Conditional particle filters with bridge backward sampling

Conditional particle filters (CPFs) with backward/ancestor sampling are powerful methods for sampling from the posterior distribution of the latent states of a dynamic model such as a hidden Markov model. However, the performance of these methods deteriorates with models involving weakly informative observations and/or slowly mixing dynamics. Both of these complications arise when sampling finely time-discretised continuous-time path integral models, but can occur with hidden Markov models too. Multinomial resampling, which is commonly employed with CPFs, resamples excessively for weakly informative observations and thereby introduces extra variance. Furthermore, slowly mixing dynamics render the backward/ancestor sampling steps ineffective, leading to degeneracy issues. We detail two conditional resampling strategies suitable for the weakly informative regime: the so-called ‘killing’ resampling and the systematic resampling with mean partial order. To avoid the degeneracy issues, we introduce a generalisation of the CPF with backward sampling that involves auxiliary ‘bridging’ CPF steps that are parameterised by a blocking sequence. We present practical tuning strategies for choosing an appropriate blocking. Our experiments demonstrate that the CPF with a suitable resampling and the developed ‘bridge backward sampling’ can lead to substantial efficiency gains in the weakly informative and slow mixing regime. Supplementary materials for this article are available online.

带有后向/祖先采样的条件粒子滤波器（CPFs）是一类用于从隐马尔可夫模型（Hidden Markov Model）等动态模型的隐状态后验分布中采样的高效方法。然而，这类方法在处理含弱信息观测或慢混合动力学的模型时性能会出现退化。这两类复杂场景既会出现在精细时间离散化的连续时间路径积分模型的采样任务中，也可能在隐马尔可夫模型中出现。
当前条件粒子滤波器常用的多项式重采样方法，在面对弱信息观测时会进行过度重采样，进而引入额外方差；此外，慢混合动力学会使得后向/祖先采样步骤失效，最终引发退化问题。
针对弱信息场景，本文详细介绍了两种适配的条件重采样策略：即所谓的‘杀伤性’重采样，以及带均值偏序的系统重采样。为解决退化问题，我们提出了一种带后向采样的条件粒子滤波器的改进版本，其核心是引入由分块序列参数化的辅助‘桥接’CPF步骤，并给出了选取合理分块方式的实用调优策略。
实验结果表明，搭配合适重采样策略与本文提出的‘桥接后向采样’的条件粒子滤波器，在弱信息与慢混合场景下可实现显著的效率提升。本文的补充材料可在线获取。