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@xjing76
Created March 8, 2022 22:05
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import pymc3 as pm\n",
"import theano.tensor as at\n",
"import arviz as az\n",
"from pymc3_hmm.step_methods import HSStep\n",
"from pymc3_hmm.distributions import HorseShoe\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"# toy data set up\n",
"np.random.seed(2032)\n",
"M = 5\n",
"N = 50\n",
"X = np.random.normal(size=N * M).reshape((N, M))\n",
"# Design matrix with intercept in first col\n",
"X[:, 0] = 1\n",
"beta_true = np.array([5, 1, 0, 1, 0])\n",
"true_alpha = 20\n",
"y_nb = pm.NegativeBinomial.dist(np.exp(X.dot(beta_true)), true_alpha).random()\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Model 1 : Given true alpha\n",
"\n",
"When given true alpha beta samples are converaged very well. It it very close to `true beta`."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/jingx/Documents/pymc3-hmm/pymc3_hmm/distributions.py:481: UserWarning: logp of HorseShoe class is not implemented.Do not use this distribution without the `HSStep` sampler!\n",
" warnings.warn(\n",
"/Users/jingx/Documents/pymc3-hmm/pymc3_hmm/distributions.py:481: UserWarning: logp of HorseShoe class is not implemented.Do not use this distribution without the `HSStep` sampler!\n",
" warnings.warn(\n",
"Only 100 samples in chain.\n",
"Sequential sampling (1 chains in 1 job)\n",
"HSStep: [beta]\n"
]
},
{
"data": {
"text/html": [
"\n",
" <div>\n",
" <style>\n",
" /* Turns off some styling */\n",
" progress {\n",
" /* gets rid of default border in Firefox and Opera. */\n",
" border: none;\n",
" /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
" background-size: auto;\n",
" }\n",
" .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
" background: #F44336;\n",
" }\n",
" </style>\n",
" <progress value='1100' class='' max='1100' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
" 100.00% [1100/1100 00:06<00:00 Sampling chain 0, 0 divergences]\n",
" </div>\n",
" "
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"Sampling 1 chain for 1_000 tune and 100 draw iterations (1_000 + 100 draws total) took 6 seconds.\n"
]
},
{
"data": {
"text/plain": [
"array([[<AxesSubplot:title={'center':'beta'}>,\n",
" <AxesSubplot:title={'center':'beta'}>]], dtype=object)"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 864x144 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"N_draws = 100\n",
"with pm.Model():\n",
" beta = HorseShoe(\"beta\", tau=1, shape=M)\n",
" pm.NegativeBinomial(\"y\", mu=at.exp(beta.dot(X.T)), alpha=true_alpha, observed=y_nb)\n",
" step = [HSStep([beta])]\n",
" trace1 = pm.sample(\n",
" draws=N_draws,\n",
" step=step,\n",
" chains=1,\n",
" return_inferencedata=True,\n",
" compute_convergence_checks=False,\n",
" )\n",
"\n",
"beta_samples = trace1.posterior[\"beta\"][0].values \n",
"np.testing.assert_allclose(beta_samples.mean(0), beta_true, atol=0.1)\n",
"\n",
"az.plot_trace(trace1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Model 2 : Normal Alpha with given testval == True_alpha\n",
"\n",
"When we convert the alpha to a random variable and sample with NUTS, the converaged of beta stays the same. However the converaged with alpha is not optimal. It seems like always overshooting about 20%"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/jingx/Documents/pymc3-hmm/pymc3_hmm/distributions.py:481: UserWarning: logp of HorseShoe class is not implemented.Do not use this distribution without the `HSStep` sampler!\n",
" warnings.warn(\n",
"Only 100 samples in chain.\n",
"Sequential sampling (1 chains in 1 job)\n",
"CompoundStep\n",
">HSStep: [beta]\n",
">NUTS: [alpha]\n"
]
},
{
"data": {
"text/html": [
"\n",
" <div>\n",
" <style>\n",
" /* Turns off some styling */\n",
" progress {\n",
" /* gets rid of default border in Firefox and Opera. */\n",
" border: none;\n",
" /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
" background-size: auto;\n",
" }\n",
" .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
" background: #F44336;\n",
" }\n",
" </style>\n",
" <progress value='1100' class='' max='1100' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
" 100.00% [1100/1100 00:07<00:00 Sampling chain 0, 0 divergences]\n",
" </div>\n",
" "
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"Sampling 1 chain for 1_000 tune and 100 draw iterations (1_000 + 100 draws total) took 8 seconds.\n"
]
},
{
"data": {
"text/plain": [
"0.020431673196215173"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"N_draws = 100\n",
"with pm.Model():\n",
" beta = HorseShoe(\"beta\", tau=1, shape=M)\n",
" alpha = pm.Normal(\"alpha\", mu=true_alpha, sd=true_alpha/2, testval =true_alpha)\n",
" pm.NegativeBinomial(\"y\", mu=at.exp(beta.dot(X.T)), alpha=alpha, observed=y_nb)\n",
" step = [HSStep([beta]), pm.NUTS(alpha)]\n",
" trace2 = pm.sample(\n",
" draws=N_draws,\n",
" step=step,\n",
" chains=1,\n",
" return_inferencedata=True,\n",
" compute_convergence_checks=False,\n",
" )\n",
"# \n",
"beta_samples = trace2.posterior[\"beta\"][0].values \n",
"np.testing.assert_allclose(beta_samples.mean(0), beta_true, atol=0.1)\n",
"\n",
"np.abs(trace2.posterior.alpha.values[0].mean(0) - true_alpha) / true_alpha\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[<AxesSubplot:title={'center':'beta'}>,\n",
" <AxesSubplot:title={'center':'beta'}>],\n",
