Sparse Graph Learning for Spatiotemporal Time Series

Abstract

Outstanding achievements of graph neural networks for spatiotemporal time series prediction show that relational constraints introduce a positive inductive bias into neural forecasting architectures. Often, however, the relational information characterizing the underlying data generating process is unavailable; the practitioner is then left with the problem of inferring from data which relational graph to use in the subsequent processing stages. We propose novel, principled -yet practicalprobabilistic methods that learn the relational dependencies by modeling distributions over graphs while maximizing, at the same time, end-to-end the forecasting accuracy. Our novel graph learning approach, based on consolidated variance reduction techniques for Monte Carlo score-based gradient estimation, is theoretically grounded and effective. We show that tailoring the gradient estimators to the graph learning problem allows us also for achieving state-of-the-art forecasting performance while controlling, at the same time, both the sparsity of the learned graph and the computational burden. We empirically assess the effectiveness of the proposed method on synthetic and real-world benchmarks, showing that the proposed solution can be used as a stand-alone graph identification procedure as well as a learned component of an end-to-end forecasting architecture.Preprint. Under review.

Taming Local Effects in Graph-based Spatiotemporal Forecasting

“…Models of this type are fully inductive, in the sense that they can be used to make predictions for networks and time windows different from those they have been trained on, provided a certain level of similarity (e.g., homogenous sensors) between source and target node sets [15]. Among the different implementations of this general framework, we can distinguish between time-then-space (TTS) and time-and-space (T&S) models by following the terminology of previous works [16,17]. Specifically, in TTS models the sequence of representations h i,0 ≤t is encoded by a sequence model, e.g., an RNN, before propagating information along the spatial dimension through message passing (MP) [16].…”