Approximation results regarding the multiple-output mixture of linear experts model

Abstract

Mixture of experts (MoE) models are a class of artificial neural networks that can be used for functional approximation and probabilistic modeling. An important class of MoE models is the class of mixture of linear experts (MoLE) models, where the expert functions map to real topological output spaces. There are a number of powerful approximation results regarding MoLE models, when the output space is univariate. These results guarantee the ability of MoLE mean functions to approximate arbitrary continuous functions, and MoLE models themselves to approximate arbitrary conditional probability density functions. We utilize and extend upon the univariate approximation results in order to prove a pair of useful results for situations where the output spaces are multivariate.

References in corpus (5)

• Model-based clustering via linear cluster-weighted models
• Joint segmentation of multivariate time series with hidden process regression for human activity recognition
• High-Dimensional Regression with Gaussian Mixtures and Partially-Latent Response Variables
• Approximation of conditional densities by smooth mixtures of regressions
• Robust mixture of experts modeling using the $t$ distribution