "-56.443047\n"
}
]
},
{
"metadata": {
"id": "Kpx4RWll2vD-",
"colab_type": "text"
},
"cell_type": "markdown",
"source": "Metropolis–Hastings algorithm, with kernel and control flow in numpy:"
},
{
"metadata": {
"trusted": true,
"id": "ns2oNxxMCu5c",
"colab_type": "code",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
}
}
},
"cell_type": "code",
"source": "scale = 1.\nnsample = 10000",
"execution_count": 12,
"outputs": []
},
{
"metadata": {
"id": "f1sFja6ZEHWY",
"colab_type": "text"
},
"cell_type": "markdown",
"source": "Tensorflow version:"
},
{
"metadata": {
"id": "1OsCr_yD2QOS",
"executionInfo": {
"status": "ok",
"elapsed": 3596,
"user": {
"userId": "105576906394621715471",
"photoUrl": "//lh6.googleusercontent.com/-tlKDbTjNSYQ/AAAAAAAAAAI/AAAAAAAAA-0/skVQo0Ji1Pw/s50-c-k-no/photo.jpg",
"displayName": "Charles Lao"
},
"timestamp": 1520330757173,
"user_tz": -60
},
"outputId": "bca022e8-ae69-4464-fb0d-c7077ca49e44",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"base_uri": "https://localhost:8080/",
"output_extras": [
{
"item_id": 1
}
],
"height": 54
},
"colab_type": "code",
"trusted": true
},
"cell_type": "code",
"source": "%%time\n\ntrace = dict(mu=np.zeros(nsample),\n logp=np.zeros(nsample),\n accept=np.zeros(nsample))\n\nwith sess.as_default():\n logp0 = logp_tf.eval({mu0: 0.})\n\ntrace['mu'][0] = 0.\ntrace['logp'][0] = logp0\ntrace['accept'][0] = 1\n\nfor s in range(1, nsample):\n mu_ = trace['mu'][s-1]\n logp_ = trace['logp'][s-1]\n mu_p = mu_ + np.random.randn()*scale\n\n # evaluation of logp\n with sess.as_default():\n logp_p = logp_tf.eval({mu0: mu_p})\n\n if np.log(np.random.rand()) < logp_p-logp_:\n trace['mu'][s] = mu_p\n trace['logp'][s] = logp_p\n trace['accept'][s] = 1\n else:\n trace['mu'][s] = mu_\n trace['logp'][s] = logp_\n trace['accept'][s] = 0",
"execution_count": 13,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "CPU times: user 1.7 s, sys: 76 ms, total: 1.77 s\nWall time: 1.37 s\n"
}
]
},
{
"metadata": {
"id": "ORe0SH1j_wgy",
"executionInfo": {
"status": "ok",
"elapsed": 1007,
"user": {
"userId": "105576906394621715471",
"photoUrl": "//lh6.googleusercontent.com/-tlKDbTjNSYQ/AAAAAAAAAAI/AAAAAAAAA-0/skVQo0Ji1Pw/s50-c-k-no/photo.jpg",
"displayName": "Charles Lao"
},
"timestamp": 1520330758203,
"user_tz": -60
},
"outputId": "cb4ed60b-30a5-47c9-a6d5-433d6c703d4a",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"base_uri": "https://localhost:8080/",
"output_extras": [
{
"item_id": 1
}
],
"height": 154
},
"colab_type": "code",
"trusted": true
},
"cell_type": "code",
"source": "trace_tf = trace\n_, ax = plt.subplots(1, 3, figsize=(15, 2))\npm.kdeplot(trace['mu'], ax=ax[0])\nax[1].plot(trace['mu'])\nax[1].set_title('Mean acceptance ratio: {:.5f}'\n .format(trace['accept'].mean()))\nax[2].plot(trace['logp'])\nplt.tight_layout();",
"execution_count": 14,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x7fb2368dd8d0>",
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"metadata": {
"id": "_w0D97LhEqeL",
"colab_type": "text"
},
"cell_type": "markdown",
"source": "Theano version:"
