Large-Flip Importance Sampling

TL;DR

This paper introduces a novel Monte Carlo importance sampling algorithm for complex discrete distributions, inspired by the N-Fold Way, addressing its cycle-trapping issue with bias correction.

Contribution

It presents a modified N-Fold Way algorithm combined with importance sampling to improve sampling efficiency and correctness for discrete distributions.

Findings

Effective in avoiding cycles in N-Fold Way

Bias correction improves sampling accuracy

Demonstrates improved convergence properties

Abstract

We propose a new Monte Carlo algorithm for complex discrete distributions. The algorithm is motivated by the N-Fold Way, which is an ingenious event-driven MCMC sampler that avoids rejection moves at any specific state. The N-Fold Way can however get "trapped" in cycles. We surmount this problem by modifying the sampling process. This correction does introduce bias, but the bias is subsequently corrected with a carefully engineered importance sampler.