方法对比

	贝叶斯在线学习	变分推断
领域	机器学习	贝叶斯
方法族	Machine learning	Bayesian methods
起源年份	1990s–2000s	1999
提出者	Opper, M.; Sato, M. (among key contributors)	Jordan, Ghahramani, Jaakkola & Saul
类型	Probabilistic sequential learning	Approximate Bayesian inference
开创性文献	Opper, M. (1998). A Bayesian approach to on-line learning. In D. Saad (Ed.), On-Line Learning in Neural Networks (pp. 363–378). Cambridge University Press.	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	online Bayesian inference, sequential Bayesian learning, recursive Bayesian estimation, BOL	VI, variational Bayes, VB, mean-field variational inference
相关	6	4
摘要	Bayesian online learning applies Bayesian inference sequentially: each time a new observation arrives, the current posterior over model parameters becomes the prior for the next update. The result is a principled probabilistic framework that maintains calibrated uncertainty estimates throughout, making it well-suited for streaming and non-stationary data settings.	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.