مقایسهٔ روش‌ها

	استنتاج بیزی تقریبی با تمایز خودکار متغیر (ADVI)	انتشار انتظاری (EP)	زنجیره مارکوف مونت کارلو (MCMC)
حوزه	بیزی	بیزی	بیزی
خانواده	Bayesian methods	Bayesian methods	Bayesian methods
سال پیدایش	2017	2001	—
پدیدآور	Kucukelbir, Tran, Ranganath, Gelman, Blei	Thomas P. Minka	—
نوع	Variational inference algorithm	Approximate inference algorithm	Posterior sampling algorithm
منبع بنیادین	Kucukelbir, A., Tran, D., Ranganath, R., Gelman, A. & Blei, D. M. (2017). Automatic differentiation variational inference. Journal of Machine Learning Research, 18(14), 1–45.	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
نام‌های دیگر	ADVI, black-box variational inference, automatic variational inference, gradient-based variational inference	EP, expectation propagation, EP algorithm, assumed-density filtering generalisation	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)
مرتبط	3	3	3
خلاصه	Automatic Differentiation Variational Inference (ADVI) is a black-box algorithm for approximate Bayesian posterior inference, introduced by Kucukelbir, Tran, Ranganath, Gelman, and Blei (2017, JMLR). Given any probabilistic model whose log-joint density is differentiable, ADVI automatically transforms constrained latent variables to unconstrained real space, fits a Gaussian variational family by maximising the evidence lower bound (ELBO) with stochastic gradient ascent, and returns an approximate posterior without model-specific derivations. It is the default variational inference engine in Stan and is available in PyMC and NumPyro.	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.