Likelihood Ratio Tests for a Large Directed Acyclic Graph

Inference of directional pairwise relations between interacting units in a directed acyclic graph (DAG), such as a regulatory gene network, is common in practice, imposing challenges because of lack of inferential tools. For example, inferring a specific gene pathway of a regulatory gene network is...

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Veröffentlicht in:Journal of the American Statistical Association Jg. 115; H. 531; S. 1304 - 1319
Hauptverfasser: Li, Chunlin, Shen, Xiaotong, Pan, Wei
Format: Journal Article
Sprache:Englisch
Veröffentlicht: United States Taylor & Francis 02.07.2020
Taylor & Francis Ltd
Schlagworte:
Alzheimer's disease
Asymptotic properties
Chi-square test
Computational geometry
Computer simulation
Convexity
data collection
Directed acyclic graph
Distribution
Gene expression
Gene network
High-dimensional inference
Independent variables
Inference
L0-regularization
Likelihood ratio
Mathematical programming
Networks
Nonconvex minimization
Power structure
Probability distribution functions
Regression analysis
Regulation
regulator genes
Statistical methods
Statistics
Directed acyclic graph
L0-regularization
high-dimensional inference
gene network
nonconvex minimization
ISSN:0162-1459, 1537-274X, 1537-274X
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Zusammenfassung:Inference of directional pairwise relations between interacting units in a directed acyclic graph (DAG), such as a regulatory gene network, is common in practice, imposing challenges because of lack of inferential tools. For example, inferring a specific gene pathway of a regulatory gene network is biologically important. Yet, frequentist inference of directionality of connections remains largely unexplored for regulatory models. In this article, we propose constrained likelihood ratio tests for inference of the connectivity as well as directionality subject to nonconvex acyclicity constraints in a Gaussian directed graphical model. Particularly, we derive the asymptotic distributions of the constrained likelihood ratios in a high-dimensional situation. For testing of connectivity, the asymptotic distribution is either chi-squared or normal depending on if the number of testable links in a DAG model is small. For testing of directionality, the asymptotic distribution is the minimum of d independent chi-squared variables with one-degree of freedom or a generalized Gamma distribution depending on if d is small, where d is number of breakpoints in a hypothesized pathway. Moreover, we develop a computational method to perform the proposed tests, which integrates an alternating direction method of multipliers and difference convex programming. Finally, the power analysis and simulations suggest that the tests achieve the desired objectives of inference. An analysis of an Alzheimer's disease gene expression dataset illustrates the utility of the proposed method to infer a directed pathway in a gene network.
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ISSN:0162-1459
1537-274X
1537-274X
DOI:10.1080/01621459.2019.1623042