Transport Monte Carlo
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In Bayesian inference, transport map is a promising alternative to the canonical Markov chain Monte Carlo for posterior estimation: it uses optimization to find a deterministic map from an easy-to-sample reference distribution to the posterior. However, often the invertible map does not exist between the two distributions and can be difficult to parameterize with sufficient flexibility. Motivated to address these issues and substantially simplify its use, we propose Transport Monte Carlo. Instead of relying on a single deterministic map, we consider a coupling joint distribution modeled by a non-parametric mixture of several maps. Such a coupling is guaranteed to exist between the reference and posterior distributions. To automate the map parameterization and estimation, we use the invertible neural networks to replace the manual design procedure. Once the coupling is estimated, one can rapidly generate a large number of samples that are completely independent. With a carefully chosen reference distribution, the difference between the generated samples and the exact posterior is negligibly small. Both theoretic and empirical results demonstrate its advantages for solving common but challenging sampling problems.
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