Title: A divide-and-conquer approach for covariate-adjusted Gaussian graphical models
Authors: Ensiyeh Nezakati Rezazadeh - Catholic University of Louvain (Belgium) [presenting]
Eugen Pircalabelu - Université catholique de Louvain (Belgium)
Abstract: Analysis of massive data sets is challenging due to the limited capacity of available machines. To overcome this limitation, various distributed frameworks for statistical estimation and inference have been proposed. We provide statistical guarantees and asymptotic properties of the lasso estimation for covariate-adjusted Gaussian graphical models using a divide-and-conquer approach. Covariate-adjusted graphical models have many applications in the real world, especially in genomic studies when the graph structure of thousands of microRNAs is affected by thousands of DNA gene covariates. We propose a new approach to aggregate all local parallel estimators of the adjusted graphical models into a final estimator by maximizing the pseudo-log-likelihood function, which comes from the asymptotic distribution of the local debiased estimators. The asymptotic behavior of this estimator is provided when the number of parameters, covariates and machines all grow with the sample size. Due to the asymptotic distribution, statistical inference based on the final estimator is also proposed. A simulation study and a real data example are used to compare the performance of the proposed estimator relative to the naive average-based estimators.