Sequential Estimation of Gaussian Process-based Deep State-Space Models

TL;DR

This paper introduces a particle filtering approach for sequentially estimating unknown functions and latent processes in Gaussian process-based deep state-space models, effectively tracking these processes in complex, nonlinear systems.

Contribution

It proposes a novel particle filtering method that integrates out Gaussian process parameters, reducing computational complexity and enabling effective tracking of nonlinear latent processes.

Findings

Method accurately tracks latent processes up to scale and rotation.

Ensemble approach improves robustness and tracking performance.

Approach reduces the need for particles in parameter estimation.

Abstract

We consider the problem of sequential estimation of the unknowns of state-space and deep state-space models that include estimation of functions and latent processes of the models. The proposed approach relies on Gaussian and deep Gaussian processes that are implemented via random feature-based Gaussian processes. In these models, we have two sets of unknowns, highly nonlinear unknowns (the values of the latent processes) and conditionally linear unknowns (the constant parameters of the random feature-based Gaussian processes). We present a method based on particle filtering where the parameters of the random feature-based Gaussian processes are integrated out in obtaining the predictive density of the states and do not need particles. We also propose an ensemble version of the method, with each member of the ensemble having its own set of features. With several experiments, we show that the method can track the latent processes up to a scale and rotation.