Uncertainty Quantification for nonparametric regression using Empirical Bayesian neural networks

Understand

We propose a new, two-step empirical Bayes-type of approach for neural networks.

• We show in context of the nonparametric regression model that the procedure (up to a logarithmic factor) provides optimal recovery of the underlying functional parameter of interest and provides Bayesian credible sets with frequentist coverage guarantees.
• The approach requires fitting the neural network only once, hence it is substantially faster than Bootstrapping type approaches.
• We demonstrate the applicability of our method over synthetic data, observing good estimation properties and reliable uncertainty quantification.