手法を比較

	変分推論	期待伝播法 (EP)	潜在的ディリクレ配分法 (LDA)
分野	ベイズ	ベイズ	機械学習
系統	Bayesian methods	Bayesian methods	Latent structure
提唱年	1999	2001	2003
提唱者	Jordan, Ghahramani, Jaakkola & Saul	Thomas P. Minka	Blei, D. M.; Ng, A. Y.; Jordan, M. I.
種類	Approximate Bayesian inference	Approximate inference algorithm	Generative probabilistic topic model (three-level hierarchical Bayesian)
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.	Minka, T. P. (2001). Expectation propagation for approximate Bayesian inference. In Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence (UAI-01), pp. 362–369. Morgan Kaufmann.	Blei, D. M., Ng, A. Y., & Jordan, M. I. (2003). Latent Dirichlet allocation. Journal of Machine Learning Research, 3, 993–1022.
別名	VI, variational Bayes, VB, mean-field variational inference	EP, expectation propagation, EP algorithm, assumed-density filtering generalisation	LDA, topic model, Blei-Ng-Jordan model, probabilistic topic modeling
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.	Expectation Propagation (EP) is a deterministic message-passing algorithm for approximate posterior inference in Bayesian models, introduced by Thomas P. Minka at UAI 2001. It iteratively refines a set of local approximate factors — each drawn from the exponential family — so that their product closely matches the true intractable posterior, achieving higher accuracy than mean-field variational inference on many probabilistic machine learning tasks.	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.