PenPC: A Two-step Approach to Estimate the Skeletons of High Dimensional Directed Acyclic Graphs

TL;DR

PenPC is a novel two-step method for estimating the skeletons of high-dimensional DAGs, combining penalized regression and conditional independence testing, outperforming existing methods in accuracy.

Contribution

The paper introduces PenPC, a new approach that improves high-dimensional DAG skeleton estimation by integrating penalized regression with hypothesis testing.

Findings

PenPC achieves higher sensitivity and specificity than PC-stable.

The method performs well on both random and scale-free graphs.

Extensive simulations and gene expression data applications validate its effectiveness.

Abstract

Estimation of the skeleton of a directed acyclic graph (DAG) is of great importance for understanding the underlying DAG and causaleffects can be assessed from the skeleton when the DAG is notidentifiable. We propose a novel method named PenPC toestimate the skeleton of a high-dimensional DAG by a two-stepapproach. We first estimate the non-zero entries of a concentrationmatrix using penalized regression, and then fix the differencebetween the concentration matrix and the skeleton by evaluating aset of conditional independence hypotheses. For high dimensionalproblems where the number of vertices $p$ is in polynomial orexponential scale of sample size $n$, we study the asymptoticproperty of PenPC on two types of graphs: traditionalrandom graphs where all the vertices have the same expected numberof neighbors, and scale-free graphs where a few vertices may have alarge number of neighbors. As illustrated by extensive simulationsand applications on gene expression data of cancer patients, PenPChas higher sensitivity and specificity than the standard-of-the-artmethod, the PC-stable algorithm.