PenPC: A two-step approach to estimate the skeletons of high-dimensional directed acyclic graphs.

Journal Article (Journal Article)

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.

Full Text

Duke Authors

Cited Authors

  • Ha, MJ; Sun, W; Xie, J

Published Date

  • March 2016

Published In

Volume / Issue

  • 72 / 1

Start / End Page

  • 146 - 155

PubMed ID

  • 26406114

Pubmed Central ID

  • PMC4808501

Electronic International Standard Serial Number (EISSN)

  • 1541-0420

Digital Object Identifier (DOI)

  • 10.1111/biom.12415


  • eng

Conference Location

  • United States