Nonlinear Structural Equation Models for Network Topology Inference

Linear structural equation models (SEMs) have been widely adopted for inference of causal interactions in complex networks. Recent examples include unveiling topologies of hidden causal networks over which processes such as spreading diseases, or rumors propagation. However, these approaches are limited because they assume linear dependence among observable variables. The present paper advocates a more general nonlinear structural equation model based on polynomial expansions, which compensates for possible nonlinear dependencies between network nodes. To this end, a group-sparsity regularized estimator is put forth to leverage the inherent edge sparsity that is present in most real-world networks. A novel computationally-efficient proximal gradient algorithm is developed to estimate the polynomial SEM coefficients, and hence infer the edge structure. Preliminary tests on simulated data demonstrate the effectiveness of the novel approach.