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The Granger framework is widely used for discovering causal relationshipsbased on time-varying signals. Implementations of Granger causality (GC) aremostly developed for densely sampled timeseries data. A substantially differentsetting, particularly common in population health applications, is thelongitudinal study design, where multiple individuals are followed and sparselyobserved for a limited number of times. Longitudinal studies commonly trackmany variables, which are likely governed by nonlinear dynamics that might haveindividual-specific idiosyncrasies and exhibit both direct and indirect causes.Furthermore, real-world longitudinal data often suffer from widespreadmissingness. GC methods are not well-suited to handle these issues. In thispaper, we intend to fill this methodological gap. We propose to marry the GCframework with a machine learning based prediction model. We call our approachGLACIAL, which stands for "Granger and LeArning-based CausalIty Analysis forLongitudinal studies." GLACIAL treats individuals as independent samples anduses average prediction accuracy on hold-out individuals to test for effects ofcausal relationships. GLACIAL employs a multi-task neural network trained withinput feature dropout to efficiently learn nonlinear dynamic relationshipsbetween a large number of variables, handle missing values, and probe causallinks. Extensive experiments on synthetic and real data demonstrate the utilityof GLACIAL and how it can outperform competitive baselines.

GLACIAL: Granger and Learning-based Causality Analysis for Longitudinal Studies