# Particle-based adaptive-lag online marginal smoothing in general state-space models

## TL;DR

This paper introduces an adaptive-lag particle smoother for online estimation in general state-space models, which efficiently approximates marginal expectations with theoretical guarantees on its asymptotic behavior and memory efficiency.

## Contribution

It proposes a novel adaptive-lag smoothing algorithm that recursively manages estimators for each marginal, improving online approximation in state-space models.

## Key findings

- Algorithm has proven asymptotic convergence.
- Memory usage is optimized through adaptive stopping criteria.
- The method extends existing particle smoothers with adaptive features.

## Abstract

We present a novel algorithm, an adaptive-lag smoother, approximating efficiently, in an online fashion, sequences of expectations under the marginal smoothing distributions in general state-space models. The algorithm evolves recursively a bank of estimators, one for each marginal, in resemblance with the so-called particle-based, rapid incremental smoother (PaRIS). Each estimator is propagated until a stopping criterion, measuring the fluctuations of the estimates, is met. The presented algorithm is furnished with theoretical results describing its asymptotic limit and memory usage.