  We investigate the estimation properties of the mixture of experts (MoE)
model in a high-dimensional setting, where the number of predictors is much
larger than the sample size, and for which the literature is particularly
lacking in theoretical results. We consider the class of softmax-gated Gaussian
MoE (SGMoE) models, defined as MoE models with softmax gating functions and
Gaussian experts, and focus on the theoretical properties of their
$l_1$-regularized estimation via the Lasso. To the best of our knowledge, we
are the first to investigate the $l_1$-regularization properties of SGMoE
models from a non-asymptotic perspective, under the mildest assumptions, namely
the boundedness of the parameter space. We provide a lower bound on the
regularization parameter of the Lasso penalty that ensures non-asymptotic
theoretical control of the Kullback--Leibler loss of the Lasso estimator for
SGMoE models. Finally, we carry out a simulation study to empirically validate
our theoretical findings.
