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.
Type
Journal articleSubject
DAGHigh dimensional
Log penalty
PC-algorithm
Penalized regression
Skeleton
Biomarkers, Tumor
Breast Neoplasms
Computer Simulation
Data Interpretation, Statistical
Female
Gene Expression Profiling
Genetic Markers
Genetic Predisposition to Disease
Humans
Models, Statistical
Neoplasm Proteins
Prevalence
Reproducibility of Results
Risk Factors
Sensitivity and Specificity
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https://hdl.handle.net/10161/10825Published Version (Please cite this version)
10.1111/biom.12415Publication Info
Ha, Min Jin; Sun, Wei; & Xie, Jichun (2016). PenPC: A two-step approach to estimate the skeletons of high-dimensional directed
acyclic graphs. Biometrics, 72(1). pp. 146-155. 10.1111/biom.12415. Retrieved from https://hdl.handle.net/10161/10825.This is constructed from limited available data and may be imprecise. To cite this
article, please review & use the official citation provided by the journal.
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Show full item recordScholars@Duke
Jichun Xie
Associate Professor of Biostatistics & Bioinformatics

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