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Pymc3 implementation of the Dirichlet-Multinomial distribution
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import seaborn as sns\n",
"import pymc3 as pm\n",
"import numpy as np\n",
"from numpy import random as nr"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# DirichletMultinomial model\n",
"import theano.tensor as tt\n",
"from pymc3.distributions.dist_math import gammaln, bound, factln\n",
"class DirichletMultinomial(pm.Discrete):\n",
" def __init__(self, n, a, *args, **kwargs):\n",
" super(DirichletMultinomial, self).__init__(*args, **kwargs)\n",
"\n",
" self.K = tt.as_tensor_variable(a.shape[-1])\n",
" self.n = tt.as_tensor_variable(n[:, np.newaxis])\n",
"\n",
" if a.ndim == 1:\n",
" self.alphas = tt.as_tensor_variable(a[np.newaxis, :]) # alphas[1, #classes]\n",
" else:\n",
" self.alphas = tt.as_tensor_variable(a) # alphas[#samples, #classes]\n",
"\n",
" self.A = self.alphas.sum(axis=-1, keepdims=True) # A[#samples]\n",
" self.mean = self.n * (self.alphas / self.A)\n",
"\n",
" self.mode = tt.cast(pm.math.tround(self.mean), 'int32')\n",
"\n",
" def logp(self, value):\n",
" printing = False\n",
" k = self.K\n",
" a = self.alphas\n",
" A = self.A\n",
" n = self.n\n",
" res = bound(tt.squeeze(factln(n) + gammaln(A) - gammaln(A + n) +\n",
" tt.sum(gammaln(a + value) - gammaln(a) - factln(value), keepdims=True, axis=-1)),\n",
" tt.all(value >= 0),\n",
" tt.all(tt.eq(tt.sum(value, axis=-1, keepdims=True), n)),\n",
" tt.all(a > 0),\n",
" k > 1,\n",
" tt.all(tt.ge(n, 0)),\n",
" broadcast_conditions=False\n",
" )\n",
" return res\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Generate simple data (n constant)"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(200, 4)\n"
]
}
],
"source": [
"N = 200\n",
"#D = 4\n",
"d1 = np.array([5, 7, 1, 0.5])\n",
"d2 = np.array([8, 12, 5, 10])\n",
"\n",
"alphas = np.concatenate([np.repeat(d1[np.newaxis, :], N/2, axis=0), np.repeat(d2[np.newaxis, :], N/2, axis=0)])\n",
"print(alphas.shape)\n",
"#ndraws = 2000\n",
"#data_alpha = 1\n",
"#data_beta = 1/2\n",
"ndraws = np.random.randint(1, 1000, size=N)\n",
"#alphas = nr.gamma(data_alpha, 1/data_beta, size=(N, D))\n",
"\n",
"dirichlets = np.array([nr.dirichlet(alpha) for alpha in alphas])\n",
"data = np.array([nr.multinomial(n, p) for p, n in zip(dirichlets, ndraws)])\n",
"#data = np.array([nr.multinomial(ndraws, p) for p in dirichlets])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Test explicit model"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(1, 4)\n",
"(100, 4)\n",
"(200, 4)\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using advi+adapt_diag...\n",
"Average Loss = 2,741.7: 12%|█▏ | 24556/200000 [00:22<02:31, 1154.94it/s]\n",
"Convergence archived at 24600\n",
"Interrupted at 24,600 [12%]: Average Loss = 6,946.9\n",
" 0%| | 0/1800 [00:00<?, ?it/s]INFO (theano.gof.compilelock): Refreshing lock /Users/maexlich/.theano/compiledir_Darwin-16.3.0-x86_64-i386-64bit-i386-3.6.1-64/lock_dir/lock\n",
"100%|█████████▉| 1797/1800 [00:33<00:00, 64.81it/s]/Users/maexlich/.miniconda/envs/bayesian_microbiome/lib/python3.6/site-packages/pymc3/step_methods/hmc/nuts.py:473: UserWarning: Chain 0 contains 19 diverging samples after tuning. If increasing `target_accept` does not help try to reparameterize.\n",
" % (self._chain_id, n_diverging))\n",
"100%|██████████| 1800/1800 [00:33<00:00, 53.47it/s]\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"alphas:\n",
"\n",
" Mean SD MC Error 95% HPD interval\n",
" -------------------------------------------------------------------\n",
" ..............................[0, :]...............................\n",
" 5.777 0.590 0.022 [4.653, 6.962]\n",
" 7.728 0.781 0.031 [6.047, 9.120]\n",
" 1.057 0.112 0.004 [0.846, 1.272]\n",
" 0.514 0.060 0.002 [0.397, 0.633]\n",
" ..............................[1, :]...............................\n",
" 8.122 0.751 0.032 [6.848, 9.688]\n",
" 12.476 1.163 0.050 [10.270, 14.836]\n",
" 5.227 0.500 0.020 [4.418, 6.363]\n",
" 10.142 0.935 0.041 [8.286, 11.976]\n",
"\n",
" Posterior quantiles:\n",
" 2.5 25 50 75 97.5\n",
" |--------------|==============|==============|--------------|\n",
" .............................[0, :].............................\n",
" 4.693 5.375 5.740 6.181 7.057\n",
" 6.257 7.185 7.722 8.241 9.355\n",
" 0.847 0.985 1.053 1.130 1.280\n",
" 0.402 0.472 0.510 0.555 0.642\n",
" .............................[1, :].............................\n",
