Functional Relation Field: A Model-Agnostic Framework for Multivariate Time Series Forecasting

Bing Yu, Ting Li, Jianguo Li, Bin Dong, Zhanxing Zhu

Keywords: Functional Relation Field, Spatio-Temporal Forecasting, Constraint Optimization, Multivariate Time Series

TL;DR: Functional Relation Field: A Model-Agnostic Framework for Multivariate Time Series Forecasting

Abstract: In multivariate time series forecasting, the most popular strategy for modeling the relationship between multiple time series is the construction of graph, where each time series is represented as a node and related nodes are connected by edges, i.e. spatial-temporal graph neural networks. The graph structure is either given apriori or learned based the similarity between nodes. However, the relationship between multiple time series is typically complicated, for instance, the sum of outflows from upstream nodes may be equal to the inflows of downstream nodes. Such relations widely exist in many real-world multivariate time series forecasting scenarios, yet are far from well studied. In these cases, graph might only be a crude description on the dependency between nodes. To this end, we explore a new framework to model the inter-node relationship in a more precise way based our proposed inductive bias for graphs, Functional Relation Field, where a group of functions parameterized by neural networks are learned to characterize the dependency between multiple time series. These learned functions are versatile: they can then be used to discover the underlying graph structure by identifying the most relevant neighbors of the target node; and on the other hand, the learned functions will form a “field” where the nodes in the backbone prediction networks are enforced to satisfy the constraints defined by these functions. The experiment is conducted on one toy dataset to show our approach can well recover the true constraint relationship between nodes. And two real-world MiniApp calling traffic and road network datasets are also considered with various different backbone networks. Results show that the prediction error can be reduced remarkably with the aid of the proposed functional relation field framework.

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