Optimized Auxiliary Particle Filters: adapting mixture proposals via convex optimization

Understand

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 state space using an auxiliary variable to improve inference.
• In this work, we propose optimized auxiliary particle filters, a framework where the traditional APF auxiliary variables are interpreted as weights in an importance sampling mixture proposal.
• Under this interpretation, we devise a mechanism for proposing the mixture weights that is inspired by recent advances in multiple and adaptive importance sampling.