2014/05/07 by Min Jin Ha, Wei Sun, Ha, Min Jin +3 · 1 citation
Computer Science · Mathematics · Biochemistry, Genetics and Molecular Biology · #Bayesian Modeling and Causal Inference #Statistical Methods and Inference #Gene expression and cancer classification
paper · pdf · doi:10.48550/arxiv.1405.1603
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.