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Title: Estimation and inference for covariate-adjusted Gaussian graphical models via an unbalanced distributed setting Authors:  Ensiyeh Nezakati Rezazadeh - Université catholique de Louvain (Belgium) [presenting]
Eugen Pircalabelu - Université catholique de Louvain (Belgium)
Abstract: Precision matrix estimation plays an important role in statistical and machine learning framework, especially in the framework of Gaussian graphical modeling. Most current methods for precision matrix estimation assume that the random vector has zero or constant mean. However, in many real applications, like genomic data analysis, it is often important to adjust for the covariate effects on the mean of the random vector to obtain more precise estimates. On the other hand, in the estimation framework, many modern datasets are characterized by both large dimensions and sample size, such that they cannot be stored in one single machine. In this vein, new algorithms have been developed for splitting a dataset on different local machines with different capacities such that the estimation will be solvable in each machine. New unbalanced distributed estimations are provided for both the covariate mean and precision matrices in adjusted-covariate Gaussian graphical models. These estimators aggregate all local estimators into the final ones by maximizing the pseudo loglikelihood function which comes from the asymptotic distribution of debiased estimators in the subsamples. Asymptotic behavior and statistical guarantees of these estimators are provided when the number of parameters, covariates and machines all grow with the sample size. A simulation study and a real data example are used to assess the performance of these estimators.