Learning high-dimensional networks with nonlinear interactions by a novel tree-embedded graphical model

• We propose a novel network learning method that can detect network structure with both linear and nonlinear interactions.
• Most existing network learning methods focus on linear interactions.
• Integration of generalized linear model, sparse learning, and decision tree learning.
• Interesting clinical associations are discovered from a real-world application using the proposed method.

Network models have been widely used in many domains to characterize relationships between physical entities. Although extensive research efforts have been conducted for learning networks from data, many of them were developed for learning networks with linear relationships. As both linear and nonlinear relationships may appear in many applications, in this paper, we developed a novel graphical model, the sparse tree-embedded graphical model (STGM), which is able to uncover both linear and nonlinear relationships from a large number of variables. We further proposed an efficient regression-based algorithm for learning the STGM from data. We conducted simulation studies that demonstrated the superiority of the STGM over other network learning methods and applied the STGM on a real-world application that demonstrated its efficacy on discovering interesting nonlinear relationships in practice.