Online Variational Sequential Monte Carlo

TL;DR

This paper introduces online VSMC, an efficient algorithm for real-time parameter estimation and latent state inference in state-space models, combining particle methods with stochastic variational inference for streaming data.

Contribution

It extends variational sequential Monte Carlo to an online setting, enabling real-time learning and inference in state-space models with theoretical convergence guarantees.

Findings

Online VSMC performs efficiently on streaming data.

The algorithm converges as data size increases.

Numerical results show excellent convergence and applicability.

Abstract

Being the most classical generative model for serial data, state-space models (SSM) are fundamental in AI and statistical machine learning. In SSM, any form of parameter learning or latent state inference typically involves the computation of complex latent-state posteriors. In this work, we build upon the variational sequential Monte Carlo (VSMC) method, which provides computationally efficient and accurate model parameter estimation and Bayesian latent-state inference by combining particle methods and variational inference. While standard VSMC operates in the offline mode, by re-processing repeatedly a given batch of data, we distribute the approximation of the gradient of the VSMC surrogate ELBO in time using stochastic approximation, allowing for online learning in the presence of streams of data. This results in an algorithm, online VSMC, that is capable of performing efficiently, entirely on-the-fly, both parameter estimation and particle proposal adaptation. In addition, we provide rigorous theoretical results describing the algorithm's convergence properties as the number of data tends to infinity as well as numerical illustrations of its excellent convergence properties and usefulness also in batch-processing settings.