Guidance for twisted particle filter: a continuous-time perspective

TL;DR

This paper introduces the Twisted-Path Particle Filter, a novel continuous-time algorithm that uses neural networks to optimize twisting functions, improving variance reduction in high-dimensional probability distribution approximation.

Contribution

It proposes a new continuous-time twisted particle filter algorithm with neural network parameterized twisting functions trained via KL-divergence minimization.

Findings

Numerical experiments demonstrate the effectiveness of the proposed TPPF.

The neural network approach enables adaptive twisting function learning.

The method reduces variance in high-dimensional probability approximations.

Abstract

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.