},
{
"metadata": {
"id": "L_Oos5hG7Ayw",
"executionInfo": {
"status": "ok",
"elapsed": 1090,
"user": {
"userId": "105576906394621715471",
"photoUrl": "//lh6.googleusercontent.com/-tlKDbTjNSYQ/AAAAAAAAAAI/AAAAAAAAA-0/skVQo0Ji1Pw/s50-c-k-no/photo.jpg",
"displayName": "Charles Lao"
},
"timestamp": 1520330759320,
"user_tz": -60
},
"outputId": "30a29816-daf0-4196-a305-2869344b65b1",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"base_uri": "https://localhost:8080/",
"output_extras": [
{
"item_id": 1
}
],
"height": 54
},
"colab_type": "code",
"trusted": true
},
"cell_type": "code",
"source": "%%time\ntrace = dict(mu=np.zeros(nsample),\n logp=np.zeros(nsample),\n accept=np.zeros(nsample))\n\nlogp0 = logp_th.eval({mu_th: 0.})\n \ntrace['mu'][0] = 0.\ntrace['logp'][0] = logp0\ntrace['accept'][0] = 1\n\nfor s in range(1, nsample):\n mu_ = trace['mu'][s-1]\n logp_ = trace['logp'][s-1]\n mu_p = mu_ + np.random.randn()*scale\n\n # evaluation of logp\n logp_p = logp_th.eval({mu_th: mu_p})\n\n if np.log(np.random.rand()) < logp_p-logp_:\n trace['mu'][s] = mu_p\n trace['logp'][s] = logp_p\n trace['accept'][s] = 1\n else:\n trace['mu'][s] = mu_\n trace['logp'][s] = logp_\n trace['accept'][s] = 0",
"execution_count": 15,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "CPU times: user 396 ms, sys: 96 ms, total: 492 ms\nWall time: 377 ms\n"
}
]
},
{
"metadata": {
"id": "g9a2dG1Z6kmM",
"executionInfo": {
"status": "ok",
"elapsed": 1067,
"user": {
"userId": "105576906394621715471",
"photoUrl": "//lh6.googleusercontent.com/-tlKDbTjNSYQ/AAAAAAAAAAI/AAAAAAAAA-0/skVQo0Ji1Pw/s50-c-k-no/photo.jpg",
"displayName": "Charles Lao"
},
"timestamp": 1520330760413,
"user_tz": -60
},
"outputId": "77c1a2f9-8157-4c58-c000-ea94e6d384c2",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"base_uri": "https://localhost:8080/",
"output_extras": [
{
"item_id": 1
}
],
"height": 154
},
"colab_type": "code",
"trusted": true
},
"cell_type": "code",
"source": "trace_th = trace\n_, ax = plt.subplots(1, 3, figsize=(15, 2))\npm.kdeplot(trace['mu'], ax=ax[0])\nax[1].plot(trace['mu'])\nax[1].set_title('Mean acceptance ratio: {:.5f}'\n .format(trace['accept'].mean()))\nax[2].plot(trace['logp'])\nplt.tight_layout();",
"execution_count": 16,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x7fb2368dd240>",
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"metadata": {
"id": "VIph2peAE7hc",
"colab_type": "text"
},
"cell_type": "markdown",
"source": "As you can see from the timing above, the sampling is way faster in theano. Basically, if we are going to do everything in an imperative programming style, the speed comes down to how fast you can evaluate logp (and dlogp in gradient based method).\n\nUsing the MH from tensorflow is pretty fast, however, it is not quite what we used to as it does not output the whole chain, instead it ouputs the final state. In a way you can use it as if it output a chain (or a particle filter / SMC). For example, specifying the number of chain = nsample we can treat the final output as samples from the posterior."
