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Gibbs flow transport for Bayesian inference

Banff International Research Station for Mathematical Innovation and Discovery

In this work, we consider the construction of transport maps between two distributions using flows. In the Bayesian formalism, this ordinary differential equation approach is natural when one introduces a curve of distributions that connects the prior to posterior by tempering the likelihood. We present a novel approximation of the resulting partial differential equation which yields an ordinary differential equation whose drift depends on the full conditional distributions of the posterior. We discuss properties of the Gibbs flow and efficient implementation in practical settings when employing the flow as proposals within sequential Monte Carlo samplers. Gains over state-of-the-art methods at a fixed computational complexity will be illustrated on a variety of applications.

Mathematics; Statistics; Statistical mechanics, structure of matter; Statistical mechanics

video/mp4

Author affiliation: Harvard University

2019-05-13

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/70147

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/