方法对比

	带缺失数据变分推断	缺失数据下的MCMC
领域	贝叶斯	贝叶斯
方法族	Bayesian methods	Bayesian methods
起源年份	1994–2008	1987
提出者	Ghahramani & Jordan; Wainwright & Jordan (formal foundations)	Tanner & Wong (data augmentation); extended by Gelfand & Smith, Rubin
类型	Approximate Bayesian inference	Bayesian computational method
开创性文献	Ghahramani, Z. & Jordan, M. I. (1994). Supervised learning from incomplete data via an EM approach. In Cowan, J. D., Tesauro, G. & Alspector, J. (Eds.), Advances in Neural Information Processing Systems 6 (pp. 120–127). Morgan Kaufmann.	Little, R. J. A. & Rubin, D. B. (2002). Statistical Analysis with Missing Data (2nd ed.). Wiley. ISBN: 978-0471183860
别名	VI with missing data, variational EM with missing data, VB missing data, mean-field VI for incomplete data	MCMC missing data, data augmentation MCMC, Bayesian multiple imputation, MCMC imputation
相关	4	6
摘要	Variational inference with missing data is a scalable Bayesian approach that simultaneously approximates the posterior over latent variables and model parameters while imputing missing observations. Instead of integrating over all possible values of the missing entries exactly, it posits a tractable approximate distribution and optimises it to be as close as possible to the true joint posterior, yielding fast, principled inference even in high-dimensional incomplete datasets.	MCMC with missing data is a Bayesian computational strategy that treats unobserved values as additional unknown parameters. By alternating between sampling the missing values from their predictive distribution and sampling the model parameters from their posterior, the algorithm produces a valid joint posterior that fully accounts for uncertainty introduced by the missingness.