},
{
"metadata": {
"trusted": true,
"id": "QDFlFWR4dMkK",
"colab_type": "code",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
}
}
},
"cell_type": "code",
"source": "tf.reset_default_graph()\n# Generate nsample initial values randomly. Each of these would be an\n# independent starting point for a Markov chain.\nstate = tf.get_variable(\n \"state\",\n initializer=tf.random_normal([nsample],\n mean=0.,\n dtype=tf.float32,\n seed=42)*100.)\n\n# Computes the log(p(x))\ndef log_density(x):\n mu = tfd.Normal(loc=0., scale=100.)\n y = tfd.Normal(loc=x, scale=1.)\n logp2 = y.log_prob(data)+mu.log_prob(x)\n return logp2\n\n# Initial log-density value\nstate_log_density = tf.get_variable(\n \"state_log_density\",\n initializer=log_density(state.initialized_value()))\n\n# A variable to store the log_acceptance_ratio:\nlog_acceptance_ratio = tf.get_variable(\n \"log_acceptance_ratio\",\n initializer=tf.zeros([nsample], dtype=tf.float32))\n\n# Generates random proposals\ndef random_proposal(x):\n return (x + tf.random_normal(tf.shape(x), mean=0., stddev=scale,\n dtype=x.dtype, seed=12)), None",
"execution_count": 17,
"outputs": []
},
{
"metadata": {
"id": "fN6TVo0BHD7J",
"executionInfo": {
"status": "ok",
"elapsed": 416,
"user": {
"userId": "105576906394621715471",
"photoUrl": "//lh6.googleusercontent.com/-tlKDbTjNSYQ/AAAAAAAAAAI/AAAAAAAAA-0/skVQo0Ji1Pw/s50-c-k-no/photo.jpg",
"displayName": "Charles Lao"
},
"timestamp": 1520333261814,
"user_tz": -60
},
"outputId": "6a4a0d8a-1320-4181-9bbf-27220553fde1",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"base_uri": "https://localhost:8080/",
"output_extras": [
{
"item_id": 1
}
],
"height": 54
},
"colab_type": "code",
"trusted": true
},
"cell_type": "code",
"source": "%%time\n# Create the op to propagate the chain for 100 steps.\nstepper = mh.evolve(\n state, state_log_density, log_acceptance_ratio,\n log_density, random_proposal, n_steps=1000, seed=123)\n\ninit = tf.global_variables_initializer()\nwith tf.Session() as sess:\n sess.run(init)\n # Run the chains for a total of 1000 steps\n # Executing the stepper advances the chain to the next state.\n sess.run(stepper)\n samples, sample_log_density = sess.run(\n [state, state_log_density])\n\ntrace['mu'] = samples\ntrace['logp'] = sample_log_density\ntrace['accept'] = 0",
"execution_count": 18,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "CPU times: user 668 ms, sys: 60 ms, total: 728 ms\nWall time: 237 ms\n"
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "trace_tf1 = trace\n_, ax = plt.subplots(1, 3, figsize=(15, 2))\npm.kdeplot(trace['mu'], ax=ax[0])\nax[1].plot(trace['mu'])\nax[2].plot(trace['logp'])\nplt.tight_layout();",
"execution_count": 19,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x7fb2147d0e80>",
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "It is fast.\n\nBelow, we try to use multiple way to see if we can get a speed up from tensorflow, but getting the full chain:\n- Eager (In a separate notebook as Eager mode has to be turn on in the very beginning. Spoiler: it is very slow)\n- MH kernel from bayesflow\n- Modify the MH sampler from bayesflow to get the full chain"
},
{
"metadata": {
"trusted": true,
"id": "wGJkk_42DYs0",
"colab_type": "code",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
}
}
},
"cell_type": "code",
