方法对比

	自动微分变分推断 (ADVI)	Bayesian Regression	期望传播 (EP)	马尔可夫链蒙特卡洛 (MCMC)
领域	贝叶斯	贝叶斯	贝叶斯	贝叶斯
方法族	Bayesian methods	Bayesian methods	Bayesian methods	Bayesian methods
起源年份	2017	—	2001	—
提出者	Kucukelbir, Tran, Ranganath, Gelman, Blei	—	Thomas P. Minka	—
类型	Variational inference algorithm	Bayesian linear model	Approximate inference algorithm	Posterior sampling algorithm
开创性文献	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.	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.	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
别名	ADVI, black-box variational inference, automatic variational inference, gradient-based variational inference	bayesian linear regression, probabilistic regression, bayesian regresyon	EP, expectation propagation, EP algorithm, assumed-density filtering generalisation	markov chain monte carlo, MCMC sampling, MCMC (Markov Zinciri Monte Carlo)
相关	3	2	3	3
摘要	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.	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.	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.