Explainable Tensorized Neural Ordinary Differential Equations forArbitrary-step Time Series Prediction
This work addresses the problem of accurate and explainable multi-step time series prediction for researchers and practitioners working with multivariate time series data, offering an incremental improvement over existing methods.
This paper introduces Explainable Tensorized Neural Ordinary Differential Equations (ETN-ODE) for multi-step time series prediction at arbitrary time points. It models multivariate time series for arbitrary-step prediction and achieves best performance against baseline methods in standard multi-step time series prediction.
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.