"source": "from tensorflow.python.ops import variable_scope\nfrom tensorflow.python.ops import array_ops\n\ntf.reset_default_graph()\n\n# Computes the log(p(x))\ndef log_density(x):\n mu = tfd.Normal(loc=0., scale=100.)\n y = tfd.Normal(loc=x, scale=1.)\n logp2 = y.log_prob(data)+mu.log_prob(x)\n return logp2\n\nstate = variable_scope.get_variable('state', initializer=0.0)\n\n# Initial log-density value\nstate_log_density = variable_scope.get_variable(\n 'state_log_density',\n initializer=log_density(state.initialized_value()))\n\n# A variable to store the log_acceptance_ratio:\nlog_accept_ratio = variable_scope.get_variable(\n 'log_accept_ratio', initializer=0.)\n\n# Generates random proposals\ndef random_proposal(x):\n return (x + tf.random_normal(tf.shape(x), mean=0., stddev=scale,\n dtype=x.dtype, seed=12)), None",
"execution_count": 20,
"outputs": []
},
{
"metadata": {
"id": "8lZN7Xbqh7H7",
"executionInfo": {
"status": "ok",
"elapsed": 8687,
"user": {
"userId": "105576906394621715471",
"photoUrl": "//lh6.googleusercontent.com/-tlKDbTjNSYQ/AAAAAAAAAAI/AAAAAAAAA-0/skVQo0Ji1Pw/s50-c-k-no/photo.jpg",
"displayName": "Charles Lao"
},
"timestamp": 1520333235466,
"user_tz": -60
},
"outputId": "b0b1f718-5d19-4f5d-8130-dcc66d381338",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"base_uri": "https://localhost:8080/",
"output_extras": [
{
"item_id": 1
}
],
"height": 54
},
"colab_type": "code",
"trusted": true
},
"cell_type": "code",
"source": "%%time\ntrace = dict(mu=np.zeros(nsample),\n logp=np.zeros(nsample),\n accept=np.zeros(nsample))\n\n# Create the op to propagate the chain for 100 steps.\nstepper = mh.evolve(\n state, state_log_density, log_accept_ratio,\n log_density, random_proposal)\n\ninit = tf.global_variables_initializer()\nwith tf.Session() as sess:\n sess.run(init)\n for s in np.arange(nsample):\n sess.run(stepper)\n trace['mu'][s] = sess.run(state)\n trace['logp'][s] = sess.run(state_log_density)\n \ntrace['accept'][1:] = trace['mu'][1:] != trace['mu'][:-1]",
"execution_count": 21,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "CPU times: user 4.76 s, sys: 580 ms, total: 5.34 s\nWall time: 2.97 s\n"
}
]
},
{
"metadata": {
"id": "7bRkamAGkHiI",
"executionInfo": {
"status": "ok",
"elapsed": 995,
"user": {
"userId": "105576906394621715471",
"photoUrl": "//lh6.googleusercontent.com/-tlKDbTjNSYQ/AAAAAAAAAAI/AAAAAAAAA-0/skVQo0Ji1Pw/s50-c-k-no/photo.jpg",
"displayName": "Charles Lao"
},
"timestamp": 1520333246317,
"user_tz": -60
},
"outputId": "a4d7baec-c462-47e1-c3a9-bd286ac5151c",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"base_uri": "https://localhost:8080/",
"output_extras": [
{
"item_id": 1
}
],
"height": 154
},
"colab_type": "code",
"trusted": true
},
"cell_type": "code",
"source": "trace_tf2 = trace\n_, ax = plt.subplots(1, 3, figsize=(15, 2))\npm.kdeplot(trace['mu'], ax=ax[0])\nax[1].plot(trace['mu'])\nax[1].set_title('Mean acceptance ratio: {:.5f}'\n .format(trace['accept'].mean()))\nax[2].plot(trace['logp'])\nplt.tight_layout();",
"execution_count": 22,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x7fb214526fd0>",
