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@dadaromeo
Last active December 24, 2024 07:06
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Implementation of the Conway-Maxwell-Poisson distribution in pymc3
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Conway-Maxwell-Poisson distribution"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I came across a distribution recently for {inter,over}-dispersion and heavy tail count data. The [Conway-Maxwell-Poisson distribution](https://en.wikipedia.org/wiki/Conway%E2%80%93Maxwell%E2%80%93Poisson_distribution).\n",
"\n",
"I think may be it can model the count data for this challenge better. In this notebook, the implementation of the log partition function is an approximation and the implementation of the random number gnerator follow the implementation in the package [Numerics](https://github.com/mathnet/mathnet-numerics/blob/master/src/Numerics/Distributions/ConwayMaxwellPoisson.cs) in C#."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"\n",
"import numpy as np\n",
"from scipy.special import gammaln\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"import pandas as pd\n",
"import theano\n",
"import theano.tensor as tt\n",
"import pymc3 as pm\n",
"from pymc3.distributions.discrete import Discrete, bound, draw_values, generate_samples\n",
"\n",
"theano.config.compute_test_value = \"ignore\"\n",
"np.random.seed(507884)\n",
"sns.set_context(\"talk\")\n",
"sns.set_style(\"darkgrid\")\n",
"sns.set_palette(\"Set2\", 20)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Generate some fake data"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"n,d = 1000, 4\n",
"X = np.abs(np.random.randn(n,d))\n",
"y = np.round(X.sum(axis=1)).astype(int)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"count 1000.000000\n",
"mean 3.192000\n",
"std 1.257266\n",
"min 0.000000\n",
"25% 2.000000\n",
"50% 3.000000\n",
"75% 4.000000\n",
"max 9.000000\n",
"dtype: float64"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pd.Series(y).describe()"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7fc775f73eb8>"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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WLl2qr7/+WgsXLpQkZWVladOmTfr444+1cuVKXXvttZo6dWpV9wMAAGBLFYY6h8OhF198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\ngAEIdQAAAAYg1AEAABiAUAcAAGCA/wNL4gBLGNruzwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fc77f8ab438>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.hist(y, bins=50)\n",
"plt.title(\"Observed data\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### The COM-Poisson model"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"class CMPoisson(Discrete):\n",
" def __init__(self, lamda, nu, *args, **kwargs):\n",
" super(CMPoisson, self).__init__(*args, **kwargs)\n",
" self.lamda = lamda\n",
" self.alpha = tt.power(lamda, 1/nu)\n",
" self.nu = nu\n",
" \n",
" def logp(self, value):\n",
" lamda = self.lamda\n",
" nu = self.nu\n",
" alpha = self.alpha\n",
" pi = tt.constant(np.pi)\n",
" \n",
" log_Z = nu * alpha - ((nu-1)/2)*tt.log(2*pi*alpha) - 0.5*tt.log(nu)\n",
" return bound(value * tt.log(lamda) - nu * tt.gammaln(value+1) - log_Z, lamda > 0, nu > 0)\n",
" \n",
" def _random(self, lamda, nu, size=None):\n",
" size = size or 1\n",
" \n",
" nu = np.atleast_1d(nu)\n",
" alpha = np.atleast_1d(np.power(lamda, 1/nu))\n",
" Z = np.exp(nu * alpha) / ((2 * np.pi * alpha)**((nu-1)/2) * np.sqrt(nu))\n",
" \n",
" U = np.random.uniform(low=0, high=1, size=size)\n",
" values = np.empty(size, dtype=int)\n",
" \n",
" for i in range(U.shape[0]):\n",
" p = 1/Z\n",
" cdf = p\n",
" k = 0\n",
" u = U[i]\n",
" \n",
" while any(u > cdf):\n",
" k += 1\n",
" p = (p * lamda)/k**nu\n",
" cdf += p\n",
" \n",
" values[i] = k\n",
" return values\n",
" \n",
" def random(self, point=None, size=None, repeat=None):\n",
" lamda,nu = draw_values([self.lamda, self.nu], point=point)\n",
