Efficient Online Variational Estimation via Monte Carlo Sampling

TL;DR

This paper introduces an efficient online variational estimation method for state-space models using Monte Carlo sampling, enabling real-time training of model parameters and latent states with theoretical guarantees.

Contribution

It presents a novel Monte Carlo-based algorithm for online variational inference that improves computational efficiency and flexibility in streaming data scenarios.

Findings

Effective on synthetic and real-world air-quality data

Theoretically grounded by asymptotic contrast function and ergodicity

Enables simultaneous training of parameters and latent states

Abstract

This article addresses online variational estimation in parametric state-space models. We propose a new procedure for efficiently computing the evidence lower bound and its gradient in a streaming-data setting, where observations arrive sequentially. The algorithm allows for the simultaneous training of the model parameters and the distribution of the latent states given the observations. It is based on i.i.d. Monte Carlo sampling, coupled with a well-chosen deep architecture, enabling both computational efficiency and flexibility. The performance of the method is illustrated on both synthetic data and real-world air-quality data. The proposed approach is theoretically motivated by the existence of an asymptotic contrast function and the ergodicity of the underlying Markov chain, and applies more generally to the computation of additive expectations under posterior distributions in state-space models.