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\n"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Still pretty slow, we can get the kernel and just update the state instead:"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "tf.reset_default_graph()\n\nfrom tensorflow.python.ops import init_ops\nfrom tensorflow.python.ops import variable_scope\nfrom tensorflow.python.ops import variables\n\n# Computes the log(p(x))\ndef log_density(x):\n mu = tfd.Normal(loc=0., scale=100.)\n y = tfd.Normal(loc=x, scale=1.)\n logp2 = y.log_prob(data)+mu.log_prob(x)\n return logp2\n\nstate = variable_scope.get_variable(\"state\", initializer=0.)\n\n# Initial log-density value\nstate_log_density = tf.get_variable(\n \"state_log_density\",\n initializer=log_density(state.initialized_value()))\n\n# A variable to store the accept:\naccept = tf.get_variable(\n \"accept\",\n initializer=tf.zeros([], dtype=tf.bool))\n\n\nnew_state, kernel_results = mh.kernel(\n target_log_prob_fn=log_density,\n proposal_fn=mh.proposal_normal(scale=1.),\n current_state=state, \n current_target_log_prob=state_log_density)\n\nmu_update = state.assign(new_state)\nlogp_update = state_log_density.assign(kernel_results.current_target_log_prob)\naccpet_update = accept.assign(kernel_results.is_accepted)",
"execution_count": 23,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "%%time\ntrace = dict(mu=np.zeros(nsample),\n logp=np.zeros(nsample),\n accept=np.zeros(nsample))\n\ninit = tf.global_variables_initializer()\nwith tf.Session() as sess:\n sess.run(init)\n mu_samples = []\n logp_samples = []\n accept_samples = []\n for s in range(nsample):\n mu_sample, logp_sample, accept_sample = sess.run(\n [mu_update, logp_update, accpet_update])\n trace['mu'][s] = mu_sample\n trace['logp'][s] = logp_sample\n trace['accept'][s] = accept_sample",
"execution_count": 24,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "CPU times: user 2.3 s, sys: 272 ms, total: 2.57 s\nWall time: 1.5 s\n"
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "trace_tf3 = trace\n_, ax = plt.subplots(1, 3, figsize=(15, 2))\npm.kdeplot(trace['mu'], ax=ax[0])\nax[1].plot(trace['mu'])\nax[1].set_title('Mean acceptance ratio: {:.5f}'\n .format(trace['accept'].mean()))\nax[2].plot(trace['logp'])\nplt.tight_layout();",
"execution_count": 25,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x7fb1e998a588>",
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\n"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Modify the while loop via tensorflow control flow to get the full chain: It is possible to go stateful"
},
{
"metadata": {
"id": "Zc4dOgvr2lQK",
"executionInfo": {
"status": "ok",
"elapsed": 3080,
"user": {
"userId": "105576906394621715471",
"photoUrl": "//lh6.googleusercontent.com/-tlKDbTjNSYQ/AAAAAAAAAAI/AAAAAAAAA-0/skVQo0Ji1Pw/s50-c-k-no/photo.jpg",
"displayName": "Charles Lao"
},
"timestamp": 1520338364097,
"user_tz": -60
},
"outputId": "31343836-4184-4f2c-8487-6c92edf287e5",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"base_uri": "https://localhost:8080/",
"output_extras": [
{
"item_id": 1
}
],
"height": 54
},
"colab_type": "code",
"trusted": true
},
"cell_type": "code",
"source": "%%time\nndim = 100\nnstep = 10000\n\ntf.reset_default_graph()\ni0 = tf.constant(0)\nm0 = tf.ones([1, ndim])\nwalk = tf.random_normal([1, ndim], mean=0., stddev=1.)\nc = lambda i, m: i < nstep\nb = lambda i, m: [i+1, \n tf.concat([m, m[-1]+tf.random_normal([1, ndim], mean=0., stddev=1.)], \n axis=0)]\nr = tf.while_loop(\n c, b, loop_vars=[i0, m0],\n shape_invariants=[i0.get_shape(), tf.TensorShape([None, ndim])])\n\ninit = tf.global_variables_initializer()\nwith tf.Session() as sess:\n sess.run(init)\n r_ = sess.run(r)",
"execution_count": 26,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "CPU times: user 3.4 s, sys: 448 ms, total: 3.85 s\nWall time: 788 ms\n"
}
