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

Biometrics ◽  
2015 ◽  
Vol 72 (1) ◽  
pp. 146-155 ◽  
Author(s):  
Min Jin Ha ◽  
Wei Sun ◽  
Jichun Xie
Keyword(s):  
Directed Acyclic Graphs ◽  
High Dimensional ◽  
Acyclic Graphs

scholarly journals An Order-Independent Algorithm for Learning Chain Graphs

2021 ◽  
Vol 34 (1) ◽  
Author(s):  
Mohammad Ali Javidian ◽  
Marco Valtorta ◽  
Pooyan Jamshidi
Keyword(s):  
Directed Acyclic Graphs ◽  
High Dimensional ◽  
P Values ◽  
Order Dependence ◽  
Error Measures ◽  
Acyclic Graphs ◽  
Simulation Results ◽  
Improved Performance ◽  
Low Dimensional ◽  
Chain Graphs

LWF chain graphs combine directed acyclic graphs and undirected graphs. We propose a PC-like algorithm, called PC4LWF, that finds the structure of chain graphs under the faithfulness assumption to resolve the problem of scalability of the proposed algorithm by Studeny (1997). We prove that PC4LWF is order dependent, in the sense that the output can depend on the order in which the variables are given. This order dependence can be very pronounced in high-dimensional settings. We propose two modifications of the PC4LWF algorithm that remove part or all of this order dependence. Simulation results with different sample sizes, network sizes, and p-values demonstrate the competitive performance of the PC4LWF algorithms in comparison with the LCD algorithm proposed by Ma et al. (2008) in low-dimensional settings and improved performance (with regard to error measures) in high-dimensional settings.

scholarly journals Learning high-dimensional directed acyclic graphs with latent and selection variables

2012 ◽  
Vol 40 (1) ◽  
pp. 294-321 ◽  
Author(s):  
Diego Colombo ◽  
Marloes H. Maathuis ◽  
Markus Kalisch ◽  
Thomas S. Richardson
Keyword(s):  
Directed Acyclic Graphs ◽  
High Dimensional ◽  
Acyclic Graphs

scholarly journals Estimation of high-dimensional directed acyclic graphs with surrogate intervention

Biostatistics ◽  
2018 ◽  
Vol 21 (4) ◽  
pp. 659-675
Author(s):  
Min Jin Ha ◽  
Wei Sun
Keyword(s):  
Observational Data ◽  
Causal Structure ◽  
Directed Acyclic Graphs ◽  
High Dimensional ◽  
Breast Cancer Patients ◽  
Expression Of Genes ◽  
Acyclic Graphs ◽  
External Variables ◽  
Trait Locus ◽  
Dna Variations

Summary Directed acyclic graphs (DAGs) have been used to describe causal relationships between variables. The standard method for determining such relations uses interventional data. For complex systems with high-dimensional data, however, such interventional data are often not available. Therefore, it is desirable to estimate causal structure from observational data without subjecting variables to interventions. Observational data can be used to estimate the skeleton of a DAG and the directions of a limited number of edges. We develop a Bayesian framework to estimate a DAG using surrogate interventional data, where the interventions are applied to a set of external variables, and thus such interventions are considered to be surrogate interventions on the variables of interest. Our work is motivated by expression quantitative trait locus (eQTL) studies, where the variables of interest are the expression of genes, the external variables are DNA variations, and interventions are applied to DNA variants during the process of a randomly selected DNA allele being passed to a child from either parent. Our method, surrogate intervention recovery of a DAG ($\texttt{sirDAG}$), first constructs a DAG skeleton using penalized regressions and the subsequent partial correlation tests, and then estimates the posterior probabilities of all the edge directions after incorporating DNA variant data. We demonstrate the utilities of $\texttt{sirDAG}$ by simulation and an application to an eQTL study for 550 breast cancer patients.

scholarly journals Directed acyclic graphs: An under-utilized tool for child maltreatment research

2019 ◽  
Vol 91 ◽  
pp. 78-87 ◽  
Author(s):  
Anna E. Austin ◽  
Tania A. Desrosiers ◽  
Meghan E. Shanahan
Keyword(s):  
Child Maltreatment ◽  
Directed Acyclic Graphs ◽  
Acyclic Graphs
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