" return generate_samples(self._random, lamda, nu, dist_shape=self.shape, size=size)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([1, 1, 2, 0, 2, 2, 2, 1, 1, 2])"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"CMPoisson.dist(lamda=3, nu=2).random(size=10)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Build The model"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Applied log-transform to nu and added transformed nu_log to model.\n"
]
}
],
"source": [
"cmp_model = pm.Model()\n",
"\n",
"with cmp_model:\n",
" alpha = pm.Normal(\"alpha\", mu=1)\n",
" beta = pm.Normal(\"beta\", mu=1, shape=d)\n",
" lam = alpha + tt.dot(X,beta)\n",
" nu = pm.HalfNormal(\"nu\", sd=10)\n",
" \n",
" like = CMPoisson(\"like\", lamda=lam, nu=nu, observed=y)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" [-----------------100%-----------------] 500 of 500 complete in 192.8 sec"
]
}
],
"source": [
"with cmp_model:\n",
" step= pm.NUTS()\n",
" cmp_trace = pm.sample(500, step=step)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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jjn333Xfk5uZy//33M2bMGK677jq++uqreJuaUPWjS07VSi9H66YTP5ymqAxM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m1a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\nCgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fc7d02cf320>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"_ = pm.traceplot(cmp_trace)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Make prediction"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"ppc = pm.sample_ppc(trace=cmp_trace, samples=1, model=cmp_model)[\"like\"][0]"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def predict(X):\n",
" alpha = cmp_trace[\"alpha\"].mean(0)\n",
" beta = cmp_trace[\"beta\"].mean(0)\n",
" nu = cmp_trace[\"nu\"].mean(0)\n",
" \n",
" lam = alpha + np.dot(X, beta)\n",
" \n",
" return CMPoisson.dist(lamda=lam, nu=nu).random()\n",
"\n",
"def score(true, pred):\n",
" \n",
" def rmsle(resp, pred):\n",
" \"\"\"Root Mean Squared Logarithm Error\"\"\"\n",
" n = resp.shape[0]\n",
" return np.sqrt(np.sum(np.square(np.log(pred + 1) - np.log(resp + 1)))/n)\n",
" \n",
" return 1 - rmsle(true, pred)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"pred = predict(X)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"0.42452095913584242"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"score(y, pred)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"0.37200824889126449"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"score(y, ppc)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### References"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Galit Shmuel et al. [A useful distribution for fitting discrete data: revival of the Conway–Maxwell–Poisson distribution](www.galitshmueli.com/system/files/JRSS-COM-Poisson.pdf)\n",
"\n",
"Burc ̧in S ̧ims ̧ek and Satish Iyengar [Approximating the Conway-Maxwell-Poisson normalizing constant](http://www.doiserbia.nb.rs/img/doi/0354-5180/2016/0354-51801604953S.pdf)"
]
},
{
"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": "3.5.2"
},
"widgets": {
"state": {},
"version": "1.1.2"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
@aloctavodia
Copy link

Hi! May be you would like to add this distribution to PyMC3! I interested about learning how this distribution compares with the negative binomial one (that is also used to model over-dispersed data). I was unable to open the first reference it seems that the correct link is www.galitshmueli.com/system/files/JRSS-COM-Poisson.pdf).

@jhurliman
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+1 to adding this to PyMC3

@giamp66
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giamp66 commented Jul 1, 2017

Hi, many thanks for the job done!
When i try to use it with nu less than 1 the code loop forever in the cycle "while any(u > cdf):"
You can try with "CMPoisson.dist(lamda= 1.24598558, nu=0.5681564).random(size=1000)"
I do not have the right mathematical background to solve the problem.
Do you have any guess or direction ?
Thanks a lot!
Regards.

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