Сравнение методов

	Распространение ожидания (EP)	Аппроксимация Лапласа	Вариационный вывод
Область	Байесовские методы	Байесовские методы	Байесовские методы
Семейство	Bayesian methods	Bayesian methods	Bayesian methods
Год появления	2001	1986	1999
Автор метода	Thomas P. Minka	Pierre-Simon Laplace (1774); Bayesian formalisation: Tierney & Kadane (1986)	Jordan, Ghahramani, Jaakkola & Saul
Тип	Approximate inference algorithm	Analytical posterior approximation	Approximate Bayesian inference
Основополагающий источник	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.	Tierney, L. & Kadane, J. B. (1986). Accurate approximations for posterior moments and marginal densities. Journal of the American Statistical Association, 81(393), 82–86.	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.
Другие названия	EP, expectation propagation, EP algorithm, assumed-density filtering generalisation	Laplace's method, saddle-point approximation (Bayesian), second-order Gaussian approximation, LA	VI, variational Bayes, VB, mean-field variational inference
Связанные	3	3	4
Сводка	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.	The Laplace approximation is a classical analytic technique that replaces an intractable posterior distribution with a multivariate Gaussian centred at the posterior mode, using the curvature of the log-posterior at that mode to set the covariance. Formalised for Bayesian statistics by Tierney and Kadane (1986) in their landmark Journal of the American Statistical Association paper, it provides a fast, deterministic alternative to Markov chain Monte Carlo and forms the mathematical core of Integrated Nested Laplace Approximations (INLA).	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.