Detecting Nonlinear Causality in Multivariate Time Series with Sparse Additive Models

Detecting causal relationships within a set of coupled stochastic processes has been an interesting and important problem that rises broadly across the fields of modern science and engineering, including financial industries (Atanasov and Black, 2016), computer science (Rodriguez et al., 2011), epidemiology (Robins et al., 2000), neural science (Quinn et al., 2011), and climatology (Runge et al., 2015). A typical problem involving causal discovery often involves a vast network containing many agents, each generating a discrete time series. As the backbone that captures the evolutionary dynamics, the underlying causal relationships, which are often depicted by a causal graph (Quinn et al., 2015), can provide guidance for estimating the values of the time series in near future. In this paper, we focus on learning Granger causality from a set of discrete time series when (i) the underlying causal graph is sparse, and (ii) when the underlying causal relationships are potentially nonlinear.