]
},
{
"metadata": {
"id": "6bztT1OKNAgr",
"executionInfo": {
"status": "ok",
"elapsed": 2204,
"user": {
"userId": "105576906394621715471",
"photoUrl": "//lh6.googleusercontent.com/-tlKDbTjNSYQ/AAAAAAAAAAI/AAAAAAAAA-0/skVQo0Ji1Pw/s50-c-k-no/photo.jpg",
"displayName": "Charles Lao"
},
"timestamp": 1520338366324,
"user_tz": -60
},
"outputId": "eb0b0255-ae79-4302-d817-131a9446a61e",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"base_uri": "https://localhost:8080/",
"output_extras": [
{
"item_id": 1
}
],
"height": 265
},
"colab_type": "code",
"trusted": true
},
"cell_type": "code",
"source": "plt.plot(r_[1], alpha=.1);",
"execution_count": 27,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x7fb1e99ef9b0>",
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\n"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true,
"id": "QDFlFWR4dMkK",
"colab_type": "code",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
}
}
},
"cell_type": "code",
"source": "tf.reset_default_graph()\n# Generate nsample initial values randomly. Each of these would be an\n# independent starting point for a Markov chain.\nstate = variable_scope.get_variable('state', initializer=[0.0])\n\n# Computes the log(p(x))\ndef log_density(x):\n mu = tfd.Normal(loc=0., scale=100.)\n y = tfd.Normal(loc=x, scale=1.)\n logp2 = y.log_prob(data)+mu.log_prob(x)\n return logp2\n\n# Initial log-density value\nstate_log_density = tf.get_variable(\n \"state_log_density\",\n initializer=log_density(state.initialized_value()))\n\n# A variable to store the log_acceptance_ratio:\nlog_acceptance_ratio = tf.get_variable(\n \"log_acceptance_ratio\",\n initializer=tf.zeros([1], dtype=tf.float32))\n\n# Generates random proposals\ndef random_proposal(x):\n return (x + tf.random_normal(tf.shape(x), mean=0., stddev=scale,\n dtype=x.dtype, seed=12)), None",
"execution_count": 28,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "from tensorflow.python.framework import ops\nfrom tensorflow.python.ops import control_flow_ops\n\ndef mhevolve(initial_sample,\n initial_log_density,\n initial_log_accept_ratio,\n target_log_prob_fn,\n proposal_fn,\n n_steps=1,\n seed=None,\n name=None):\n with ops.name_scope(name, \"metropolis_hastings\", [initial_sample]):\n current_state = tf.expand_dims(initial_sample, 0)\n current_target_log_prob = tf.expand_dims(initial_log_density, 0)\n log_accept_ratio = initial_log_accept_ratio\n\n def step(i, current_state, current_target_log_prob, log_accept_ratio):\n \"\"\"Wrap single Markov chain iteration in `while_loop`.\"\"\"\n next_state, kernel_results = mh.kernel(\n target_log_prob_fn=target_log_prob_fn,\n proposal_fn=proposal_fn,\n current_state=current_state[-1, :],\n current_target_log_prob=current_target_log_prob[-1, :],\n seed=seed)\n accepted_log_prob = kernel_results.current_target_log_prob\n log_accept_ratio = kernel_results.log_accept_ratio\n current_state = tf.concat([current_state, tf.expand_dims(next_state, 0)], \n axis=0)\n current_target_log_prob = tf.concat([current_target_log_prob,\n tf.expand_dims(accepted_log_prob, 0)], \n axis=0)\n return i + 1, current_state, current_target_log_prob, log_accept_ratio\n \n i0 = tf.constant(0)\n \n (_, accepted_state, accepted_target_log_prob, accepted_log_accept_ratio) = (\n control_flow_ops.while_loop(\n cond=lambda i, *ignored_args: i < n_steps,\n body=step,\n loop_vars=[\n i0, # i\n current_state,\n current_target_log_prob,\n log_accept_ratio,\n ],\n # the magic here\n shape_invariants=[\n i0.get_shape(),\n tf.TensorShape([None, 1]),\n tf.TensorShape([None, 1]),\n log_accept_ratio.get_shape(),\n ],\n parallel_iterations=1 if seed is not None else 10,\n # TODO(b/73775595): Confirm optimal setting of swap_memory.\n swap_memory=1))\n\n forward_step = control_flow_ops.group(\n accepted_target_log_prob,\n accepted_state,\n accepted_log_accept_ratio\n )\n\n return accepted_state, accepted_target_log_prob, accepted_log_accept_ratio",
