  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.
