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PyMC source program to determine the number of clusters in multi-dimensional data by WBIC.

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bayesian-information-criterion gmm gmm-clustering mcmc pymc wbic

gmm-wbic_with_pymc's Introduction

GMM-WBIC_with_PyMC

PyMC source program to determine the number of clusters in multi-dimensional data by WBIC.

Gaussian Mixture Model(GMM)のWBICを計算するプログラムをPyMCと呼ばれるベイズ推定用のライブラリを用いて実装しました。 用途としては、多次元データの潜在的なクラスタ数の決定などに使用できます。

逆温度つきのGMMの尤度関数をtheanoを使って自前で設計しています。
多次元かつ潜在的に複数のクラスターを持つようなデータに対応しており、テンソルとしてデータを投げればどんなデータでもGMMのWBICが計算できます。

使用したライブラリは以下のとおりです。

・pymc3
・theano

計算の流れ 
Step1 ) GMMの逆温度付き尤度関数を用いたベイズ事後分布からのパラメータをMCMCで生成する。
Step2 ) Step1で生成したパラメータを用いて、通常のGMMの尤度関数(逆温度=1)の期待値(=WBIC)を求める。

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