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We extend the modeling with mixtures-of-experts (ME), as a framework of choice in modeling heterogeneity in data for prediction with vectorial observations, to this functional data analysis context. We first present a new family of ME models, named functional ME (FME), in which the predictors are potentially noisy observations, from entire functions. Furthermore, the data generating process of the predictor and the real response, is governed by a hidden discrete variable representing an unknown partition. Second, by imposing sparsity on derivatives of the underlying functional parameters via Lasso-like regularizations, we provide sparse and interpretable functional representations of the FME models called iFME. We develop dedicated expectation\u2013maximization algorithms for Lasso-like regularized maximum-likelihood parameter estimation strategies to fit the models. The proposed models and algorithms are studied in simulated scenarios and in applications to two real data sets, and the obtained results demonstrate their performance in accurately capturing complex nonlinear relationships and in clustering the heterogeneous regression data.<\/jats:p>","DOI":"10.1007\/s11222-023-10379-0","type":"journal-article","created":{"date-parts":[[2024,3,18]],"date-time":"2024-03-18T05:01:52Z","timestamp":1710738112000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Functional mixtures-of-experts"],"prefix":"10.1007","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5894-3103","authenticated-orcid":false,"given":"Fa\u00efcel","family":"Chamroukhi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nhat Thien","family":"Pham","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Van H\u00e0","family":"Hoang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Geoffrey J.","family":"McLachlan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,3,18]]},"reference":[{"key":"10379_CR1","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1016\/j.jmva.2015.09.008","volume":"143","author":"\u00c9lodie Brunel","year":"2016","unstructured":"Brunel, \u00c9lodie., Mas, A., Roche, A.: Non-asymptotic adaptive prediction in functional linear models. 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