手法を比較

	変分推論	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	1999	2003	—
提唱者	Jordan, Ghahramani, Jaakkola & Saul	Blei, D. M.; Ng, A. Y.; Jordan, M. I.	—
種類	Approximate Bayesian inference	Generative probabilistic topic model (three-level hierarchical Bayesian)	Posterior sampling algorithm
原典	Jordan, M. I., Ghahramani, Z., Jaakkola, T. S., & Saul, L. K. (1999). An introduction to variational methods for graphical models. Machine Learning, 37(2), 183–233.	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	VI, variational Bayes, VB, mean-field variational inference	LDA, topic model, Blei-Ng-Jordan model, probabilistic topic modeling	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)
関連	4	3	3
概要	Variational inference (VI) is a family of techniques that turn Bayesian posterior computation into an optimisation problem. Instead of drawing samples from the exact posterior — as Markov chain Monte Carlo does — VI posits a simpler, tractable family of distributions and finds the member of that family closest to the true posterior by maximising the evidence lower bound (ELBO). Introduced in its modern graphical-model form by Jordan, Ghahramani, Jaakkola and Saul (1999) and given a comprehensive statistical treatment by Blei, Kucukelbir and McAuliffe (2017), VI is now the standard scalable inference engine in probabilistic machine learning.	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.