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

arXiv: https://arxiv.org/abs/1605.03122 · HTML: https://mlsanity.com/paper/1605.03122/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 May 2016.

## Built on by (most cited first, 8 of 8)

- [Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond](https://mlsanity.com/paper/2101.05510/) (2021)
- [Multiple Kernel Representation Learning on Networks](https://mlsanity.com/paper/2106.05057/) (2021)
- [Graph Laplacian Learning with Exponential Family Noise](https://mlsanity.com/paper/2306.08201/) (2023)
- [Network Topology Inference from Smooth Signals Under Partial Observability](https://mlsanity.com/paper/2410.05707/) (2024)
- [GKNet: Graph Kalman Filtering and Model Inference via Model-based Deep Learning](https://mlsanity.com/paper/2506.22004/) (2025)
- [Deploying AI for Signal Processing education: Selected challenges and intriguing opportunities](https://mlsanity.com/paper/2509.08950/) (2025)
- [Reconstruction of Graph Signals on Complex Manifolds with Kernel Methods](https://mlsanity.com/paper/2505.15202/) (2025)
- [Topology Identification and Inference over Graphs](https://mlsanity.com/paper/2512.10183/) (2025)

## Abstract (arXiv)

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.