  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.
