Title: Distributed estimation and inference for conditional Gaussian graphical models under an unbalanced distributed setting Authors:  Eugen Pircalabelu - Université catholique de Louvain (Belgium) [presenting]
Ensiyeh Nezakati Rezazadeh - Catholic University of Louvain (Belgium)
Abstract: A distributed estimation and inferential framework are introduced for sparse multivariate regression and conditional Gaussian graphical models under the unbalanced splitting setting. This type of data splitting arises when the datasets from different sources cannot be aggregated on one single machine or when the available machines are of different powers. The number of covariates, responses and machines grows with the sample size while sparsity is imposed. Debiased estimators of the coefficient matrix and the precision matrix are proposed on every single machine, and theoretical guarantees are provided. Moreover, new aggregated estimators that pool information across the machines using a pseudo log-likelihood function are presented, and it is shown that they enjoy consistency and asymptotic normality as the number of machines grows with the sample size. The performance of these estimators is investigated via a simulation study and a real data example. It is shown empirically that the performances of these estimators are close to those of the non-distributed estimators, which use the entire dataset.