Statistics > Machine Learning
arXiv:2312.14027 (stat)
[Submitted on 21 Dec 2023 (v1), last revised 5 Dec 2024 (this version, v3)]
Title:AdamMCMC: Combining Metropolis Adjusted Langevin with Momentum-based Optimization
View a PDF of the paper titled AdamMCMC: Combining Metropolis Adjusted Langevin with Momentum-based Optimization, by Sebastian Bieringer and 3 other authors
View PDFHTML (experimental)Abstract: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.
| Comments: | 16 pages, 5 figures; adapted Theorem 2 |
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG); High Energy Physics - Phenomenology (hep-ph); Computation (stat.CO) |
| Cite as: | arXiv:2312.14027 [stat.ML] |
| (orarXiv:2312.14027v3 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2312.14027 arXiv-issued DOI via DataCite |
Submission history
From: Sebastian Bieringer [view email][v1] Thu, 21 Dec 2023 16:58:49 UTC (40 KB)
[v2] Thu, 15 Aug 2024 18:00:14 UTC (655 KB)
[v3] Thu, 5 Dec 2024 10:49:37 UTC (739 KB)
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View a PDF of the paper titled AdamMCMC: Combining Metropolis Adjusted Langevin with Momentum-based Optimization, by Sebastian Bieringer and 3 other authors
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