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Abstract:
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Bridge sampling is an effective Monte Carlo method for estimating the ratio of normalizing constants of two probability densities. The Monte Carlo error of the bridge sampling estimator is determined by the amount of overlap between the two densities. In the case of uni-modal densities, the Warp-I, II, and III transformations (Meng and Schilling, 2002) are effective for increasing the initial overlap, but they are less effective in the case of multi-modal densities. We introduce Warp-U stochastic transformations that aim to transform multi-modal densities into uni-modal ones without altering their normalizing constants. We prove that our transformation increases overlap, as measured by any f-divergence. We then illustrate our method using 10 and 50 dimensional highly irregular multi-modal densities, and demonstrate how Warp-U sampling can be used to improve the final estimation step of the Generalized Wang-Landau algorithm (Liang, 2005), a powerful sampling and estimation approach. We also discuss how Warp-U transformation can be used to more efficiently sample from multi-modal densities.
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