Bayesian Neural Network (BNN) offers a more principled, robust, and interpretable framework for analyzing high-dimensional data. They address the typical challenges associated with conventional deep learning methods, such as data insatiability, ad-hoc nature, and susceptibility to overfitting. However, their implementation typically relies on Markov chain Monte Carlo (MCMC) methods that are characterized by their computational intensity and inefficiency in a high-dimensional space. To address this issue, we propose a novel Calibration-Emulation-Sampling (CES) strategy to significantly enhance the computational efficiency of BNN. In this CES framework, during the initial calibration stage, we collect a small set of samples from the parameter space. These samples serve as training data for the emulator. Here, we employ a Deep Neural Network (DNN) emulator to approximate the forward mapping, i.e., the process that input data go through various layers to generate predictions. The trained emulator is then used for sampling from the posterior distribution at substantially higher speed compared to the original BNN. Using simulated and real data, we demonstrate that our proposed method improves computational efficiency of BNN, while maintaining similar performance in terms of prediction accuracy and uncertainty quantification.

翻译：贝叶斯神经网络为分析高维数据提供了更严谨、稳健且可解释的框架。它解决了传统深度学习方法中常见的挑战，如数据不稳定性、临时性以及易过拟合问题。然而，其实现通常依赖于马尔可夫链蒙特卡洛方法，这类方法在高维空间中具有计算密集且效率低下的特点。为解决此问题，我们提出了一种新颖的校准-仿真-采样（CES）策略，以显著提升贝叶斯神经网络的计算效率。在该CES框架中，初始校准阶段我们从参数空间中收集少量样本。这些样本作为仿真器的训练数据。我们采用深度神经网络仿真器来逼近前向映射，即输入数据经过各层生成预测的过程。随后，利用训练好的仿真器从后验分布中采样，其速度远超原始贝叶斯神经网络。通过模拟数据和真实数据的实验，我们证明所提方法在提升贝叶斯神经网络计算效率的同时，能够保持与原始方法相当的预测精度和不确定性量化性能。