" [<AxesSubplot:title={'center':'alpha'}>,\n",
" <AxesSubplot:title={'center':'alpha'}>]], dtype=object)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x288 with 4 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"az.plot_trace(trace2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Model 3 : Same set up without testval\n",
"\n",
"It is pretty much just like model 2."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/jingx/Documents/pymc3-hmm/pymc3_hmm/distributions.py:481: UserWarning: logp of HorseShoe class is not implemented.Do not use this distribution without the `HSStep` sampler!\n",
" warnings.warn(\n",
"Only 100 samples in chain.\n",
"Sequential sampling (1 chains in 1 job)\n",
"CompoundStep\n",
">HSStep: [beta]\n",
">NUTS: [alpha]\n"
]
},
{
"data": {
"text/html": [
"\n",
" <div>\n",
" <style>\n",
" /* Turns off some styling */\n",
" progress {\n",
" /* gets rid of default border in Firefox and Opera. */\n",
" border: none;\n",
" /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
" background-size: auto;\n",
" }\n",
" .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
" background: #F44336;\n",
" }\n",
" </style>\n",
" <progress value='1100' class='' max='1100' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
" 100.00% [1100/1100 00:07<00:00 Sampling chain 0, 0 divergences]\n",
" </div>\n",
" "
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"Sampling 1 chain for 1_000 tune and 100 draw iterations (1_000 + 100 draws total) took 8 seconds.\n"
]
},
{
"data": {
"text/plain": [
"0.03075310348473472"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"N_draws = 100\n",
"with pm.Model():\n",
" beta = HorseShoe(\"beta\", tau=1, shape=M)\n",
" alpha = pm.Normal(\"alpha\", mu=true_alpha, sd=true_alpha/2)\n",
" pm.NegativeBinomial(\"y\", mu=at.exp(beta.dot(X.T)), alpha=alpha, observed=y_nb)\n",
" step = [HSStep([beta]), pm.NUTS(alpha)]\n",
" trace3 = pm.sample(\n",
" draws=N_draws,\n",
" step=step,\n",
" chains=1,\n",
" return_inferencedata=True,\n",
" compute_convergence_checks=False,\n",
" )\n",
"# \n",
"beta_samples = trace3.posterior[\"beta\"][0].values \n",
"np.testing.assert_allclose(beta_samples.mean(0), beta_true, atol=0.1)\n",
"\n",
"\n",
"# Mean absolute relative error @ around 20%\n",
"np.abs(trace3.posterior.alpha.values[0].mean(0) - true_alpha) / true_alpha\n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[<AxesSubplot:title={'center':'beta'}>,\n",
" <AxesSubplot:title={'center':'beta'}>],\n",
" [<AxesSubplot:title={'center':'alpha'}>,\n",
" <AxesSubplot:title={'center':'alpha'}>]], dtype=object)"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 864x288 with 4 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"az.plot_trace(trace3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Model 4: When true beta is used\n",
"\n",
"When true beta is provided the alpha does seem to be converging better but yet it still tends to overshoot. "
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Only 100 samples in chain.\n",
"Sequential sampling (1 chains in 1 job)\n",
"NUTS: [alpha]\n"
]
},
{
"data": {
"text/html": [
"\n",
" <div>\n",
" <style>\n",
" /* Turns off some styling */\n",
" progress {\n",
" /* gets rid of default border in Firefox and Opera. */\n",
" border: none;\n",
" /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
" background-size: auto;\n",
" }\n",
" .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
" background: #F44336;\n",
" }\n",
" </style>\n",
" <progress value='1100' class='' max='1100' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
" 100.00% [1100/1100 00:01<00:00 Sampling chain 0, 0 divergences]\n",
" </div>\n",
" "
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"Sampling 1 chain for 1_000 tune and 100 draw iterations (1_000 + 100 draws total) took 1 seconds.\n"
]
},
{
"data": {
"text/plain": [
"0.0243349563951746"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"N_draws = 100\n",
"with pm.Model():\n",
" alpha = pm.Normal(\"alpha\", mu=true_alpha, sd=true_alpha/2)\n",
" pm.NegativeBinomial(\"y\", mu=at.exp(beta_true.dot(X.T)), alpha=alpha, observed=y_nb)\n",
" step = [pm.NUTS(alpha)]\n",
" trace4 = pm.sample(\n",
" draws=N_draws,\n",
" step=step,\n",
" chains=1,\n",
" return_inferencedata=True,\n",
" compute_convergence_checks=False,\n",
" )\n",
"\n",
"# Mean absolute relative error @ around 20%\n",
"np.abs(trace4.posterior.alpha.values[0].mean(0) - true_alpha) / true_alpha\n"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[<AxesSubplot:title={'center':'alpha'}>,\n",
" <AxesSubplot:title={'center':'alpha'}>]], dtype=object)"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x144 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"az.plot_trace(trace4)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "pmd2",
"language": "python",
"name": "pmd2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.5"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
@brandonwillard
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brandonwillard commented Mar 8, 2022

The following will produce trace plots for each dimension in beta and superimpose the corresponding true values:

az.plot_trace(
    trace1,
    compact=False,
    lines=[
        ("beta", {"beta_dim_0": dim}, [true_val])
        for dim, true_val in enumerate(beta_true)
    ],
)

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