A parallel algorithm for penalized learning of the multivariate exponential family from data of mixed types

TL;DR

This paper introduces a parallel Newton-Raphson algorithm for efficiently estimating penalized multivariate exponential family models, including mixed data types, with proven consistency and demonstrated performance in simulations and real data applications.

Contribution

It presents a novel parallel optimization method for penalized estimators in multivariate exponential families, suitable for mixed data types and high-dimensional settings.

Findings

The estimator is shown to be consistent.

The parallel algorithm converges under specified conditions.

Performance is validated through simulations and an omics data application.

Abstract

Computational efficient evaluation of penalized estimators of multivariate exponential family distributions is sought. These distributions encompass among others Markov random fields with variates of mixed type (e.g. binary and continuous) as special case of interest. The model parameter is estimated by maximization of the pseudo-likelihood augmented with a convex penalty. The estimator is shown to be consistent. With a world of multi-core computers in mind, a computationally efficient parallel Newton-Raphson algorithm is presented for numerical evaluation of the estimator alongside conditions for its convergence. Parallelization comprises the division of the parameter vector into subvectors that are estimated simultaneously and subsequently aggregated to form an estimate of the original parameter. This approach may also enable efficient numerical evaluation of other high-dimensional estimators. The performance of the proposed estimator and algorithm are evaluated and compared in a simulation study. Finally, the paper concludes with an illustration of the presented methodology in the reconstruction of the conditional independence network from data of an integrative omics study.