方法对比

	变分推断	期望传播 (EP)	潜在狄利克雷分配 (LDA)	马尔可夫链蒙特卡洛 (MCMC)
领域	贝叶斯	贝叶斯	机器学习	贝叶斯
方法族	Bayesian methods	Bayesian methods	Latent structure	Bayesian methods
起源年份	1999	2001	2003	—
提出者	Jordan, Ghahramani, Jaakkola & Saul	Thomas P. Minka	Blei, D. M.; Ng, A. Y.; Jordan, M. I.	—
类型	Approximate Bayesian inference	Approximate inference algorithm	Generative probabilistic topic model (three-level hierarchical Bayesian)	Posterior sampling algorithm
开创性文献	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.	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
别名	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	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)
相关	4	3	3	3
摘要	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.	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.