用更少参数实现与传统贝叶斯神经网络相当的不确定性量化。
Partial Trace-Class Bayesian Neural Networks
- 基于迹类先验设计三种新型网络架构，自动排序参数以降低复杂度。
- 相比标准BNN，参数量大幅减少，速度更快、内存占用更低。
- 适合需要高效可靠不确定性的实际应用，如医疗或自动驾驶。
贝叶斯神经网络（BNN）可实现深度学习中的严格不确定性量化，但计算成本高昂。本文提出三种创新的局部迹类贝叶斯神经网络（PaTraC BNN）架构，可在保持与标准BNN相当的不确定性量化能力的同时，显著减少贝叶斯参数数量。这些架构在计算和统计上均优于标准BNN，具有更高的速度和更低的内存需求。方法基于迹类神经网络先验，自然地对网络参数进行排序。数值模拟验证了其优势，并在真实数据集上展示了性能表现。
原文摘要 · Abstract (English)
Bayesian neural networks (BNNs) allow rigorous uncertainty quantification in deep learning, but often come at a prohibitive computational cost. We propose three different innovative architectures of partial trace-class Bayesian neural networks (PaTraC BNNs) that enable uncertainty quantification comparable to standard BNNs but use significantly fewer Bayesian parameters. These PaTraC BNNs have computational and statistical advantages over standard Bayesian neural networks in terms of speed and memory requirements. Our proposed methodology therefore facilitates reliable, robust, and scalable uncertainty quantification in neural networks. The three architectures build on trace-class neural network priors which induce an ordering of the neural network parameters, and are thus a natural choice in our framework. In a numerical simulation study, we verify the claimed benefits, and further illustrate the performance of our proposed methodology on a real-world dataset.
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