JMLR

The surrogate Gibbs-posterior of a corrected stochastic MALA: Towards uncertainty quantification for neural networks

校正的随机MALA的替代Gibbs后验：面向神经网络的不确定性量化

Sebastian Bieringer, Gregor Kasieczka, Maximilian F. Steffen, Mathias Trabs

机构 * Universität Hamburg（汉堡大学） ； Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院） 纠错

AI总结 本文提出校正的随机MALA（csMALA），通过简单修正项减少替代后验与原始Gibbs后验之间的距离，同时保持可扩展性，并在非参数回归模型中证明了PAC-Bayes oracle不等式，展示了对神经网络的不确定性量化。

Comments The first version of this manuscript was entitled "Statistical guarantees for stochastic Metropolis-Hastings''. Some preliminary results were initially presented in the first version of arXiv:2204.12392, but have been moved to this manuscript, where they have been further developed

Journal ref Journal of Machine Learning Research, 27 (1), 1-50, 2026