A parallel algorithm for ridge-penalized estimation of the multivariate exponential family from data of mixed types

Computationally 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 presented methodology is applied to data of an integrative omics study.

Automated summary

Efficient computation of penalized estimators for multivariate exponential family distributions, including Markov random fields with mixed variable types, is studied. The model parameter is estimated through maximizing pseudo-likelihood with a convex penalty, leading to a consistent estimator. A computationally efficient parallel Newton-Raphson algorithm is introduced for numerical evaluation of the estimator, with considerations for convergence.