Optimized Auxiliary Particle Filters: adapting mixture proposals via convex optimization
| Autor: | Branchini, Nicola, Elvira, Víctor |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. In particular, we propose to select the mixture weights by formulating a convex optimization problem, with the aim of approximating the filtering posterior at each timestep. Further, we propose a weighting scheme that generalizes previous results on the APF (Pitt et al. 2012), proving unbiasedness and consistency of our estimators. Our framework demonstrates significantly improved estimates on a range of metrics compared to state-of-the-art particle filters at similar computational complexity in challenging and widely used dynamical models. Comment: Accepted version at Uncertainty in Artificial Intelligence (UAI) 2021 |
| Databáze: | arXiv |
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