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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.14027 |
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| _version_ | 1866909416255651840 |
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| author | Bieringer, Sebastian Kasieczka, Gregor Steffen, Maximilian F. Trabs, Mathias |
| author_facet | Bieringer, Sebastian Kasieczka, Gregor Steffen, Maximilian F. Trabs, Mathias |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_14027 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | AdamMCMC: Combining Metropolis Adjusted Langevin with Momentum-based Optimization Bieringer, Sebastian Kasieczka, Gregor Steffen, Maximilian F. Trabs, Mathias Machine Learning High Energy Physics - Phenomenology Computation 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. |
| title | AdamMCMC: Combining Metropolis Adjusted Langevin with Momentum-based Optimization |
| topic | Machine Learning High Energy Physics - Phenomenology Computation |
| url | https://arxiv.org/abs/2312.14027 |