Twisted Particle Filter
Organizer
Speaker
Zeju Sun
Time
Wednesday, September 25, 2024 8:00 PM - 9:00 PM
Venue
Online
Abstract
In this talk, I will review a paper discussing the twisted particle filter. The abstract of this paper is: “The particle filter (PF), also known as the sequential Monte Carlo (SMC), is designed to approximate high-dimensional probability distributions and their normalizing constants in the discrete-time setting. To reduce the variance of the Monte Carlo approximation, several twisted particle filters (TPF) have been proposed by researchers, where one chooses or learns a twisting function that modifies the Markov transition kernel. In this paper, we study the TPF from a continuous-time perspective. Under suitable settings, we show that the discrete-time model converges to a continuous-time limit, which can be solved through a series of well-studied control-based importance sampling algorithms. This discrete-continuous connection allows the design of new TPF algorithms inspired by established continuous-time algorithms. As a concrete example, guided by existing importance sampling algorithms in the continuous-time setting, we propose a novel algorithm called “Twisted-Path Particle Filter” (TPPF), where the twist function, parameterized by neural networks, minimizes specific KL divergence between path measures. Some numerical experiments are given to illustrate the capability of the proposed algorithm.”