Kernel-Based Structural Equation Models for Topology Identification of Directed Networks

TL;DR

This paper introduces a kernel-based nonlinear SEM framework for topology identification in directed networks, outperforming linear models in accuracy and revealing new insights in gene regulatory networks.

Contribution

It proposes a novel convex regularized kernel-based SEM approach with efficient optimization algorithms, extending SEM capabilities to nonlinear dependencies in network inference.

Findings

Outperforms linear SEMs in edge detection accuracy.

Reveals new gene regulatory edges in real data.

Provides scalable optimization methods for kernel SEMs.

Abstract

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 propagate. The appeal of SEMs in these settings stems from their simplicity and tractability, since they typically assume linear dependencies among observable variables. Acknowledging the limitations inherent to adopting linear models, the present paper advocates nonlinear SEMs, which account for (possible) nonlinear dependencies among network nodes. The advocated approach leverages kernels as a powerful encompassing framework for nonlinear modeling, and an efficient estimator with affordable tradeoffs is put forth. Interestingly, pursuit of the novel kernel-based approach yields a convex regularized estimator that promotes edge sparsity, and is amenable to proximal-splitting optimization methods. To this end, solvers with complementary merits are developed by leveraging the alternating direction method of multipliers, and proximal gradient iterations. Experiments conducted on simulated data demonstrate that the novel approach outperforms linear SEMs with respect to edge detection errors. Furthermore, tests on a real gene expression dataset unveil interesting new edges that were not revealed by linear SEMs, which could shed more light on regulatory behavior of human genes.