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

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

Laman Trip, J.D.S. (TU Delft BN/Greg Bokinsky Lab; Kavli institute of nanoscience Delft)
Wieringen, Wessel N.van (Vrije Universiteit Amsterdam; Amsterdam UMC)

2021

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.

Block-wise Newton–Raphson
Consistency
Graphical model
Markov random field
Network
Parallel algorithm
Pseudo-likelihood

http://resolver.tudelft.nl/uuid:c3a33015-076b-4132-a19e-f315a2bc8c73

https://doi.org/10.1007/s11222-021-10013-x

0960-3174

Statistics and Computing, 31 (4)

Institutional Repository

journal article

© 2021 J.D.S. Laman Trip, Wessel N.van Wieringen