MotifDisco: Motif Causal Discovery For Time Series Motifs

Abstract: Many time series, particularly health data streams, can be best understood as a sequence of phenomenon or events, which we call \textit{motifs}. A time series motif is a short trace segment which may implicitly capture an underlying phenomenon within the time series. Specifically, we focus on glucose traces collected from continuous glucose monitors (CGMs), which inherently contain motifs representing underlying human behaviors such as eating and exercise. The ability to identify and quantify \textit{causal} relationships amongst motifs can provide a mechanism to better understand and represent these patterns, useful for improving deep learning and generative models and for advanced technology development (e.g., personalized coaching and artificial insulin delivery systems). However, no previous work has developed causal discovery methods for time series motifs. Therefore, in this paper we develop MotifDisco (\textbf{motif} \textbf{disco}very of causality), a novel causal discovery framework to learn causal relations amongst motifs from time series traces. We formalize a notion of \textit{Motif Causality (MC)}, inspired from Granger Causality and Transfer Entropy, and develop a Graph Neural Network-based framework that learns causality between motifs by solving an unsupervised link prediction problem. We integrate MC with three model use cases of forecasting, anomaly detection and clustering, to showcase the use of MC as a building block for downstream tasks. Finally, we evaluate our framework on different health data streams and find that Motif Causality provides a significant performance improvement in all use cases.