Asynchronous Distributed ECME Algorithm for Matrix Variate Non-Gaussian Responses

TL;DR

This paper introduces a scalable asynchronous distributed ECME algorithm for matrix-variate skew-t regression models, enabling efficient analysis of irregular longitudinal data with heavy tails and skewness.

Contribution

It develops an ADECME algorithm for scalable parameter estimation in matrix-variate skew-t models, improving computational efficiency and convergence over existing methods.

Findings

ADECME outperforms alternatives in efficiency and convergence.

Simulation and case studies validate the method's effectiveness.

Theoretical analysis supports empirical results.

Abstract

We propose a regression model with matrix-variate skew-t response (REGMVST) for analyzing irregular longitudinal data with skewness, symmetry, or heavy tails. REGMVST models matrix-variate responses and predictors, with rows indexing longitudinal measurements per subject. It uses the matrix-variate skew-t (MVST) distribution to handle skewness and heavy tails, a damped exponential correlation (DEC) structure for row-wise dependencies across irregular time profiles, and leaves the column covariance unstructured. For estimation, we initially develop an ECME algorithm for parameter estimation and further mitigate its computational bottleneck via an asynchronous and distributed ECME (ADECME) extension. ADECME accelerates the E-step through parallelization, and retains the simplicity of the conditional M-step, enabling scalable inference. Simulations using synthetic data and a case study exploring matrix-variate periodontal disease endpoints derived from electronic health records demonstrate ADECME's superiority in efficiency and convergence, over the alternatives. We also provide theoretical support for our empirical observations and identify regularity assumptions for ADECME's optimal performance. An accompanying R package is available at https://github.com/rh8liuqy/STMATREG.