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Optimal mixture weights in multiple importance sampling
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In multiple importance sampling we combine samples from a finite list of proposal distributions. When those proposal distributions are used to create control variates, it is possible (Owen and Zhou, 2000) to bound the ratio of the resulting variance to that of the unknown best proposal distribution in our list. The minimax regret arises by taking a uniform mixture of proposals, but that is conservative when there are many components. In this paper we optimize the mixture component sampling rates to gain further efficiency. We show that the sampling variance of mixture importance sampling with control variates is jointly convex in the mixture probabilities and control variate regression coefficients. We also give a sequential importance sampling algorithm to estimate the optimal mixture from the sample data.
Forward citations
Cited by 3 Pith papers
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Resampling in conditional SMC algorithms
A general framework for valid resampling in SMC and CSMC that handles most known schemes, including exotic ones, under only weak assumptions and without random permutation of ancestor indices.
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From Minimax Optimal Importance Sampling to Uniformly Ergodic Importance-tempered MCMC
A minimax analysis identifies the optimal importance-sampling proposal for atomic targets, and an exact uniform ergodicity criterion is proved for importance-tempered random-walk Metropolis on polynomial-tail targets.
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Revisiting the balance heuristic for estimating normalising constants
The balance heuristic estimator is recast on an extended space, yielding an unbiased parallel annealed importance sampling scheme and a general framework for estimators when proposal marginals are intractable.
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