方法对比

	变分推断	Bayesian Regression	期望传播 (EP)	潜在狄利克雷分配 (LDA)
领域	贝叶斯	贝叶斯	贝叶斯	机器学习
方法族	Bayesian methods	Bayesian methods	Bayesian methods	Latent structure
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	Bayesian linear model	Approximate inference algorithm	Generative probabilistic topic model (three-level hierarchical Bayesian)
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.	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	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.
别名	VI, variational Bayes, VB, mean-field variational inference	bayesian linear regression, probabilistic regression, bayesian regresyon	EP, expectation propagation, EP algorithm, assumed-density filtering generalisation	LDA, topic model, Blei-Ng-Jordan model, probabilistic topic modeling
相关	4	2	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.	Bayesian regression is a probabilistic version of linear regression that treats the model parameters as uncertain quantities. Instead of returning a single best-fit estimate, it combines prior knowledge with the observed data to produce a full posterior probability distribution for each parameter, from which credible intervals and predictions are read off.	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.