Black-Box Inference for Non-Linear Latent Force Models

TL;DR

This paper introduces a black-box variational inference approach with advanced flow-based approximations for jointly estimating states and unknown forces in non-linear latent force models, improving inference in complex dynamical systems.

Contribution

It develops a multivariate extension of local inverse autoregressive flows for flexible posterior approximation in non-linear latent force models.

Findings

Effective approximation demonstrated on systems with known posteriors

Improved inference in non-linear, multi-output, and non-Gaussian models

Comparable or superior to existing methods in complex dynamics

Abstract

Latent force models are systems whereby there is a mechanistic model describing the dynamics of the system state, with some unknown forcing term that is approximated with a Gaussian process. If such dynamics are non-linear, it can be difficult to estimate the posterior state and forcing term jointly, particularly when there are system parameters that also need estimating. This paper uses black-box variational inference to jointly estimate the posterior, designing a multivariate extension to local inverse autoregressive flows as a flexible approximater of the system. We compare estimates on systems where the posterior is known, demonstrating the effectiveness of the approximation, and apply to problems with non-linear dynamics, multi-output systems and models with non-Gaussian likelihoods.