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.

寻求计算有效评估多元指数族分布的惩罚估计量。这些分布包括马尔科夫随机域，其中马尔科夫随机域具有混合类型的变量（例如，二进制和连续变量）作为关注的特殊情况。通过最大化凸凸惩罚增加的伪似然来估计模型参数。估计量是一致的。考虑到多核计算机的世界，提出了一种计算效率高的并行Newton-Raphson算法，用于对估计量进行数值评估以及其收敛条件。并行化包括将参数向量划分为多个子向量，这些子向量将同时进行估算，然后再进行汇总以形成原始参数的估算值。这种方法还可以实现对其他高维估计量的有效数值评估。仿真研究评估并比较了所提出的估计器和算法的性能。最后，所提出的方法被应用于综合组学研究的数据。