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.
@article{arxiv.1310.6740,
title = {Active Learning of Linear Embeddings for Gaussian Processes},
author = {Roman Garnett and Michael A. Osborne and Philipp Hennig},
journal= {arXiv preprint arXiv:1310.6740},
year = {2013}
}