Particle Smoothing for Hidden Diffusion Processes: Adaptive Path Integral Smoother

Smoothing methods are used for inference of stochastic processes given noisy observations. The estimation of the marginal posterior distribution given all observations is typically a computationally intensive task. We propose a novel algorithm based on path integral control theory to efficiently estimate the smoothing distribution of continuous-time diffusion processes from partial observations. In particular, we use an adaptive importance sampling method to improve the effective sampling size of the posterior and the reliability of the estimation of the marginals. This is achieved by estimating a feedback controller, together with an adaptive initialization and an annealing scheme to sample efficiently from the joint smoothing distribution. We compare the results with estimations obtained from the standard Forward Filter/Backward Simulator (FFBSi) for two diffusion processes of different complexity. We show that the proposed method gives more accurate estimates than the standard FFBSi.