The particle filter (PF), also known as sequential Monte Carlo (SMC), approximates high-dimensional probability distributions and their normalizing constants in the discrete-time setting. To reduce the variance of the Monte Carlo approximation, various twisted particle filters (TPFs) have been proposed, in which a twisting function is chosen or learned to modify the Markov transition kernel. Guided by existing control-based importance sampling algorithms in the continuous-time setting, we propose a novel algorithm called the ``Twisted-Path Particle Filter'' (TPPF), in which the twisting function is parameterized by a neural network and trained to minimize a specific KL-divergence between path measures. Numerical experiments illustrate the capability of the proposed algorithm.

翻译：粒子滤波器（PF），也称为序列蒙特卡洛（SMC），可近似离散时间设置中的高维概率分布及其归一化常数。为降低蒙特卡洛近似的方差，研究者提出了多种扭转变形粒子滤波器（TPF），通过选择或学习扭转函数来修改马尔可夫转移核。受连续时间设置中现有基于控制的重要性采样算法启发，我们提出一种名为“扭转变形路径粒子滤波器”（TPPF）的新算法，其中扭转函数由神经网络参数化，并通过最小化路径测度间的特定KL散度进行训练。数值实验展示了所提算法的有效性。