手法を比較

	ラプラス近似	期待伝播法 (EP)
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	1986	2001
提唱者	Pierre-Simon Laplace (1774); Bayesian formalisation: Tierney & Kadane (1986)	Thomas P. Minka
種類	Analytical posterior approximation	Approximate inference algorithm
原典	Tierney, L. & Kadane, J. B. (1986). Accurate approximations for posterior moments and marginal densities. Journal of the American Statistical Association, 81(393), 82–86.	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.
別名	Laplace's method, saddle-point approximation (Bayesian), second-order Gaussian approximation, LA	EP, expectation propagation, EP algorithm, assumed-density filtering generalisation
関連	3	3
概要	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).	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.