Optimized Auxiliary Particle Filters

Auxiliary particle filters (APFs) are a class of sequential Monte Carlo (SMC) methods for Bayesian inference in state-space models. In their original derivation, APFs operate in an extended space using an auxiliary variable to improve the inference. Later works have re-interpreted APFs from a multiple importance sampling perspective. In this perspective, the proposal is a mixture composed of kernels and weights that are selected by taking into account the latest observation. In this work, we further exploit this perspective by proposing an online, flexible framework for APFs that adapts the mixture proposal by convex optimization and allows for a controllable computational complexity. We minimize the discrepancy between the proposal and the filtering distribution at a set of relevant points, which are chosen by leveraging the structure of SMC. We compare our method to state-of-the-art particle filters, showing better performance in challenging and widely used dynamical models.