方法对比

	带缺失数据变分推断	变分推断
领域	贝叶斯	贝叶斯
方法族	Bayesian methods	Bayesian methods
起源年份	1994–2008	1999
提出者	Ghahramani & Jordan; Wainwright & Jordan (formal foundations)	Jordan, Ghahramani, Jaakkola & Saul
类型	Approximate Bayesian inference	Approximate Bayesian inference
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.	Jordan, M. I., Ghahramani, Z., Jaakkola, T. S., & Saul, L. K. (1999). An introduction to variational methods for graphical models. Machine Learning, 37(2), 183–233.
别名	VI with missing data, variational EM with missing data, VB missing data, mean-field VI for incomplete data	VI, variational Bayes, VB, mean-field variational inference
相关	4	4
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.	Variational inference (VI) is a family of techniques that turn Bayesian posterior computation into an optimisation problem. Instead of drawing samples from the exact posterior — as Markov chain Monte Carlo does — VI posits a simpler, tractable family of distributions and finds the member of that family closest to the true posterior by maximising the evidence lower bound (ELBO). Introduced in its modern graphical-model form by Jordan, Ghahramani, Jaakkola and Saul (1999) and given a comprehensive statistical treatment by Blei, Kucukelbir and McAuliffe (2017), VI is now the standard scalable inference engine in probabilistic machine learning.