PenPC: A two-step approach to estimate the skeletons of high-dimensional directed acyclic graphs.
PenPC: A two-step approach to estimate the skeletons of high-dimensional directed acyclic graphs.
复制标题
PENPC：一种两步方法，用于估计高维定向无环图的骨骼。
作者：
Ha MJ;Sun W;Xie J
Estimation of the skeleton of a directed acyclic graph (DAG) is of great importance for understanding the underlying DAG and causal e ects 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 non-zero 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.
