论文标题
优化的辅助粒子过滤器：通过凸优化调整混合物建议
Optimized Auxiliary Particle Filters: adapting mixture proposals via convex optimization
论文作者
论文摘要
辅助粒子过滤器（APF）是一类用于状态空间模型中贝叶斯推断的顺序蒙特卡洛（SMC）方法。在其原始推导中，APFS使用辅助变量在扩展状态空间中运行以改进推理。在这项工作中，我们提出了优化的辅助粒子过滤器，该框架将传统的APF辅助变量解释为重量采样混合物建议中的权重。在这种解释下，我们设计了一种提出混合物权重的机制，该机制受到最新和适应性重要性采样的最新进展的启发。特别是，我们建议通过制定凸优化问题来选择混合物权重，以近似每个时间步中的过滤后验。此外，我们提出了一种加权方案，该方案将先前的结果推广到APF（Pitt等，2012），证明了我们的估计器的无偏见和一致性。我们的框架表明，与最新的粒子过滤器相比，在具有挑战性和广泛使用的动态模型中，与最先进的粒子过滤器相比，对一系列指标的估计值有了显着改善。
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.
