Bayesian methods
Variational Inference
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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Sources
- 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: 10.1023/A:1007665907178 ↗
- Blei, D. M., Kucukelbir, A., & McAuliffe, J. D. (2017). Variational inference: A review for statisticians. Journal of the American Statistical Association, 112(518), 859–877. DOI: 10.1080/01621459.2017.1285773 ↗
- Bishop, C. M. (2006). Pattern Recognition and Machine Learning. Springer. (Chapter 10: Approximate Inference.) ISBN: 978-0387310732
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Referenced by
Bayesian Online LearningDynamic Hamiltonian Monte CarloDynamic Variational InferenceExpectation PropagationGibbs SamplingHamiltonian Monte CarloHierarchical Bayesian InferenceHierarchical Markov Chain Monte CarloHierarchical Variational InferenceMCMCMultilevel Bayesian InferenceMultilevel MCMCMultilevel Variational InferenceNo-U-Turn SamplerOnline Gaussian ProcessRobust Bayesian InferenceRobust Bayesian Model AveragingRobust Hamiltonian Monte CarloRobust Variational InferenceSpatial Variational InferenceTime series variational inferenceVariational Inference with Measurement ErrorVariational Inference with Missing Data