"execution_count": 29,
"outputs": []
},
{
"metadata": {
"id": "fN6TVo0BHD7J",
"executionInfo": {
"status": "ok",
"elapsed": 416,
"user": {
"userId": "105576906394621715471",
"photoUrl": "//lh6.googleusercontent.com/-tlKDbTjNSYQ/AAAAAAAAAAI/AAAAAAAAA-0/skVQo0Ji1Pw/s50-c-k-no/photo.jpg",
"displayName": "Charles Lao"
},
"timestamp": 1520333261814,
"user_tz": -60
},
"outputId": "6a4a0d8a-1320-4181-9bbf-27220553fde1",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"base_uri": "https://localhost:8080/",
"output_extras": [
{
"item_id": 1
}
],
"height": 54
},
"colab_type": "code",
"trusted": true
},
"cell_type": "code",
"source": "%%time\n# Create the op to propagate the chain for 100 steps.\naccepted_state, accepted_target_log_prob, accepted_log_accept_ratio = mhevolve(\n state, state_log_density, log_acceptance_ratio,\n log_density, random_proposal, n_steps=nsample, seed=123)\n\ninit = tf.global_variables_initializer()\nwith tf.Session() as sess:\n sess.run(init)\n # Run the chains for a total of 1000 steps\n # Executing the stepper advances the chain to the next state.\n samples, alog_prob, a_ratio = sess.run(\n [accepted_state, accepted_target_log_prob, accepted_log_accept_ratio])",
"execution_count": 30,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "CPU times: user 1.54 s, sys: 252 ms, total: 1.79 s\nWall time: 735 ms\n"
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "trace = dict(mu=np.zeros(nsample),\n logp=np.zeros(nsample),\n accept=np.zeros(nsample))\n\ntrace['mu'] = samples[1:].squeeze()\ntrace['logp'] = alog_prob[1:].squeeze()\ntrace['accept'][1:] = trace['mu'][1:] != trace['mu'][:-1]",
"execution_count": 31,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "trace_tf3 = trace\n_, ax = plt.subplots(1, 3, figsize=(15, 2))\npm.kdeplot(trace['mu'], ax=ax[0])\nax[1].plot(trace['mu'])\nax[1].set_title('Mean acceptance ratio: {:.5f}'\n .format(trace['accept'].mean()))\nax[2].plot(trace['logp'])\nplt.tight_layout();",
"execution_count": 32,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x7fb1e98be5c0>",
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"metadata": {
"id": "OeSGPojjmrf_",
"executionInfo": {
"status": "ok",
"elapsed": 10975,
"user": {
"userId": "105576906394621715471",
"photoUrl": "//lh6.googleusercontent.com/-tlKDbTjNSYQ/AAAAAAAAAAI/AAAAAAAAA-0/skVQo0Ji1Pw/s50-c-k-no/photo.jpg",
"displayName": "Charles Lao"
},
"timestamp": 1520284717460,
"user_tz": -60
},
"outputId": "359dd08d-2361-4943-df96-89e0fc00e133",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"base_uri": "https://localhost:8080/",
"output_extras": [
{}
],
"height": 190
},
"colab_type": "code",
"trusted": true
},
"cell_type": "code",
"source": "with pm.Model() as model:\n mu = pm.Normal('mu', mu=0., sd=100.)\n y = pm.Normal('y', mu=mu, sd=1., observed=data)\n trace = pm.sample(10000, tune=0, step=pm.Metropolis())",
"execution_count": 33,
"outputs": [
{
"output_type": "stream",
