Explainable nonlinear modelling of multiple time series with invertible neural networks

TL;DR

This paper introduces an explainable nonlinear modeling approach for multiple time series using invertible neural networks, enabling better predictions and interpretability through a novel invertible mapping and gradient computation method.

Contribution

It proposes a new nonlinear topology identification method with invertible neural networks, allowing for explainability and improved prediction accuracy in time series analysis.

Findings

Prediction error is reduced compared to linear models.

Model explainability remains similar to linear VAR processes.

Gradient computation is achieved via implicit differentiation.

Abstract

A method for nonlinear topology identification is proposed, based on the assumption that a collection of time series are generated in two steps: i) a vector autoregressive process in a latent space, and ii) a nonlinear, component-wise, monotonically increasing observation mapping. The latter mappings are assumed invertible, and are modelled as shallow neural networks, so that their inverse can be numerically evaluated, and their parameters can be learned using a technique inspired in deep learning. Due to the function inversion, the back-propagation step is not straightforward, and this paper explains the steps needed to calculate the gradients applying implicit differentiation. Whereas the model explainability is the same as that for linear VAR processes, preliminary numerical tests show that the prediction error becomes smaller.