Uncertainty Quantification for Sparse Deep Learning

Yuexi Wang, Veronika Ročková

Research output: Contribution to journalConference articlepeer-review


Deep learning methods continue to have a decided impact on machine learning, both in theory and in practice. Statistical theoretical developments have been mostly concerned with approximability or rates of estimation when recovering infinite dimensional objects (curves or densities). Despite the impressive array of available theoretical results, the literature has been largely silent about uncertainty quantification for deep learning. This paper takes a step forward in this important direction by taking a Bayesian point of view. We study Gaussian approximability of certain aspects of posterior distributions of sparse deep ReLU architectures in non-parametric regression. Building on tools from Bayesian non-parametrics, we provide semi-parametric Bernstein-von Mises theorems for linear and quadratic functionals, which guarantee that implied Bayesian credible regions have valid frequentist coverage. Our results provide new theoretical justifications for (Bayesian) deep learning with ReLU activation functions, highlighting their inferential potential.

Original languageEnglish (US)
Pages (from-to)298-308
Number of pages11
JournalProceedings of Machine Learning Research
StatePublished - 2020
Externally publishedYes
Event23rd International Conference on Artificial Intelligence and Statistics, AISTATS 2020 - Virtual, Online
Duration: Aug 26 2020Aug 28 2020

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


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