手法を比較

	欠損データを含む変分推論	欠損値を含むベイズ推論
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	1994–2008	1976–1987
提唱者	Ghahramani & Jordan; Wainwright & Jordan (formal foundations)	Rubin, D. B. (missing-data mechanisms); Tanner & Wong (data augmentation)
種類	Approximate Bayesian inference	Bayesian probabilistic model
原典	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
別名	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
関連	4	6
概要	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.