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@taku-y
Last active January 31, 2017 16:01
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import sys, os\n",
"sys.path.insert(0, os.path.expanduser('~/work/git/github/taku-y/pymc3'))\n",
"\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import pandas as pd\n",
"import pymc3 as pm\n",
"from pymc3.distributions.timeseries import GaussianRandomWalk\n",
"import seaborn as sns"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"2016-07-09 Taku Yoshioka\n",
"\n",
"This notebook is an example of ppc with ADVI (https://github.com/pymc-devs/pymc3/pull/1229). The model is borrowed from a PyMC3 tutorial (http://pymc-devs.github.io/pymc3/notebooks/posterior_predictive.html). In the following, accurate_elbo is set to `True`, but it works with `False`. "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Applied log-transform to sd and added transformed sd_log to model.\n",
"Iteration 0 [0%]: ELBO = -820.08\n",
"Iteration 10 [10%]: Average ELBO = -429.64\n",
"Iteration 20 [20%]: Average ELBO = -248.87\n",
"Iteration 30 [30%]: Average ELBO = -195.16\n",
"Iteration 40 [40%]: Average ELBO = -175.87\n",
"Iteration 50 [50%]: Average ELBO = -163.47\n",
"Iteration 60 [60%]: Average ELBO = -157.61\n",
"Iteration 70 [70%]: Average ELBO = -152.14\n",
"Iteration 80 [80%]: Average ELBO = -149.9\n",
"Iteration 90 [90%]: Average ELBO = -148.68\n",
"Finished [100%]: Average ELBO = -147.91\n"
]
}
],
"source": [
"data = np.random.RandomState(0).randn(100)\n",
"\n",
"with pm.Model() as model:\n",
" mu = pm.Normal('mu', mu=0, sd=1, testval=0)\n",
" sd = pm.HalfNormal('sd', sd=1)\n",
" n = pm.Normal('n', mu=mu, sd=sd, observed=data)\n",
"\n",
"# step = pm.NUTS()\n",
"# trace = pm.sample(5000, step)\n",
"\n",
" v_params = pm.variational.advi(\n",
" n=100, learning_rate=1e-1, accurate_elbo=True\n",
" )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plot the trace of ELBO. "
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f904eec1b00>]"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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77DJsQ2cSL1myBL/fD8BTTz3F8uXLcTgczJkzh+rqalpaWujo6CAYDFJTUwPAypUr2bp1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\n8pACXkREJA8p4EVERPKQAl5ERCQP/f/aDZrPv7YMYQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f90d0d8c668>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(v_params.elbo_vals)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plot trace of samples drawn from the variational posterior by using `sample_vp()`. Also check the random variables included in the trace. "
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"['mu', 'sd']\n"
]
},
{
"data": {
"image/png": 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jGuITLjbOdFjx3Lb9cHn8+NF14/G9qUPzLdKAof7qKjjcPuw50IGX3j6AB5de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+MYPqg9h0/31UOWJsYD88dhHAVTiMqw4hw8/aMb8Pc9l/Dpvnps/ugkdn7biKXThncpYSFB9Hb+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\nCAQCIUr+P6WjBjcSktktAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f904c26b320>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"with model:\n",
" trace = pm.variational.sample_vp(v_params)\n",
"pm.traceplot(trace);\n",
"print(trace.varnames)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Draw samples with `hide_transformed=False`. Note that transformed variable `sd_log_` is included in the trace, but not shown in the trace plot. The plot function automatically hides transformed variables. "
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"['mu', 'sd_log_', 'sd']\n"
]
},
{
"data": {
"image/png": 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jGuITLjbOdFjx3Lb9cHn8+NF14/G9qUPzLdKAof7qKjjcPuw50IGX3j6AB5de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+MYPqg9h0/31UOWJsYD88dhHAVTiMqw4hw8/aMb8Pc9l/Dpvnps/ugkdn7biKXThncpYSFB9Hb+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\nCAQCIUr+P6WjBjcSktktAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f904c050b70>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"with model:\n",
" trace = pm.variational.sample_vp(v_params, hide_transformed=False)\n",
"pm.traceplot(trace);\n",
"print(trace.varnames)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Posterior predictive check also works as in the original example. "
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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7Y2OjLrnkEhUUFGjatGltfgKn06kNGzaourpa1113nf79738fdRGa5i5K05y4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\nRK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f9047443a58>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ppc = pm.sample_ppc(trace, samples=500, model=model, size=100)\n",
"ax = plt.subplot()\n",
"sns.distplot([n.mean() for n in ppc['n']], kde=False, ax=ax)\n",
"ax.axvline(data.mean())\n",
"ax.set(title='Posterior predictive of the mean', xlabel='mean(x)', ylabel='Frequency');"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.5.1"
},
"widgets": {
"state": {},
"version": "1.1.1"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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