Source-linked AI summary
Irreversible Monte Carlo Algorithms for Efficient Sampling
Konstantin S. Turitsyn, Michael Chertkov, Marija Vucelja
TL;DR
The paper asks whether reversible MCMC is the most efficient strategy for sampling, given that traditional methods can mix slowly because of high barriers or high-entropy state basins. It deforms a reversible chain using replicas and tuned switching probabilities; in a spin-cluster example, the irreversible version removes critical slowdown.
Problem
The paper questions whether reversible MCMC is the most efficient sampling strategy, as traditional methods can mix slowly across high barriers or high-entropy state basins.
Source: p. 1Method
The method deforms an existing reversible chain using replicas, compressible probability flows, and tuned inter-replica switching probabilities to preserve the target distribution.
Source: p. 2Results
The irreversible modification removes critical slowdown in the mean-field spin-cluster example.
Source: pp. 3–4Takeaways & Limitations
The authors suggest irreversible algorithms may especially accelerate mixing in systems with multiple soft and zero modes that standard reversible schemes cannot access.
Source: p. 4The construction assumes a reversible transition matrix that obeys detailed balance and converges to the target equilibrium distribution.
Source: p. 2
Abstract
from arXiv · showhide
Equilibrium systems evolve according to Detailed Balance (DB). This principe guided development of the Monte-Carlo sampling techniques, of which Metropolis-Hastings (MH) algorithm is the famous representative. It is also known that DB is sufficient but not necessary. We construct irreversible deformation of a given reversible algorithm capable of dramatic improvement of sampling from known distribution. Our transformation modifies transition rates keeping the structure of transitions intact. To illustrate the general scheme we design an Irreversible version of Metropolis-Hastings (IMH) and test it on example of a spin cluster. Standard MH for the model suffers from the critical slowdown, while IMH is free from critical slowdown.