Enriched Mixtures of Gaussian Process Experts

TL;DR

This paper introduces an advanced mixture of Gaussian process experts model that automatically determines the number of components and effectively handles diverse data types, improving scalability and predictive accuracy.

Contribution

The authors develop a nested partitioning scheme for mixtures of GP experts that infers the number of components automatically and accommodates multiple data types within a unified framework.

Findings

Effective in high-dimensional synthetic data

Accurate probabilistic modeling of Alzheimer's dataset

Improved scalability and component inference

Abstract

Mixtures of experts probabilistically divide the input space into regions, where the assumptions of each expert, or conditional model, need only hold locally. Combined with Gaussian process (GP) experts, this results in a powerful and highly flexible model. We focus on alternative mixtures of GP experts, which model the joint distribution of the inputs and targets explicitly. We highlight issues of this approach in multi-dimensional input spaces, namely, poor scalability and the need for an unnecessarily large number of experts, degrading the predictive performance and increasing uncertainty. We construct a novel model to address these issues through a nested partitioning scheme that automatically infers the number of components at both levels. Multiple response types are accommodated through a generalised GP framework, while multiple input types are included through a factorised exponential family structure. We show the effectiveness of our approach in estimating a parsimonious probabilistic description of both synthetic data of increasing dimension and an Alzheimer's challenge dataset.