方法对比

	带缺失数据变分推断	带缺失数据的吉布斯抽样
领域	贝叶斯	贝叶斯
方法族	Bayesian methods	Bayesian methods
起源年份	1994–2008	1987–1990
提出者	Ghahramani & Jordan; Wainwright & Jordan (formal foundations)	Tanner & Wong (data augmentation), Gelfand & Smith (Gibbs sampler)
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.	Tanner, M. A. & Wong, W. H. (1987). The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association, 82(398), 528–540.
别名	VI with missing data, variational EM with missing data, VB missing data, mean-field VI for incomplete data	data augmentation Gibbs sampler, Gibbs sampler with data augmentation, Bayesian imputation via Gibbs sampling, MCMC missing data 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.	Gibbs sampling with missing data treats unobserved values as additional unknowns alongside model parameters and samples all of them jointly within a Markov chain Monte Carlo loop. The method alternates between drawing the missing values from their conditional distribution given the parameters and drawing the parameters from their conditional distribution given the completed data, producing a posterior over both simultaneously.