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 an invariant distribution and converges to this Gibbs posterior in total variation distance. Numerical evaluations are postponed to a first revision.

翻译：不确定性估计是深度神经网络方法在科学与工程应用中面临的关键问题。本文提出了一种新算法，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，以高效地从后验分布中采样。我们证明，所构建的马尔可夫链以Gibbs后验为不变分布，并在全变差距离意义下收敛至该Gibbs后验。数值评估将在首次修订中补充。