NeurIPS 2022accept20 citations
On the inability of Gaussian process regression to optimally learn compositional functions
Matteo Giordano, Kolyan Ray, Johannes Schmidt-Hieber
Abstract
We rigorously prove that deep Gaussian process priors can outperform Gaussian process priors if the target function has a compositional structure. To this end, we study information-theoretic lower bounds for posterior contraction rates for Gaussian process regression in a continuous regression model. We show that if the true function is a generalized additive function, then the posterior based on any mean-zero Gaussian process can only recover the truth at a rate that is strictly slower than the minimax rate by a factor that is polynomially suboptimal in the sample size $n$.
Gaussian processesBayesian nonparametricsposterior contractionminimax estimationlarge-sample asymptotics
BibTeX
@inproceedings{
giordano2022on,
title={On the inability of Gaussian process regression to optimally learn compositional functions},
author={Matteo Giordano and Kolyan Ray and Johannes Schmidt-Hieber},
booktitle={Advances in Neural Information Processing Systems},
editor={Alice H. Oh and Alekh Agarwal and Danielle Belgrave and Kyunghyun Cho},
year={2022},
url={https://openreview.net/forum?id=fhO6vCGuuag}
}