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Auxiliary particle filters (APFs) are a class of sequential Monte Carlo (SMC)methods for Bayesian inference in state-space models. In their originalderivation, APFs operate in an extended state space using an auxiliary variableto improve inference. In this work, we propose optimized auxiliary particlefilters, a framework where the traditional APF auxiliary variables areinterpreted as weights in an importance sampling mixture proposal. Under thisinterpretation, we devise a mechanism for proposing the mixture weights that isinspired by recent advances in multiple and adaptive importance sampling. Inparticular, we propose to select the mixture weights by formulating a convexoptimization problem, with the aim of approximating the filtering posterior ateach timestep. Further, we propose a weighting scheme that generalizes previousresults on the APF (Pitt et al. 2012), proving unbiasedness and consistency ofour estimators. Our framework demonstrates significantly improved estimates ona range of metrics compared to state-of-the-art particle filters at similarcomputational complexity in challenging and widely used dynamical models.

Optimized Auxiliary Particle Filters: adapting mixture proposals via convex optimization