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Hit and run
sampling from tropically convex sets
Ruriko Yoshida, Keiji Miura and David Barnhill |
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Vol. 14 (2023), No. 1, 37–69
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Abstract |
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We propose hit and run (HAR) sampling from a tropically convex set. The key ingredient of HAR sampling from a tropically convex set is sampling uniformly from a tropical line segment over the tropical projective torus, which runs linearly in computational complexity. We show that this HAR sampling method samples uniformly from a tropical polytope which is the smallest tropical convex set of finitely many vertices. Finally, we apply this novel method to any given distribution using Metropolis–Hastings filtering over a tropical polytope. |
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Keywords
hit and run sampling, tropical geometry, Markov chain Monte
Carlo, tropical convexity
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Mathematical Subject Classification
Primary: 52B05, 62D99
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Milestones
Received: 29 September 2022
Revised: 12 May 2023
Accepted: 14 May 2023
Published: 28 November 2023
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Authors |
| Ruriko Yoshida | |
| Department of Operations
Research Naval Postgraduate School Monterey, CA United States |
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| Keiji Miura | |
| Kwansei Gakuin University Sanda Hyogo Japan |
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| David Barnhill | |
| Department of Operations
Research Naval Postgraduate School Monterey, CA United States |
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| © 2023 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). |
