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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Vydáno v:	Journal of the American Statistical Association Ročník 115; číslo 531; s. 1304 - 1319
Hlavní autoři:	Li, Chunlin, Shen, Xiaotong, Pan, Wei
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	United States Taylor & Francis 02.07.2020 Taylor & Francis Ltd
Témata:	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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Shrnutí:	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.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23
ISSN:	0162-1459 1537-274X 1537-274X
DOI:	10.1080/01621459.2019.1623042