A Distributed and Integrated Method of Moments for High-Dimensional Correlated Data Analysis

TL;DR

This paper introduces a scalable distributed method for high-dimensional correlated data analysis, combining divide-and-conquer strategies with generalized method of moments, demonstrated on EEG neuroimaging data.

Contribution

It develops a novel distributed and parallelized estimation framework using pairwise composite likelihood and GMM for high-dimensional correlated responses.

Findings

Efficient estimation and inference for high-dimensional correlated data.

Successful application to EEG data revealing significant associations.

Provides an R package for implementation.

Abstract

This paper is motivated by a regression analysis of electroencephalography (EEG) neuroimaging data with high-dimensional correlated responses with multi-level nested correlations. We develop a divide-and-conquer procedure implemented in a fully distributed and parallelized computational scheme for statistical estimation and inference of regression parameters. Despite significant efforts in the literature, the computational bottleneck associated with high-dimensional likelihoods prevents the scalability of existing methods. The proposed method addresses this challenge by dividing responses into subvectors to be analyzed separately and in parallel on a distributed platform using pairwise composite likelihood. Theoretical challenges related to combining results from dependent data are overcome in a statistically efficient way using a meta-estimator derived from Hansen's generalized method of moments. We provide a rigorous theoretical framework for efficient estimation, inference, and goodness-of-fit tests. We develop an R package for ease of implementation. We illustrate our method's performance with simulations and the analysis of the EEG data, and find that iron deficiency is significantly associated with two auditory recognition memory related potentials in the left parietal-occipital region of the brain.