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

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