Minimaxity and Admissibility of Bayesian Neural Networks
Bayesian neural networks (BNNs) offer a natural probabilistic formulation for inference in deep learning models. Despite their popularity, their optimality has received limited attention through the lens of statistical decision theory. In this paper, we study decision rules induced by deep, fully connected feedforward ReLU BNNs in the normal location model under quadratic loss. We show that, for fixed prior scales, the induced Bayes decision rule is not minimax. We then propose a hyperprior on the effective output variance of the BNN prior that yields a superharmonic square-root marginal density, establishing that the resulting decision rule is simultaneously admissible and minimax. We fu...
| Authors | Daniel Andrew Coulson, Martin T. Wells |
|---|---|
| Primary category | math.ST |
| Published | 6 April 2026 |
| Last updated at source | 6 April 2026 |
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