Online Variational Filtering and Parameter Learning

TL;DR

This paper introduces an online variational filtering method for state-space models that efficiently updates state estimates and parameters in real-time without revisiting past data, suitable for high-dimensional and sequential data applications.

Contribution

It presents a novel online variational approach that maintains constant update costs and handles growing posterior dimensions using backward decompositions and Bellman recursions.

Findings

Effective in high-dimensional SSMs

Performs well on sequential Variational Auto-Encoders

Maintains constant update cost over time

Abstract

We present a variational method for online state estimation and parameter learning in state-space models (SSMs), a ubiquitous class of latent variable models for sequential data. As per standard batch variational techniques, we use stochastic gradients to simultaneously optimize a lower bound on the log evidence with respect to both model parameters and a variational approximation of the states' posterior distribution. However, unlike existing approaches, our method is able to operate in an entirely online manner, such that historic observations do not require revisitation after being incorporated and the cost of updates at each time step remains constant, despite the growing dimensionality of the joint posterior distribution of the states. This is achieved by utilizing backward decompositions of this joint posterior distribution and of its variational approximation, combined with Bellman-type recursions for the evidence lower bound and its gradients. We demonstrate the performance of this methodology across several examples, including high-dimensional SSMs and sequential Variational Auto-Encoders.