Nonlinear directed acyclic graph estimation based on the kernel partial correlation coefficient

Abstract

Directed acyclic graphs (DAGs) are powerful tools for detecting causality among variables and thus, they have attracted increasing interest in recent years. In most previous studies, DAGs were estimated under the assumption of linearity between variables; however, this assumption is not usually true in real-world applications. Therefore, developing DAG estimation methods for nonlinear scenarios is of great interest. In this work, we propose a DAG estimation method based on the kernel partial correlation (KPC) coefficient to identify nonlinear interactions among variables. The method consists of three steps: neighborhood selection, skeleton estimation and direction detection. While all the steps are grounded on the KPC coefficient, we develop a threshold-based criterion to address the falsely discovered edges in the skeleton estimation step and utilize the asymmetric property of the KPC coefficient in the direction detection step. Numerical simulations demonstrate the advantages of the proposed method over various competing methods. Finally, we apply the proposed method to construct networks in three real-world structural equation modeling examples in the social sciences and on one DNA binding site dataset to demonstrate its effectiveness.