Title: Distributed high-dimensional estimation and inference for precision matrices
Authors: Ensiyeh Nezakati Rezazadeh - Université catholique de Louvain (Belgium) (Belgium) [presenting]
Eugen Pircalabelu - Université catholique de Louvain (Belgium)
Abstract: Precision matrix estimation plays an important role in statistical and machine learning framework. When the sample size $n$ or the dimension of the dataset is large, estimation of the precision matrix using one single computer is computationally challenging. An attractive approach for down-scaling the problem size is splitting dataset to subsets and fit models using distributed algorithms. The dataset can be split either based on the observations or based on the variables. Much of the attention has been focused on splitting the observations into $K$ independent sub-samples that are analyzed in parallel. While splitting on the p variables is more effective when $p >> n$. We present a lasso-type distributed estimator of the precision matrix for high-dimensional Gaussian graphical models by implementing a partitioning procedure on both the observations and the features at the same time. A new combined estimator in each sub-sample is introduced by `glueing' together the local estimators of every subset of variables and the cross estimators of every two subsets of variables. We use the asymptotic distribution of these combined estimators and introduce a confidence distribution-based method to aggregate the estimators and build a new final estimator. Theoretical properties are investigated, and a simulation study and a real data example are used to assess the performance of this estimator.