Predictive uncertainty quantification is crucial for reliable decision-making
in various applied domains. Bayesian neural networks offer a powerful framework
for this task. However, defining meaningful priors and ensuring computational
efficiency remain significant challenges, especially for complex real-world
applications. This paper addresses these challenges by proposing a novel neural
adaptive empirical Bayes (NA-EB) framework. NA-EB leverages a class of implicit
generative priors derived from low-dimensional distributions. This allows for
efficient handling of complex data structures and effective capture of
underlying relationships in real-world datasets. The proposed NA-EB framework
combines variational inference with a gradient ascent algorithm. This enables
simultaneous hyperparameter selection and approximation of the posterior
distribution, leading to improved computational efficiency. We establish the
theoretical foundation of the framework through posterior and classification
consistency. We demonstrate the practical applications of our framework through
extensive evaluations on a variety of tasks, including the two-spiral problem,
regression, 10 UCI datasets, and image classification tasks on both MNIST and
CIFAR-10 datasets. The results of our experiments highlight the superiority of
our proposed framework over existing methods, such as sparse variational
Bayesian and generative models, in terms of prediction accuracy and uncertainty
quantification.

本文提出了一种新颖的神经自适应经验贝叶斯（NA-EB）框架，该框架结合了变分推断和梯度上升算法，以实现同步超参数选择和后验分布的近似，从而提高计算效率，并通过对各种任务的广泛评估展示了我们提出框架在预测准确性和不确定性量化方面的优越性。