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@taku-y
Last active June 27, 2017 09:30
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Mean-field approximation for Dirichlet distribution in stick-breaking transformed space\n",
"The below figures indicate the limitation of the mean-field approximation of Dirichlet distribution. "
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import sys, os\n",
"sys.path.insert(0, os.path.expanduser('~/work/git/github/pymc-devs/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": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Applied stickbreaking-transform to theta and added transformed theta_stickbreaking to model.\n",
" [-----------------100%-----------------] 2000 of 2000 complete in 3.0 sec"
]
},
{
"data": {
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LNWvuSbg2lyz5CqZMqQMA7NjxGhiGwVe+8lWcd94FePfdd3D11VeirMyI733vQQDAgQNN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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f34b6a0c160>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"with pm.Model() as model:\n",
" theta = pm.Dirichlet('theta', a=np.array([1, 100, 100]))\n",
" step = pm.NUTS()\n",
" trace_nuts = pm.sample(2000, step)\n",
" \n",
"theta_sb = trace_nuts['theta_stickbreaking']\n",
"df = pd.DataFrame({'x': theta_sb[:, 0], 'y': theta_sb[:, 1]})\n",
"sns.jointplot(x=\"x\", y=\"y\", data=df);"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1. , 100.6721122 , 100.06815526])"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.mean(trace_nuts['theta'], axis=0) / np.min(np.mean(trace_nuts['theta'], axis=0))"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Applied stickbreaking-transform to theta and added transformed theta_stickbreaking to model.\n",
"Iteration 0 [0%]: ELBO = -9.73\n",
"Iteration 1000 [10%]: Average ELBO = -16.35\n",
"Iteration 2000 [20%]: Average ELBO = -10.88\n",
"Iteration 3000 [30%]: Average ELBO = -6.61\n",
"Iteration 4000 [40%]: Average ELBO = -4.0\n",
"Iteration 5000 [50%]: Average ELBO = -2.52\n",
"Iteration 6000 [60%]: Average ELBO = -1.46\n",
"Iteration 7000 [70%]: Average ELBO = -0.83\n",
"Iteration 8000 [80%]: Average ELBO = -0.64\n",
"Iteration 9000 [90%]: Average ELBO = -0.29\n",
"Finished [100%]: Average ELBO = -0.33\n"
]
},
{
"data": {
"image/png": 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1r2/jS18asg6nT5+BN954m3/9ta99FU8//RzKysoyPj8hh8SKILJk6tRpeO21l/HAA/fi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\nIAjV8/8BPhcmuHhROU0AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f34af086c50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"with pm.Model() as model:\n",
" theta = pm.Dirichlet('theta', a=np.array([1, 100, 100]))\n",
" v_params = pm.advi(n=10000)\n",
" trace_advi = pm.sample_vp(v_params, draws=2000)\n",
" \n",
"theta_sb = trace_advi['theta_stickbreaking']\n",
"df = pd.DataFrame({'x': theta_sb[:, 0], 'y': theta_sb[:, 1]})\n",
"sns.jointplot(x=\"x\", y=\"y\", data=df);"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1. , 74.80203987, 74.99411425])"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.mean(trace_advi['theta'], axis=0) / np.min(np.mean(trace_advi['theta'], axis=0))"
]
}
],
"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": 1
}
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