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

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posted on 2021-09-08, 04:00 authored by Hien Nguyen, TT Nguyen, Faicel 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.


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Journal of Statistical Distributions and Applications



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Springer Nature



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