# Functional Mixtures-of-Experts

arXiv: https://arxiv.org/abs/2202.02249 · HTML: https://mlsanity.com/paper/2202.02249/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in MoE theory and gating functions, one of 12 directions in Mixture-of-experts.
- Builds on 7 of its 54 references that are in the map.
- First posted on arXiv 4 Feb 2022.

## Placed in

- Mixture-of-experts / [MoE theory and gating functions](https://mlsanity.com/moe/moe-theory-and-gating-functions/)

## Builds on (most cited first, 7 of 7)

- [Algorithms for Fitting the Constrained Lasso](https://mlsanity.com/paper/1611.01511/) (2016)
- [Regularized Estimation and Feature Selection in Mixtures of Generalized Linear Experts](https://mlsanity.com/paper/1907.06994/) (2019)
- [Regularized Maximum Likelihood Estimation and Feature Selection in Mixtures-of-Experts Models](https://mlsanity.com/paper/1810.12161/) (2018)
- [Non-asymptotic model selection in block-diagonal mixture of polynomial experts models](https://mlsanity.com/paper/2104.08959/) (2021)
- [Model-Based Clustering and Classification of Functional Data](https://mlsanity.com/paper/1803.00276/) (2018)
- [Regularized Estimation and Feature Selection in Mixtures of Gaussian-Gated Experts Models](https://mlsanity.com/paper/1909.05494/) (2019)
- [Wavelet-Based Scalar-on-Function Finite Mixture Regression Models](https://mlsanity.com/paper/1312.0652/) (2013)

## Built on by (most cited first, 2 of 2)

- [Functional mixture-of-experts for classification](https://mlsanity.com/paper/2202.13934/) (2022)
- [Varying-coefficient mixture of experts model for dynamic heterogeneous populations: application to mouse cortical development](https://mlsanity.com/paper/2601.01699/) (2026)

## Abstract (arXiv)

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.