耦合粒子滤波器轨迹研究
On Coupling Particle Filter Trajectories
摘要：
粒子滤波器是对状态空间模型进行推理的强大而灵活的工具。它们涉及通过取样和重新取样步骤的组合，收集随时间演变的样本。重采样步骤是必要的，以确保避免权重退化。在几种统计感兴趣的情况下，重要的是能够比较由两个不同的粒子滤波器产生的估计;因此，能够有效地耦合两个粒子滤波器轨迹通常是至关重要的。在本文中，我们提出了几种方法来做到这一点。特别是，我们利用最佳运输文献的想法。在一般情况下，虽然，计算最佳的运输地图是非常昂贵的计算，为了处理这个问题，我们引入计算上易于处理的近似最佳运输耦合。我们证明，我们得到的算法耦合两个粒子滤波器轨迹往往执行数量级更有效地比更标准的方法。
英文摘要：
Particle filters are a powerful and flexible tool for performing inference on state-space models. They involve a collection of samples evolving over time through a combination of sampling and re-sampling steps. The re-sampling step is necessary to ensure that weight degeneracy is avoided. In several situations of statistical interest, it is important to be able to compare the estimates produced by two different particle filters; consequently, being able to efficiently couple two particle filter trajectories is often of paramount importance. In this text, we propose several ways to do so. In particular, we leverage ideas from the optimal transportation literature. In general, though, computing the optimal transport map is extremely computationally expensive; to deal with this, we introduce computationally tractable approximations to optimal transport couplings. We demonstrate that our resulting algorithms for coupling two particle filter trajectories often perform orders of magnitude more efficiently than more standard approaches.
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