  Mixture of Experts (MoE) are successful models for modeling heterogeneous
data in many statistical learning problems including regression, clustering and
classification. Generally fitted by maximum likelihood estimation via the
well-known EM algorithm, their application to high-dimensional problems is
still therefore challenging. We consider the problem of fitting and feature
selection in MoE models, and propose a regularized maximum likelihood
estimation approach that encourages sparse solutions for heterogeneous
regression data models with potentially high-dimensional predictors. Unlike
state-of-the art regularized MLE for MoE, the proposed modelings do not require
an approximate of the penalty function. We develop two hybrid EM algorithms: an
Expectation-Majorization-Maximization (EM/MM) algorithm, and an EM algorithm
with coordinate ascent algorithm. The proposed algorithms allow to
automatically obtaining sparse solutions without thresholding, and avoid matrix
inversion by allowing univariate parameter updates. An experimental study shows
the good performance of the algorithms in terms of recovering the actual sparse
solutions, parameter estimation, and clustering of heterogeneous regression
data.
