On the Inability of Gaussian Process Regression to Optimally Learn Compositional Functions
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 $n$.
Cite
Text
Giordano et al. "On the Inability of Gaussian Process Regression to Optimally Learn Compositional Functions." Neural Information Processing Systems, 2022.Markdown
[Giordano et al. "On the Inability of Gaussian Process Regression to Optimally Learn Compositional Functions." Neural Information Processing Systems, 2022.](https://mlanthology.org/neurips/2022/giordano2022neurips-inability/)BibTeX
@inproceedings{giordano2022neurips-inability,
title = {{On the Inability of Gaussian Process Regression to Optimally Learn Compositional Functions}},
author = {Giordano, Matteo and Ray, Kolyan and Schmidt-Hieber, Johannes},
booktitle = {Neural Information Processing Systems},
year = {2022},
url = {https://mlanthology.org/neurips/2022/giordano2022neurips-inability/}
}