"name": "stderr",
"text": "Multiprocess sampling (4 chains in 4 jobs)\nMetropolis: [mu]\n100%|██████████| 10000/10000 [00:01<00:00, 9129.99it/s]\nINFO (theano.gof.compilelock): Waiting for existing lock by process '2130' (I am process '2131')\nINFO (theano.gof.compilelock): To manually release the lock, delete /home/laoj/.theano/compiledir_Linux-4.4--generic-x86_64-with-Ubuntu-16.04-xenial-x86_64-3.5.2-64/lock_dir\nINFO (theano.gof.compilelock): Waiting for existing lock by process '2130' (I am process '2132')\nINFO (theano.gof.compilelock): To manually release the lock, delete /home/laoj/.theano/compiledir_Linux-4.4--generic-x86_64-with-Ubuntu-16.04-xenial-x86_64-3.5.2-64/lock_dir\nINFO (theano.gof.compilelock): Waiting for existing lock by process '2131' (I am process '2132')\nINFO (theano.gof.compilelock): To manually release the lock, delete /home/laoj/.theano/compiledir_Linux-4.4--generic-x86_64-with-Ubuntu-16.04-xenial-x86_64-3.5.2-64/lock_dir\nThe number of effective samples is smaller than 25% for some parameters.\n"
}
]
},
{
"metadata": {
"id": "6IAQMAwoqgZO",
"executionInfo": {
"status": "ok",
"elapsed": 428,
"user": {
"userId": "105576906394621715471",
"photoUrl": "//lh6.googleusercontent.com/-tlKDbTjNSYQ/AAAAAAAAAAI/AAAAAAAAA-0/skVQo0Ji1Pw/s50-c-k-no/photo.jpg",
"displayName": "Charles Lao"
},
"timestamp": 1520281736751,
"user_tz": -60
},
"outputId": "889796df-f4a4-4863-d6c2-6364da9e044c",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"base_uri": "https://localhost:8080/",
"output_extras": [
{
"item_id": 1
}
],
"height": 34
},
"colab_type": "code",
"trusted": true
},
"cell_type": "code",
"source": "model.logp({'mu': 1.})",
"execution_count": 34,
"outputs": [
{
"metadata": {},
"output_type": "execute_result",
"data": {
"text/plain": "array(-46.94309725)"
},
"execution_count": 34
}
]
},
{
"metadata": {
"id": "kGE2JPLjCBPj",
"executionInfo": {
"status": "ok",
"elapsed": 699,
"user": {
"userId": "105576906394621715471",
"photoUrl": "//lh6.googleusercontent.com/-tlKDbTjNSYQ/AAAAAAAAAAI/AAAAAAAAA-0/skVQo0Ji1Pw/s50-c-k-no/photo.jpg",
"displayName": "Charles Lao"
},
"timestamp": 1520284763264,
"user_tz": -60
},
"outputId": "cad74043-4287-41ef-9051-e9233d1e497c",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"base_uri": "https://localhost:8080/",
"output_extras": [
{}
],
"height": 153
},
"colab_type": "code",
"trusted": true
},
"cell_type": "code",
"source": "pm.traceplot(trace);",
"execution_count": 35,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x7fb1f2c1cc50>",
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\n"
},
"metadata": {}
}
]
}
],
"metadata": {
"_draft": {
"nbviewer_url": "https://gist.github.com/1518c75a815de36156cabd3aedf494ba"
},
"colab": {
"views": {},
"name": "Barebone Bayesian.ipynb",
"version": "0.3.2",
"collapsed_sections": [],
"provenance": [],
"default_view": {}
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3",
"language": "python"
},
"gist": {
"id": "1518c75a815de36156cabd3aedf494ba",
"data": {
"description": "Documents/Github/Human_Learning/Miscellaneous/Barebone_Bayesian.ipynb",
"public": false
}
},
"language_info": {
"nbconvert_exporter": "python",
"mimetype": "text/x-python",
"name": "python",
"version": "3.5.2",
"file_extension": ".py",
"pygments_lexer": "ipython3",
"codemirror_mode": {
"version": 3,
"name": "ipython"
}
}
},
"nbformat": 4,
"nbformat_minor": 1
}
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