手法を比較

	ディリクレ過程混合モデル (Dirichlet Process Mixture Model, DPMM)	潜在的ディリクレ配分法 (LDA)	マルコフ連鎖モンテカルロ法 (MCMC)
分野	ベイズ	機械学習	ベイズ
系統	Bayesian methods	Latent structure	Bayesian methods
提唱年	1973	2003	—
提唱者	Ferguson (1973); mixture model formulation by Lo (1984)	Blei, D. M.; Ng, A. Y.; Jordan, M. I.	—
種類	Nonparametric Bayesian mixture model	Generative probabilistic topic model (three-level hierarchical Bayesian)	Posterior sampling algorithm
原典	Ferguson, T. S. (1973). A Bayesian analysis of some nonparametric problems. The Annals of Statistics, 1(2), 209–230.	Blei, D. M., Ng, A. Y., & Jordan, M. I. (2003). Latent Dirichlet allocation. Journal of Machine Learning Research, 3, 993–1022.	Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. ISBN: 978-1439840955
別名	DPMM, DP mixture model, infinite mixture model, Dirichlet process mixture	LDA, topic model, Blei-Ng-Jordan model, probabilistic topic modeling	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)
関連	3	3	3
概要	The Dirichlet Process Mixture Model (DPMM) is a nonparametric Bayesian clustering method introduced through Ferguson's (1973) Dirichlet process prior that places a probability distribution over distributions. Unlike finite mixture models, the DPMM does not require the analyst to specify the number of clusters in advance; instead it infers the number of components from the data, allowing an effectively unbounded mixture that grows as more observations arrive.	Latent Dirichlet Allocation (LDA) is a generative probabilistic model for collections of discrete data, introduced by Blei, Ng, and Jordan in 2003. It treats each document as a mixture of latent topics and each topic as a probability distribution over words, enabling unsupervised discovery of thematic structure across large text corpora. It is one of the most cited papers in machine learning and natural language processing.	Markov Chain Monte Carlo (MCMC) is a family of computational algorithms for sampling from complex probability distributions, most commonly the posterior distributions that arise in Bayesian inference. Rather than computing posteriors analytically — which is rarely possible for realistic models — MCMC constructs a Markov chain whose stationary distribution is the target posterior and draws dependent samples from it, enabling full probabilistic inference for virtually any model.