Relation Discovery in Nonlinearly Related Large-Scale Settings

Mohammad Ali Vosoughi, Adora M. DSouza, Anas Z. Abidin, Axel Wismüller

Abstract: Causal inquiries provide crucial insight into the advancement of scientific discoveries. In real-world studies like climatology, sensory data acquired from nodal measurements are nonlinearly related and complex. At the same time, they have information from millions of sensors with only a few decades’ temporal samples, which leads to the curse of dimensionality in large-scale systems. Despite a rich literature on causal discovery, the problem is challenging for largescale datasets. We put forth a novel method that utilizes a radial basis function (RBF) to tackle curse-of-dimensionality in complex systems. The proposed method is probabilistic, encompasses nonlinear relations, and is suitable for large-scale data in two steps. Extensive simulations on synthetic data of different sizes and real-world climatology data show that our method outperforms all other methods when nodal observations are temporally scarce.