Particle Smoothing for Hidden Diffusion Processes: Adaptive Path Integral Smoother

TL;DR

This paper introduces an adaptive path integral smoother for continuous-time diffusion processes, improving the efficiency and reliability of particle smoothing in stochastic process inference with noisy data.

Contribution

It presents a novel adaptive importance sampling algorithm based on path integral control theory for better estimation of smoothing distributions in diffusion processes.

Findings

Outperforms standard FFBSi in poorly represented smoothing distributions

Uses feedback control to enhance sampling efficiency

Provides more reliable marginal estimates in complex diffusion models

Abstract

Particle smoothing methods are used for inference of stochastic processes based on noisy observations. Typically, the estimation of the marginal posterior distribution given all observations is cumbersome and computational intensive. In this paper, we propose a simple algorithm based on path integral control theory to estimate the smoothing distribution of continuous-time diffusion processes with partial observations. In particular, we use an adaptive importance sampling method to improve the effective sampling size of the posterior over processes given the observations and the reliability of the estimation of the marginals. This is achieved by estimating a feedback controller to sample efficiently from the joint smoothing distributions. We compare the results with estimations obtained from the standard Forward Filter/Backward Simulator for two diffusion processes of different complexity. We show that the proposed method gives more reliable estimations than the standard FFBSi when the smoothing distribution is poorly represented by the filter distribution.