  Mixture of Experts (MoE) is a popular framework for modeling heterogeneity in
data for regression, classification and clustering. For continuous data which
we consider here in the context of regression and cluster analysis, MoE usually
use normal experts, that is, expert components following the Gaussian
distribution. However, for a set of data containing a group or groups of
observations with asymmetric behavior, heavy tails or atypical observations,
the use of normal experts may be unsuitable and can unduly affect the fit of
the MoE model. In this paper, we introduce new non-normal mixture of experts
(NNMoE) which can deal with these issues regarding possibly skewed,
heavy-tailed data and with outliers. The proposed models are the skew-normal
MoE and the robust $t$ MoE and skew $t$ MoE, respectively named SNMoE, TMoE and
STMoE. We develop dedicated expectation-maximization (EM) and expectation
conditional maximization (ECM) algorithms to estimate the parameters of the
proposed models by monotonically maximizing the observed data log-likelihood.
We describe how the presented models can be used in prediction and in
model-based clustering of regression data. Numerical experiments carried out on
simulated data show the effectiveness and the robustness of the proposed models
in terms modeling non-linear regression functions as well as in model-based
clustering. Then, to show their usefulness for practical applications, the
proposed models are applied to the real-world data of tone perception for
musical data analysis, and the one of temperature anomalies for the analysis of
climate change data.
