Hit and Run Sampling from Tropically Convex Sets
Abstract
In this paper 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 its computational time 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-Hasting filtering over a tropical polytope.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2022
- DOI:
- 10.48550/arXiv.2209.15045
- arXiv:
- arXiv:2209.15045
- Bibcode:
- 2022arXiv220915045Y
- Keywords:
-
- Mathematics - Combinatorics;
- Mathematics - Probability
- E-Print:
- Alg. Stat. 14 (2023) 37-69