Particle Filtering (PF) methods are an established class of procedures for performing inference in non-linear state-space models. Resampling is a key ingredient of PF, necessary to obtain low variance likelihood and states estimates. However, traditional resampling methods result in PF-based loss functions being non-differentiable with respect to model and PF parameters. In a variational inference context, resampling also yields high variance gradient estimates of the PF-based evidence lower bound. By leveraging optimal transport ideas, we introduce a principled differentiable particle filter and provide convergence results. We demonstrate this novel method on a variety of applications.

翻译：粒子过滤法(PF)是非线性国家空间模型中进行推断的既定程序类别。再抽样是PF的一个关键组成部分,对于获得低差异可能性和国家估计数是必要的。然而,传统的再抽样方法导致基于PF的损失功能在模型和PF参数方面是无法区分的。在变式推断中,再抽样还得出基于PFF的证据较低约束度的高差异梯度估计值。通过利用最佳运输理念,我们引入了有原则的不同粒子过滤器并提供趋同结果。我们在各种应用中展示了这种新颖方法。