A flexible state space model for learning nonlinear dynamical systems

TL;DR

This paper introduces a flexible nonlinear state-space model using basis functions and Gaussian process priors, enabling effective learning and regularization for dynamical systems with promising results on benchmarks.

Contribution

It develops a novel basis function expansion approach with Gaussian process priors for nonlinear state-space modeling, improving flexibility and preventing overfitting.

Findings

Effective learning of coefficients with sequential Monte Carlo methods

Demonstrates promising results on benchmark and real data

Provides theoretical guarantees for the learning algorithm

Abstract

We consider a nonlinear state-space model with the state transition and observation functions expressed as basis function expansions. The coefficients in the basis function expansions are learned from data. Using a connection to Gaussian processes we also develop priors on the coefficients, for tuning the model flexibility and to prevent overfitting to data, akin to a Gaussian process state-space model. The priors can alternatively be seen as a regularization, and helps the model in generalizing the data without sacrificing the richness offered by the basis function expansion. To learn the coefficients and other unknown parameters efficiently, we tailor an algorithm using state-of-the-art sequential Monte Carlo methods, which comes with theoretical guarantees on the learning. Our approach indicates promising results when evaluated on a classical benchmark as well as real data.