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B1524
Title: Mixtures-of-experts with functional predictors Authors:  Faicel Chamroukhi - IRT SystemX (France) [presenting]
Nhat-Thien Pham - Caen University (France)
Van Ha Hoang - University of Science Vietnam National University in Ho Chi Minh City (Vietnam)
Geoffrey McLachlan - University of Queensland (Australia)
Abstract: Mixtures-of-experts (ME) modeling is a popular and successful framework in prediction and clustering of heterogeneous observations with associated vectorial covariates. We consider the model-based clustering and prediction with ME models in the presence of functional covariates, and present extensions to the functional data context. The new functional ME (FME) model allows to accurately capturing complex nonlinear relationships between a scalar response and a set of predictors $\{X(t), t\in\mathbb{T} \subset \mathbb{R}\}$, which are observed continuously (i.e, over time for time series), from entire functions and are potentially noisy, and the pair $(\{X(t)\},Y)$ is governed by an unknown hidden structure $Z$. We provide sparse and interpretable functional representations of the FME model, thanks to Lasso-like regularizations, notably on the derivatives of the underlying functional parameters of the model, projected onto a set of continuous basis functions. We develop dedicated EM algorithms for the regularized maximum-likelihood parameter estimation. The good performance of the proposed FME model and the developed algorithms is shown in simulated scenarios and via application to some real data sets.