Hit and Run Sampling from Tropically Convex Sets

TL;DR

This paper introduces a novel Hit and Run sampling method for tropically convex sets, enabling efficient uniform sampling from tropical polytopes and extending to arbitrary distributions via Metropolis-Hastings filtering.

Contribution

It presents the first efficient HAR sampling technique for tropically convex sets, with linear time complexity for sampling from tropical line segments.

Findings

Samples uniformly from tropical polytopes

Sampling complexity is linear in segment length

Applicable to arbitrary distributions using Metropolis-Hastings

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.