Fast and numerically stable particle-based online additive smoothing: the AdaSmooth algorithm

TL;DR

The paper introduces AdaSmooth, a fast, stable, and easy-to-implement particle-based online smoothing algorithm that balances computational efficiency with numerical stability in path-space models.

Contribution

AdaSmooth is a novel adaptive backward-sampling particle smoother that improves stability and speed over existing methods for online additive smoothing.

Findings

AdaSmooth is computationally faster than existing algorithms.

It maintains numerical stability over long sequences.

Empirical results show AdaSmooth's superiority in accuracy and efficiency.

Abstract

We present a novel sequential Monte Carlo approach to online smoothing of additive functionals in a very general class of path-space models. Hitherto, the solutions proposed in the literature suffer from either long-term numerical instability due to particle-path degeneracy or, in the case that degeneracy is remedied by particle approximation of the so-called backward kernel, high computational demands. In order to balance optimally computational speed against numerical stability, we propose to furnish a (fast) naive particle smoother, propagating recursively a sample of particles and associated smoothing statistics, with an adaptive backward-sampling-based updating rule which allows the number of (costly) backward samples to be kept at a minimum. This yields a new, function-specific additive smoothing algorithm, AdaSmooth, which is computationally fast, numerically stable and easy to implement. The algorithm is provided with rigorous theoretical results guaranteeing its consistency, asymptotic normality and long-term stability as well as numerical results demonstrating empirically the clear superiority of AdaSmooth to existing algorithms.