方法对比
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| 分层贝叶斯推断× | 变分推断× | |
|---|---|---|
| 领域 | 贝叶斯 | 贝叶斯 |
| 方法族 | Bayesian methods | Bayesian methods |
| 起源年份≠ | 1972 (Lindley & Smith); consolidated 1995–2013 | 1999 |
| 提出者≠ | Lindley & Smith; Gelman et al. | Jordan, Ghahramani, Jaakkola & Saul |
| 类型≠ | Bayesian multilevel model | Approximate Bayesian inference |
| 开创性文献≠ | Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. ISBN: 978-1439840955 | 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. DOI ↗ |
| 别名≠ | multilevel Bayesian modeling, Bayesian hierarchical model, nested Bayesian model, partial pooling model | VI, variational Bayes, VB, mean-field variational inference |
| 相关≠ | 6 | 4 |
| 摘要≠ | Hierarchical Bayesian inference is a probabilistic modeling framework that organises parameters into levels, placing priors on the group-level parameters and hyperpriors on the parameters governing those priors. It enables partial pooling of information across groups, balancing the extremes of treating each group as independent or merging them into a single estimate. | 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. |
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