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A Universal Approximation Theorem for Mixture-of-Experts Models.

Hien D Nguyen¹, Luke R Lloyd-Jones², Geoffrey J McLachlan³

¹School of Mathematics and Physics, University of Queensland, Brisbane, Queensland 4072, Australia hien1988@gmail.com.

Neural Computation

|September 15, 2016

Summary

This summary is machine-generated.

Mixture-of-experts (MoE) models can approximate any continuous function, offering a universal approximation capability. This finding ensures MoE models are reliable for complex data, even with nonlinear and nondifferentiable processes.

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Area of Science:

Machine Learning
Artificial Intelligence
Neural Networks

Background:

Mixture-of-experts (MoE) models are widely used for nonlinear regression and classification.
Existing theory shows MoE mean functions uniformly converge to target functions under specific differentiability and domain constraints.

Purpose of the Study:

To establish a universal approximation theorem for MoE models.
To demonstrate the density of MoE mean functions within the space of all continuous functions over arbitrary compact domains.

Main Methods:

Theoretical analysis of MoE model properties.
Development of a new convergence result for MoE mean functions.

Main Results:

The class of MoE mean functions is dense in the space of all continuous functions on arbitrary compact domains.
This result extends the applicability of MoE models beyond strictly differentiable functions.

Conclusions:

MoE models possess universal approximation capabilities for continuous functions.
This theoretical foundation provides confidence in applying MoE models to complex, nonlinear, and nondifferentiable data generation processes.