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@taku-y
Created June 14, 2016 10:36
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{
"cells": [
{
"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 seaborn as sns\n",
"\n",
"import pymc3 as pm\n",
"from pymc3.variational.advi import advi, sample_vp\n",
"from pymc3.distributions import transforms\n",
"from pymc3.distributions.continuous import Continuous\n",
"from pymc3.distributions.dist_math import bound"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"class MyBound(object):\n",
" \"\"\"Creates a new bounded distribution\"\"\"\n",
" def __init__(self, distribution, lower=-np.inf, upper=np.inf):\n",
" self.distribution = distribution\n",
" self.lower = lower\n",
" self.upper = upper\n",
" \n",
" def __call__(self, *args, **kwargs):\n",
" first, args = args[0], args[1:]\n",
"\n",
" return MyBounded(first, self.distribution, self.lower, self.upper,\n",
" *args, **kwargs)\n",
"\n",
" def dist(self, *args, **kwargs):\n",
" return MyBounded.dist(self.distribution, self.lower, self.upper,\n",
" *args, **kwargs)\n",
"\n",
"class MyBounded(Continuous):\n",
" \"\"\"A bounded distribution.\"\"\"\n",
" def __init__(self, distribution, lower, upper, transform, *args, **kwargs):\n",
" self.dist = distribution.dist(*args, **kwargs)\n",
"\n",
" self.__dict__.update(self.dist.__dict__)\n",
" self.__dict__.update(locals())\n",
"\n",
" if hasattr(self.dist, 'mode'):\n",
" self.mode = self.dist.mode\n",
" \n",
" if transform == 'interval':\n",
" self.transform = transforms.interval(lower, upper)\n",
"\n",
" def _random(self, lower, upper, point=None, size=None):\n",
" samples = np.zeros(size).flatten()\n",
" i, n = 0, len(samples)\n",
" while i < len(samples):\n",
" sample = self.dist.random(point=point, size=n)\n",
" select = sample[np.logical_and(sample > lower, sample <= upper)]\n",
" samples[i:(i+len(select))] = select[:]\n",
" i += len(select)\n",
" n -= len(select)\n",
" if size is not None:\n",
" return np.reshape(samples, size)\n",
" else:\n",
" return samples\n",
"\n",
" def random(self, point=None, size=None, repeat=None):\n",
" lower, upper = draw_values([self.lower, self.upper], point=point)\n",
" return generate_samples(self._random, lower, upper, point,\n",
" dist_shape=self.shape,\n",
" size=size)\n",
"\n",
" def logp(self, value):\n",
" return bound(self.dist.logp(value),\n",
" value >= self.lower, value <= self.upper)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Applied interval-transform to th and added transformed th_interval to model.\n",
"Iteration 0 [0%]: ELBO = -2.62\n",
"Iteration 1000 [10%]: ELBO = -0.22\n",
"Iteration 2000 [20%]: ELBO = -0.53\n",
"Iteration 3000 [30%]: ELBO = 0.0\n",
"Iteration 4000 [40%]: ELBO = 0.57\n",
"Iteration 5000 [50%]: ELBO = 0.14\n",
"Iteration 6000 [60%]: ELBO = 0.07\n",
"Iteration 7000 [70%]: ELBO = 0.26\n",
"Iteration 8000 [80%]: ELBO = -0.27\n",
"Iteration 9000 [90%]: ELBO = 0.45\n",
"Finished [100%]: ELBO = -0.61\n",
" [-----------------100%-----------------] 2000 of 2000 complete in 1.5 sec"
]
},
{
"data": {
"text/plain": [
"array([[<matplotlib.axes._subplots.AxesSubplot object at 0x7f0bd52bd9e8>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x7f0bd4851978>]], dtype=object)"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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L8N+3zsG8meVZj3WaUq3Fv19cC4cnhOfe2pOY0HI0eu655/D000/jxRdfBABEIhE88MAD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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f0bdd4aac88>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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61xQ/Fi8vwAJD08jWIQQIfKQmcL+eSGWhqeHgkZP4u1YKAqSYGCkWIVAuh/oC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\nCAEAmUzmem02myHwsR/mciwjhJDxiB7tCyyqBSmtVousrCzXe41Gg+b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"text/plain": [
"<matplotlib.figure.Figure at 0x7f0be293c6a0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"with pm.Model() as model:\n",
" boundedNormal = MyBound(pm.Normal, lower=-10, upper=1.0)\n",
" th = boundedNormal('th', mu=0.0, sd=1.0, transform='interval')\n",
" v_params = pm.variational.advi(n=10000)\n",
" traceADVI = pm.variational.sample_vp(v_params, draws=5000)\n",
"\n",
"with pm.Model() as model:\n",
" boundedNormal = pm.Bound(pm.Normal, upper=1.0)\n",
" th = boundedNormal('th', mu=0.0, sd=1.0)\n",
" traceNUTS = pm.sample(2000, pm.NUTS())\n",
"\n",
"pm.traceplot(traceADVI)\n",
"pm.traceplot(traceNUTS)"
]
}
],
"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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