AdamMCMC: Combining Metropolis Adjusted Langevin with Momentum-based Optimization
This addresses uncertainty quantification for deep learning applications in science and engineering, representing an incremental improvement over existing methods.
The authors tackled uncertainty estimation in deep neural networks by introducing AdamMCMC, a novel algorithm combining Metropolis Adjusted Langevin with momentum-based optimization to sample from tempered posteriors, demonstrating efficiency on a state-of-the-art classifier from high-energy particle physics.
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.