So sánh phương pháp

	Expectation Propagation (EP)	Chuỗi Markov Monte Carlo (MCMC)	Suy diễn biến phân
Lĩnh vực	Bayes	Bayes	Bayes
Họ	Bayesian methods	Bayesian methods	Bayesian methods
Năm ra đời	2001	—	1999
Người khởi xướng	Thomas P. Minka	—	Jordan, Ghahramani, Jaakkola & Saul
Loại	Approximate inference algorithm	Posterior sampling algorithm	Approximate Bayesian inference
Công trình gốc	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.	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	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.
Tên gọi khác	EP, expectation propagation, EP algorithm, assumed-density filtering generalisation	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)	VI, variational Bayes, VB, mean-field variational inference
Liên quan	3	3	4
Tóm tắt	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.	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.	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.