Functional Mixtures-of-Experts

TL;DR

This paper introduces functional Mixtures-of-Experts models for heterogeneous functional data, incorporating sparsity and interpretability, with algorithms validated on simulations and real datasets.

Contribution

It extends Mixtures-of-Experts to functional data, proposing sparse, interpretable models with specialized EM algorithms for estimation.

Findings

Models accurately capture complex nonlinear relationships.

Effective in clustering heterogeneous functional data.

Validated on simulated and real datasets.

Abstract

We consider the statistical analysis of heterogeneous data for prediction in situations where the observations include functions, typically time series. 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--maximization algorithms for Lasso-like (EM-Lasso) 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.