Particle Smoothing for Hidden Diffusion Processes: Adaptive Path Integral Smoother
This work addresses a computational bottleneck in particle smoothing for hidden diffusion processes, offering an incremental improvement for researchers in stochastic process inference.
The paper tackled the problem of estimating the smoothing distribution for continuous-time diffusion processes with partial observations, proposing an adaptive importance sampling method based on path integral control theory, which showed more reliable estimations than the standard Forward Filter/Backward Simulator in cases where the smoothing distribution is poorly represented by the filter distribution.
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.