手法を比較

	欠損データを含むハミルトニアン・モンテカルロ法	欠損データを含む変分推論
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	1996–2011	1994–2008
提唱者	Radford M. Neal (HMC, 1996/2011); missing-data treatment via Bayesian data augmentation (Tanner & Wong, 1987)	Ghahramani & Jordan; Wainwright & Jordan (formal foundations)
種類	Bayesian computational sampler	Approximate Bayesian inference
原典	Neal, R. M. (2011). MCMC using Hamiltonian dynamics. In S. Brooks, A. Gelman, G. Jones & X.-L. Meng (Eds.), Handbook of Markov Chain Monte Carlo (pp. 113-162). CRC Press. ISBN: 978-1420079418	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.
別名	HMC with missing data, HMC data augmentation, Bayesian HMC imputation, HMC with data augmentation	VI with missing data, variational EM with missing data, VB missing data, mean-field VI for incomplete data
関連	6	4
概要	Hamiltonian Monte Carlo with missing data extends the gradient-based HMC sampler to handle incomplete observations by treating missing values as additional unknown parameters. The posterior over model parameters and missing values is sampled jointly in one efficient pass, exploiting gradient information to explore the high-dimensional joint space with far fewer rejected proposals than random-walk MCMC.	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.