" 6.803 7.614 8.075 8.607 9.674\n",
" 10.346 11.710 12.395 13.249 14.928\n",
" 4.258 4.871 5.205 5.555 6.294\n",
" 8.369 9.518 10.076 10.761 12.096\n",
"\n"
]
},
{
"data": {
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WoZHOJHYUVEJKTF0bE6k1r0ZOz5LWBwUf4lXKPM8HD9AlviswtXETKhQUADW3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\nZp5aScWv1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xPXFThhbQ8nriu0elf2hcjzqNx3L1GthgwDQs9jcmYHYbkM1Ro9lSpnlis8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\nCQkJ+8j/D8nB8oNVXP4BAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1157868d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"with pm.Model() as model:\n",
" lowerbound = pm.Bound(pm.Flat, lower=0)\n",
" a = lowerbound('alphas', shape=(2, int(alphas.shape[1])))\n",
" a1padded = tt.shape_padleft(a[0])\n",
" a2padded = tt.shape_padleft(a[1])\n",
" print(a1padded.tag.test_value.shape)\n",
" d1s = tt.repeat(a1padded, int(N/2), axis=0)\n",
" d2s = tt.repeat(a2padded, int(N/2), axis=0)\n",
" print(d1s.tag.test_value.shape)\n",
" aconcat = tt.concatenate([d1s, d2s], axis=0)\n",
" print(aconcat.tag.test_value.shape)\n",
" d = pm.Dirichlet('dirichlets', aconcat, shape=(N, alphas.shape[1]))\n",
" obs = pm.Multinomial('data', n=ndraws[:, np.newaxis], p=d, observed=data)\n",
"\n",
"with model:\n",
" #step = pm.Metropolis()\n",
" trace = pm.sample(tune=800, draws=1000)\n",
" pm.traceplot(trace, ['alphas'])\n",
" pm.summary(trace, ['alphas'])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Test implicit model"
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using advi+adapt_diag...\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"(1, 4)\n",
"(100, 4)\n",
"(200, 4)\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"Average Loss = 2,753.7: 7%|▋ | 14413/200000 [00:05<01:02, 2975.60it/s]\n",
"Convergence archived at 14600\n",
"Interrupted at 14,600 [7%]: Average Loss = 2,934.9\n",
"100%|██████████| 1800/1800 [00:13<00:00, 135.19it/s]\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"alphas:\n",
"\n",
" Mean SD MC Error 95% HPD interval\n",
" -------------------------------------------------------------------\n",
" ..............................[0, :]...............................\n",
" 5.762 0.573 0.021 [4.552, 6.828]\n",
" 7.731 0.785 0.030 [6.106, 9.142]\n",
" 1.052 0.110 0.004 [0.832, 1.255]\n",
" 0.515 0.060 0.002 [0.401, 0.630]\n",
" ..............................[1, :]...............................\n",
" 8.167 0.791 0.036 [6.624, 9.703]\n",
" 12.536 1.175 0.054 [9.998, 14.543]\n",
" 5.253 0.521 0.023 [4.278, 6.303]\n",
" 10.166 0.964 0.040 [8.301, 11.994]\n",
"\n",
" Posterior quantiles:\n",
" 2.5 25 50 75 97.5\n",
" |--------------|==============|==============|--------------|\n",
" .............................[0, :].............................\n",
" 4.662 5.389 5.735 6.112 6.992\n",
" 6.255 7.162 7.696 8.231 9.388\n",
" 0.855 0.976 1.047 1.123 1.284\n",
" 0.402 0.475 0.512 0.554 0.634\n",
" .............................[1, :].............................\n",
" 6.730 7.638 8.135 8.660 9.859\n",
" 10.413 11.719 12.466 13.286 15.083\n",
" 4.330 4.882 5.215 5.566 6.364\n",
" 8.426 9.519 10.113 10.774 12.278\n",
"\n"
]
},
{
"data": {
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hm3pQox7U9o3iHAWr7XLVfgnYPzoEg45T//PSOiD6NUwyZWC13dE6oTEO1ex8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\ngg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11fef6be0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"with pm.Model() as implicit_model:\n",
" lowerbound = pm.Bound(pm.Flat, lower=0)\n",
" a = lowerbound('alphas', shape=(2, int(alphas.shape[1])))\n",
" a1padded = tt.shape_padleft(a[0])\n",
" a2padded = tt.shape_padleft(a[1])\n",
" print(a1padded.tag.test_value.shape)\n",
" d1s = tt.repeat(a1padded, int(N/2), axis=0)\n",
" d2s = tt.repeat(a2padded, int(N/2), axis=0)\n",
" print(d1s.tag.test_value.shape)\n",
" aconcat = tt.concatenate([d1s, d2s], axis=0)\n",
" print(aconcat.tag.test_value.shape)\n",
" n=ndraws#np.array([ndraws]*N)\n",
" obs = DirichletMultinomial('data', n=n, a=aconcat, observed=data)\n",
"\n",
"with implicit_model:\n",
" #step=pm.Metropolis()\n",
" implicit_trace = pm.sample(tune=800, draws=1000)\n",
" pm.traceplot(implicit_trace, ['alphas'])\n",
" pm.summary(implicit_trace, ['alphas'])"
]
}
],
"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": "3.6.1"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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