Uncertainty estimation is a key issue when considering the application of deep neural network methods in science and engineering. In this work, we introduce a novel algorithm that quantifies epistemic uncertainty via Monte Carlo sampling from a tempered posterior distribution. It combines the well established Metropolis Adjusted Langevin Algorithm (MALA) with momentum-based optimization using Adam and leverages a prolate proposal distribution, to efficiently draw from the posterior. We prove that the constructed chain admits the Gibbs posterior as invariant distribution and approximates this posterior in total variation distance. Furthermore, we demonstrate the efficiency of the resulting algorithm and the merit of the proposed changes on a state-of-the-art classifier from high-energy particle physics.

翻译：不确定性估计是考虑深度神经网络方法在科学与工程领域应用时的关键问题。本文提出一种新颖算法，通过从退火后验分布进行蒙特卡洛采样来量化认知不确定性。该算法将成熟的Metropolis调整Langevin算法（MALA）与基于Adam的动量优化相结合，并利用长椭球提议分布实现后验分布的高效采样。我们证明所构建的马尔可夫链以吉布斯后验为不变分布，并在全变差距离下逼近该后验分布。此外，我们通过高能粒子物理领域的前沿分类器验证了所提算法的效率及改进方案的优势。