Particle filters are a frequent choice for inference tasks in nonlinear and non-Gaussian state-space models. They can either be used for state inference by approximating the filtering distribution or for parameter inference by approximating the marginal data (observation) likelihood. A good proposal distribution and a good resampling scheme are crucial to obtain low variance estimates. However, traditional methods like multinomial resampling introduce nondifferentiability in PF-based loss functions for parameter estimation, prohibiting gradient-based learning tasks. This work proposes a differentiable resampling scheme by deterministic sampling from an empirical cumulative distribution function. We evaluate our method on parameter inference tasks and proposal learning.

翻译：粒子滤波是处理非线性和非高斯状态空间模型中推理任务的常用方法。该方法既可通过近似滤波分布实现状态推理，也可通过近似边际数据（观测）似然进行参数推断。良好的提议分布与重采样方案对于获得低方差估计至关重要。然而，传统方法（如多项式重采样）会导致基于粒子滤波的损失函数出现不可微性，从而阻碍基于梯度的学习任务。本文提出一种通过确定性采样经验累积分布函数的可微分重采样方案，并在参数推断任务和提议学习任务中验证了该方法的有效性。