Bayesian Analysis

Fixed-Form Variational Posterior Approximation through Stochastic Linear Regression

Tim Salimans and David A. Knowles

Full-text: Open access

Abstract

We propose a general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribution. Our method can be used to approximate any posterior distribution, provided that it is given in closed form up to the proportionality constant. The approximation can be any distribution in the exponential family or any mixture of such distributions, which means that it can be made arbitrarily precise. Several examples illustrate the speed and accuracy of our approximation method in practice.

Article information

Source
Bayesian Anal. Volume 8, Number 4 (2013), 837-882.

Dates
First available in Project Euclid: 4 December 2013

Permanent link to this document
https://projecteuclid.org/euclid.ba/1386166315

Digital Object Identifier
doi:10.1214/13-BA858

Mathematical Reviews number (MathSciNet)
MR3150471

Zentralblatt MATH identifier
1329.62142

Keywords
variational Bayes approximate inference stochastic approximation

Citation

Salimans, Tim; Knowles, David A. Fixed-Form Variational Posterior Approximation through Stochastic Linear Regression. Bayesian Anal. 8 (2013), no. 4, 837--882. doi:10.1214/13-BA858. https://projecteuclid.org/euclid.ba/1386166315.


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