  Mixtures-of-Experts (MoE) are conditional mixture models that have shown
their performance in modeling heterogeneity in data in many statistical
learning approaches for prediction, including regression and classification, as
well as for clustering. Their estimation in high-dimensional problems is still
however challenging. We consider the problem of parameter estimation and
feature selection in MoE models with different generalized linear experts
models, and propose a regularized maximum likelihood estimation that
efficiently encourages sparse solutions for heterogeneous data with
high-dimensional predictors. The developed proximal-Newton EM algorithm
includes proximal Newton-type procedures to update the model parameter by
monotonically maximizing the objective function and allows to perform efficient
estimation and feature selection. 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, compared to the main state-of-the art competitors.
