@article {14667,
title = {PenPC: A two-step approach to estimate the skeletons of high-dimensional directed acyclic graphs.},
journal = {Biometrics},
volume = {72},
year = {2016},
month = {2016 Mar},
pages = {146-55},
abstract = {Estimation of the skeleton of a directed acyclic graph (DAG) is of great importance for understanding the underlying DAG and causal effects can be assessed from the skeleton when the DAG is not identifiable. We propose a novel method named PenPC to estimate the skeleton of a high-dimensional DAG by a two-step approach. We first estimate the nonzero entries of a concentration matrix using penalized regression, and then fix the difference between the concentration matrix and the skeleton by evaluating a set of conditional independence hypotheses. For high-dimensional problems where the number of vertices p is in polynomial or exponential scale of sample size n, we study the asymptotic property of PenPC on two types of graphs: traditional random graphs where all the vertices have the same expected number of neighbors, and scale-free graphs where a few vertices may have a large number of neighbors. As illustrated by extensive simulations and applications on gene expression data of cancer patients, PenPC has higher sensitivity and specificity than the state-of-the-art method, the PC-stable algorithm.},
issn = {1541-0420},
doi = {10.1111/biom.12415},
author = {Ha, Min Jin and Sun, Wei and Xie, Jichun}
}