title: PenPC: A two-step approach to estimate the skeletons of high-dimensional directed acyclic graphs.
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.
authors.affiliation: Department of Biostatistics, MD Anderson Cancer Center, Houston, Texas, 77030, U.S.A.
authors.forename: Min Jin
authors.initials: MJ
authors.lastname: Ha
authors.affiliation: Department of Biostatistics, Department of Genetics, UNC Chapel Hill, North Carolina, 27514, U.S.A.|Public Health Sciences Division, Fred Hutchinson Cancer Research Center, Seattle, WA, 98109, USA.
authors.forename: Wei
authors.initials: W
authors.lastname: Sun
authors.affiliation: Department of Biostatistics & Bioinformatics, Duke University, Durham, North Carolina, 27708, U.S.A.
authors.forename: Jichun
authors.initials: J
authors.lastname: Xie
mesh_terms: D014408:Biomarkers, Tumor / Q000235:genetics*; D001943:Breast Neoplasms / Q000453:epidemiology* / Q000235:genetics*; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D005260:Female; D020869:Gene Expression Profiling / Q000379:methods*; D005819:Genetic Markers / Q000235:genetics; D020022:Genetic Predisposition to Disease / Q000453:epidemiology / Q000235:genetics*; D006801:Humans; D015233:Models, Statistical; D009363:Neoplasm Proteins / Q000235:genetics; D015995:Prevalence; D015203:Reproducibility of Results; D012307:Risk Factors; D012680:Sensitivity and Specificity
chemical_list: D014408:Biomarkers, Tumor; D005819:Genetic Markers; D009363:Neoplasm Proteins
keywords: DAG; High dimensional; Log penalty; PC-algorithm; Penalized regression; Skeleton