Explainable Tensorized Neural Ordinary Differential Equations forArbitrary-step Time Series Prediction

TL;DR

This paper introduces ETN-ODE, an explainable continuous neural network architecture that models multivariate time series for arbitrary-step prediction, combining tensorized RNNs with ODEs for improved accuracy and interpretability.

Contribution

The paper presents a novel ETN-ODE model that extends multi-step time series prediction to arbitrary time points with explainability, combining tensorized RNNs and neural ODEs.

Findings

ETN-ODE achieves superior prediction accuracy compared to baselines.

The model provides interpretable insights through tandem attention mechanisms.

ETN-ODE performs well on multiple multi-step and arbitrary-step prediction tasks.

Abstract

We propose a continuous neural network architecture, termed Explainable Tensorized Neural Ordinary Differential Equations (ETN-ODE), for multi-step time series prediction at arbitrary time points. Unlike the existing approaches, which mainly handle univariate time series for multi-step prediction or multivariate time series for single-step prediction, ETN-ODE could model multivariate time series for arbitrary-step prediction. In addition, it enjoys a tandem attention, w.r.t. temporal attention and variable attention, being able to provide explainable insights into the data. Specifically, ETN-ODE combines an explainable Tensorized Gated Recurrent Unit (Tensorized GRU or TGRU) with Ordinary Differential Equations (ODE). The derivative of the latent states is parameterized with a neural network. This continuous-time ODE network enables a multi-step prediction at arbitrary time points. We quantitatively and qualitatively demonstrate the effectiveness and the interpretability of ETN-ODE on five different multi-step prediction tasks and one arbitrary-step prediction task. Extensive experiments show that ETN-ODE can lead to accurate predictions at arbitrary time points while attaining best performance against the baseline methods in standard multi-step time series prediction.