Joint Optimization and Variable Selection of High-Dimensional Gaussian Processes
Abstract
Maximizing high-dimensional, nonconvex functions through noisy observations is a notoriously hard problem, but one that arises in many applications. In this paper, we tackle this challenge by modeling the unknown function as a sample from a high-dimensional Gaussian process (GP) distribution. Assuming that the unknown function only depends on few relevant variables, we show that it is possible to perform joint variable selection and GP optimization. We provide strong performance guarantees for our algorithm, bounding the sample complexity of variable selection, and as well as providing cumulative regret bounds. We further provide empirical evidence on the effectiveness of our algorithm on several benchmark optimization problems.
Cite
Text
Chen et al. "Joint Optimization and Variable Selection of High-Dimensional Gaussian Processes." International Conference on Machine Learning, 2012.Markdown
[Chen et al. "Joint Optimization and Variable Selection of High-Dimensional Gaussian Processes." International Conference on Machine Learning, 2012.](https://mlanthology.org/icml/2012/chen2012icml-joint/)BibTeX
@inproceedings{chen2012icml-joint,
title = {{Joint Optimization and Variable Selection of High-Dimensional Gaussian Processes}},
author = {Chen, Bo and Castro, Rui M. and Krause, Andreas},
booktitle = {International Conference on Machine Learning},
year = {2012},
url = {https://mlanthology.org/icml/2012/chen2012icml-joint/}
}