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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.13454 |
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| _version_ | 1866911763853737984 |
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| author | Luke, D. Russell Schultze, Steffen Grubmüller, Helmut |
| author_facet | Luke, D. Russell Schultze, Steffen Grubmüller, Helmut |
| contents | We apply a recently developed framework for analyzing the convergence of stochastic algorithms to the general problem of large-scale nonconvex composite optimization more generally, and nonconvex likelihood maximization in particular. Our theory is demonstrated on a stochastic gradient descent algorithm for determining the electron density of a molecule from random samples of its scattering amplitude. Numerical results on an idealized synthetic example provide a proof of concept. This opens the door to a broad range of algorithmic possibilities and provides a basis for evaluating and comparing different strategies. While this case study is very specific, it shares a structure that transfers easily to many problems of current interest, particularly in machine learning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13454 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stochastic Algorithms for Large-Scale Composite Optimization: the Case of Single-Shot X-FEL Imaging Luke, D. Russell Schultze, Steffen Grubmüller, Helmut Optimization and Control 65C40, 90C26, 90C06 We apply a recently developed framework for analyzing the convergence of stochastic algorithms to the general problem of large-scale nonconvex composite optimization more generally, and nonconvex likelihood maximization in particular. Our theory is demonstrated on a stochastic gradient descent algorithm for determining the electron density of a molecule from random samples of its scattering amplitude. Numerical results on an idealized synthetic example provide a proof of concept. This opens the door to a broad range of algorithmic possibilities and provides a basis for evaluating and comparing different strategies. While this case study is very specific, it shares a structure that transfers easily to many problems of current interest, particularly in machine learning. |
| title | Stochastic Algorithms for Large-Scale Composite Optimization: the Case of Single-Shot X-FEL Imaging |
| topic | Optimization and Control 65C40, 90C26, 90C06 |
| url | https://arxiv.org/abs/2401.13454 |