Functional Mixtures of Experts model and application to some real data sets

We are interested in the problem of clustering and prediction of heterogeneous datawith functional predictors, when the heterogeneous population is composed of several sub-populations,  leading to complex distributions. By investigating Mixtures-of-Experts models, a family of conditional mixture models that have shown their performance in modeling heterogeneity in data in many statistical learning problems, and adopting a projection onto finite bases approach, we present a new framework called FME to deal with the interesting problem. We develop an adapted EM algorithm for the maximum likelihood parameter estimation and consider a regularized version encouraging sparsity to deal with such high-dimensional settings. The models and algorithms are evaluated on simulations and real data sets (Phonemes, Canadian weather data, ...) Keywords: functional data analysis, mixture of experts, B-spline basis, wavelet basis, PCA, maximum likelihood, Dantzig selector,...