An interpretable LSTM neural network for autoregressive exogenous model

TL;DR

This paper introduces an interpretable multi-variable LSTM model with tensorized hidden states that captures variable importance and temporal dynamics, showing promise for forecasting and knowledge discovery in time series with exogenous variables.

Contribution

The paper develops a novel multi-variable LSTM with tensorized hidden states that provides variable-specific representations and attention, enhancing interpretability over existing models.

Findings

Comparable prediction performance to encoder-decoder baselines.

Variable attention aligns with Granger causality results.

Demonstrates potential for combined forecasting and knowledge discovery.

Abstract

In this paper, we propose an interpretable LSTM recurrent neural network, i.e., multi-variable LSTM for time series with exogenous variables. Currently, widely used attention mechanism in recurrent neural networks mostly focuses on the temporal aspect of data and falls short of characterizing variable importance. To this end, our multi-variable LSTM equipped with tensorized hidden states is developed to learn variable specific representations, which give rise to both temporal and variable level attention. Preliminary experiments demonstrate comparable prediction performance of multi-variable LSTM w.r.t. encoder-decoder based baselines. More interestingly, variable importance in real datasets characterized by the variable attention is highly in line with that determined by statistical Granger causality test, which exhibits the prospect of multi-variable LSTM as a simple and uniform end-to-end framework for both forecasting and knowledge discovery.