A PAC-Bayes oracle inequality for sparse neural networks

Fuente: arXiv
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Autori principali: Steffen, Maximilian F., Trabs, Mathias
Natura: Preprint
Pubblicazione: 2022
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author Steffen, Maximilian F.
Trabs, Mathias
author_facet Steffen, Maximilian F.
Trabs, Mathias
contents We study the Gibbs posterior distribution for sparse deep neural nets in a nonparametric regression setting. The posterior can be accessed via Metropolis-adjusted Langevin algorithms. Using a mixture over uniform priors on sparse sets of network weights, we prove an oracle inequality which shows that the method adapts to the unknown regularity and hierarchical structure of the regression function. The estimator achieves the minimax-optimal rate of convergence (up to a logarithmic factor).
format Preprint
id arxiv_https___arxiv_org_abs_2204_12392
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle A PAC-Bayes oracle inequality for sparse neural networks
Steffen, Maximilian F.
Trabs, Mathias
Statistics Theory
Machine Learning
62G08, 62F15, 68T05
We study the Gibbs posterior distribution for sparse deep neural nets in a nonparametric regression setting. The posterior can be accessed via Metropolis-adjusted Langevin algorithms. Using a mixture over uniform priors on sparse sets of network weights, we prove an oracle inequality which shows that the method adapts to the unknown regularity and hierarchical structure of the regression function. The estimator achieves the minimax-optimal rate of convergence (up to a logarithmic factor).
title A PAC-Bayes oracle inequality for sparse neural networks
topic Statistics Theory
Machine Learning
62G08, 62F15, 68T05
url https://arxiv.org/abs/2204.12392