Sampling via Rejection-Free Partial Neighbor Search

TL;DR

This paper introduces Partial Neighbor Search, an enhanced Rejection-Free Metropolis algorithm that considers only a subset of neighbors to improve efficiency on specialized hardware, demonstrated through various tests.

Contribution

The paper proposes Partial Neighbor Search, a novel modification of Rejection-Free Metropolis that limits neighbor evaluations to enhance efficiency on hardware with limited parallel units.

Findings

Effective in reducing computation time

Maintains accuracy with partial neighbor consideration

Demonstrates advantages across multiple examples

Abstract

The Metropolis algorithm involves producing a Markov chain to converge to a specified target density $\pi$. In order to improve its efficiency, we can use the Rejection-Free version of the Metropolis algorithm, which avoids the inefficiency of rejections by evaluating all neighbors. Rejection-Free can be made more efficient through the use of parallelism hardware. However, for some specialized hardware, such as Digital Annealing Unit, the number of units will limit the number of neighbors being considered at each step. Hence, we propose an enhanced version of Rejection-Free known as Partial Neighbor Search, which only considers a portion of the neighbors while using the Rejection-Free technique. This method will be tested on several examples to demonstrate its effectiveness and advantages under different circumstances.