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Computational efficient evaluation of penalized estimators of multivariateexponential family distributions is sought. These distributions encompass amongothers Markov random fields with variates of mixed type (e.g. binary andcontinuous) as special case of interest. The model parameter is estimated bymaximization of the pseudo-likelihood augmented with a convex penalty. Theestimator is shown to be consistent. With a world of multi-core computers inmind, a computationally efficient parallel Newton-Raphson algorithm ispresented for numerical evaluation of the estimator alongside conditions forits convergence. Parallelization comprises the division of the parameter vectorinto subvectors that are estimated simultaneously and subsequently aggregatedto form an estimate of the original parameter. This approach may also enableefficient numerical evaluation of other high-dimensional estimators. Theperformance of the proposed estimator and algorithm are evaluated and comparedin a simulation study. Finally, the paper concludes with an illustration of thepresented methodology in the reconstruction of the conditional independencenetwork from data of an integrative omics study.

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