Recent studies have shown that the generalization ability of deep neural networks (DNNs) is closely related to the Fisher information matrix (FIM) calculated during the early training phase. Several methods have been proposed to regularize the FIM for increased generalization of DNNs. However, they cannot be used directly for Bayesian neural networks (BNNs) because the variable parameters of BNNs make it difficult to calculate the FIM. To address this problem, we achieve regularization of the FIM of BNNs by specifying a new suitable prior distribution called the inverse-reference (IR) prior. To regularize the FIM, the IR prior is derived as the inverse of the reference prior that imposes minimal prior knowledge on the parameters and maximizes the trace of the FIM. We demonstrate that the IR prior can enhance the generalization ability of BNNs for large-scale data over previously used priors while providing adequate uncertainty quantifications using various benchmark image datasets and BNN structures.

Several out-of-distribution (OOD) detection scores have been recently proposed for deep generative models because the direct use of the likelihood threshold for OOD detection has been shown to be problematic. In this paper, we propose a new OOD score based on a Bayesian hypothesis test called the locally most powerful Bayesian test (LMPBT). The LMPBT is locally most powerful in that the alternative hypothesis (the representative parameter for the OOD sample) is specified to maximize the probability that the Bayes factor exceeds the evidence threshold in favor of the alternative hypothesis provided that the parameter specified under the alternative hypothesis is in the neighborhood of the parameter specified under the null hypothesis. That is, under this neighborhood parameter condition, the test with the proposed alternative hypothesis maximizes the probability of correct detection of OOD samples. We also propose numerical strategies for more efficient and reliable computation of the LMPBT for practical application to deep generative models. Evaluations conducted of the OOD detection performance of the LMPBT on various benchmark datasets demonstrate its superior performance over existing OOD detection methods.