方法对比

	鲁棒变分推断	马尔可夫链蒙特卡洛 (MCMC)
领域	贝叶斯	仿真
方法族	Bayesian methods	Process / pipeline
起源年份	2008-2018	1953 (Metropolis-Hastings); 1984 (Gibbs)
提出者	Fujisawa & Eguchi (2008); Futami, Sato & Sugiyama (2018)	Metropolis et al. (1953); Gibbs sampler formalised by Geman & Geman (1984)
类型	Robust approximate Bayesian inference	Simulation-based Bayesian inference / numerical integration
开创性文献	Futami, F., Sato, I. & Sugiyama, M. (2018). Variational inference based on robust divergences. Proceedings of the 21st International Conference on Artificial Intelligence and Statistics (AISTATS), PMLR 84:813-822.	Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A. & Rubin, D.B. (2013). Bayesian Data Analysis (3rd ed.). Chapman & Hall/CRC.
别名	RVI, robust VI, outlier-robust variational Bayes, power-divergence variational inference	MCMC, Metropolis-Hastings, Gibbs sampling, Markov Zinciri Monte Carlo (MCMC — Metropolis-Hastings, Gibbs)
相关	6	5
摘要	Robust variational inference (RVI) extends standard variational inference by replacing the Kullback-Leibler divergence with a divergence measure that is less sensitive to outliers and model misspecification — such as the beta-divergence or a Renyi-type divergence. This yields posterior approximations that remain well-behaved even when a fraction of the data departs from the assumed model.	Markov Chain Monte Carlo (MCMC) is a family of simulation algorithms that constructs a Markov chain whose stationary distribution is the target posterior, enabling Bayesian inference and high-dimensional integral computation that would otherwise be analytically intractable. Pioneered by Metropolis and colleagues in 1953 and extended by Hastings in 1970, MCMC underpins modern Bayesian statistics. The two most widely used variants are Metropolis-Hastings, which proposes moves from a general proposal distribution, and Gibbs sampling, which draws each parameter in turn from its full conditional distribution.