Active Learning of Linear Embeddings for Gaussian Processes

TL;DR

This paper introduces an active learning approach to identify low-dimensional structures in high-dimensional Gaussian process tasks, improving efficiency and robustness in regression, quadrature, and Bayesian optimization.

Contribution

It presents a novel active learning method for discovering low-dimensional structures and a technique for marginalizing GP hyperparameters approximately, enhancing high-dimensional GP applications.

Findings

Efficient identification of low-dimensional structures in high-dimensional GPs.

Robust marginal predictions despite hyperparameter mis-specification.

Applicable to regression, quadrature, and Bayesian optimization tasks.

Abstract

We propose an active learning method for discovering low-dimensional structure in high-dimensional Gaussian process (GP) tasks. Such problems are increasingly frequent and important, but have hitherto presented severe practical difficulties. We further introduce a novel technique for approximately marginalizing GP hyperparameters, yielding marginal predictions robust to hyperparameter mis-specification. Our method offers an efficient means of performing GP regression, quadrature, or Bayesian optimization in high-dimensional spaces.