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Abstract:
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The proposal step of Sequential Monte Carlo (SMC) methods such as SMC samplers or particle filters is a key step which critically affects their performances. Bad choices can lead to terrible waste of computational power, variance explosion, and dramatic sample depletion. We introduce new adaptive algorithms for approximating the optimal proposal and backward kernels, accounting for possible multimodality, outlying observations, or even slight errors in the model. Relying on recent theoretical analysis of widely used quality criteria such as the Coefficient of Variation and the entropy of the weights, we minimize a function-free risk criterion between the optimal kernel and a mixture of experts, i.e. a mixture of integrated curved exponential distributions with logistic weights. To this intent, we use powerful tools deeply related to MCEM, cross-entropy, and stochastic approximation.
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