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-discretized 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 generalization of the CPF with backward sampling that involves auxiliary “bridging” CPF steps that are parameterized 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.

带反向/祖先采样（backward/ancestor sampling）的条件粒子滤波器（Conditional Particle Filters, CPFs）是一类用于从动态模型（如隐马尔可夫模型（Hidden Markov Model））的隐状态后验分布中采样的强有力方法。然而，这类方法在涉及弱信息观测或慢混合动力学的模型中性能会出现下降。这两种复杂情况在对精细时间离散化的连续时间路径积分模型进行采样时均会出现，且也可能出现在隐马尔可夫模型中。

条件粒子滤波器常用的多项式重采样（multinomial resampling）会在弱信息观测场景下过度重采样，进而引入额外方差。此外，慢混合动力学会使得反向/祖先采样步骤失效，引发采样退化问题。

我们详述了两种适用于弱信息场景的条件重采样策略：即所谓"杀伤性"重采样（killing resampling）与带均值偏序的系统重采样（systematic resampling with mean partial order）。为规避采样退化问题，我们提出了一种带反向采样的条件粒子滤波器的推广框架，该框架引入了由分块序列（blocking sequence）参数化的辅助"桥接"条件粒子滤波器步骤。同时，我们给出了选择合适分块方式的实用调优策略。

实验结果表明，采用合适重采样策略并结合所提出的"桥接反向采样"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。