Multivariate Time Series Forecasting with Latent Graph Inference

Victor Garcia Satorras, Syama Sundar Rangapuram, Tim Januschowski

Keywords: Time Series Forecasting, Graph Neural Networks, Graph Inference, Multivariate Time Series

Abstract: This paper introduces a new architecture for multivariate time series forecasting that simultaneously infers and leverages relations among time series. We cast our method as a modular extension to univariate architectures where relations among individual time series are dynamically inferred in the latent space obtained after encoding the whole input signal. Our approach is flexible enough to scale gracefully according to the needs of the forecasting task under consideration. In its most straight-forward and general version, we infer a potentially fully connected graph to model the interactions between time series, which allows us to obtain competitive forecast accuracy compared with the state-of-the-art in graph neural networks for forecasting. In addition, whereas previous latent graph inference methods scale O(N^2) w.r.t. the number of nodes N (representing the time series), we show how to configure our approach to cater for the scale of modern time series panels. By assuming the inferred graph to be bipartite where one partition consists of the original N nodes and we introduce K nodes (taking inspiration from low-rank-decompositions) we reduce the time complexity of our procedure to O(NK). This allows us to leverage the dependency structure with a small trade-off in forecasting accuracy. We demonstrate the effectiveness of our method for a variety of datasets where it performs better or very competitively to previous methods under both the fully connected and bipartite assumptions.

Community Implementations: [ 3 code implementations](https://www.catalyzex.com/paper/arxiv:2203.03423/code)