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Title: Network inference Authors:  Peng Wang - University of Cincinnati (United States) [presenting]
Abstract: Network regression links a network's structures to covariates of interest, modeling pairwise conditional dependencies of interacting units as a function of covariates. For instance, in gene network analysis of a certain lung cancer, the network structures may vary over clinical attributes differentiating four different subtypes of the cancer. Within the framework of Gaussian structure equation models, we infer a network's structures, defined by an undirected graph, in in relation to covariates, through testing regression coefficients. To increase the power of hypothesis testing, we de-correlate the structure equation models, develop a combined constrained likelihood ratio test, combining independent marginal likelihoods and unregularizing hypothesized parameters whereas regularizing nuisance parameters through $L_0$-constraints controlling the individual degree of sparseness. On this ground, we derive asymptotic distributions of the combined constrained likelihood ratio, which is chi-square or normal depending on if the co-dimension of a test is finite or increases with the sample size. This leads to likelihood based tests in a high-dimensional situation permitting a network's size to increase in the sample size. Numerically, we demonstrate that the proposed method performs well in various situations. Finally, we apply the proposed method to infer a structural change of a gene network of a lung cancer with respect to four subtypes and other covariates of interest.