方法对比

	带缺失数据变分推断	缺失数据的贝叶斯推断
领域	贝叶斯	贝叶斯
方法族	Bayesian methods	Bayesian methods
起源年份	1994–2008	1976–1987
提出者	Ghahramani & Jordan; Wainwright & Jordan (formal foundations)	Rubin, D. B. (missing-data mechanisms); Tanner & Wong (data augmentation)
类型	Approximate Bayesian inference	Bayesian probabilistic model
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-Interscience. ISBN: 978-0471183860
别名	VI with missing data, variational EM with missing data, VB missing data, mean-field VI for incomplete data	Bayesian missing data analysis, Bayesian data augmentation, Bayesian imputation, missing data Bayesian model
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.	Bayesian inference with missing data treats unobserved values as unknown parameters and integrates them out of the posterior distribution. Rather than deleting or ad hoc imputing incomplete records, the method jointly models observed and missing data under an explicit missing-data mechanism, producing fully calibrated posterior uncertainty that honestly reflects what the data cannot tell us.