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Approximations of conditional probability density functions in Lebesgue spaces via mixture of experts models

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posted on 08.09.2021, 04:00 by Hien NguyenHien Nguyen, TT Nguyen, Faicel ChamroukhiFaicel Chamroukhi, GJ McLachlan
Mixture of experts (MoE) models are widely applied for conditional probability density estimation problems. We demonstrate the richness of the class of MoE models by proving denseness results in Lebesgue spaces, when inputs and outputs variables are both compactly supported. We further prove an almost uniform convergence result when the input is univariate. Auxiliary lemmas are proved regarding the richness of the soft-max gating function class, and their relationships to the class of Gaussian gating functions.

History

Publication Date

01/12/2021

Journal

Journal of Statistical Distributions and Applications

Volume

8

Article Number

13

Pagination

15p.

Publisher

Springer Nature

ISSN

2195-5832

Rights Statement

© The Author(s). 2021. Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.