Reproducible Adaptive MCMC via Sharing a Pretrained Generator Matrix across Runs and Structures

Area of Science:

• Computational Chemistry
• Statistical Physics
• Biophysics

Background:

• Adaptive Markov chain Monte Carlo (MCMC) methods accelerate sampling but introduce irreproducibility via path-dependent proposal kernel adaptation.
• Naive on-the-fly learning in adaptive MCMC can lead to run-to-run variability and sampler freezing, particularly with insufficient training or replication.

Purpose of the Study:

• To systematically analyze the impact of path-dependent adaptation on MCMC reproducibility.
• To develop a theoretically sound strategy for reproducible adaptive MCMC sampling.
• To provide practical guidelines for selecting training lengths in adaptive MCMC.

Main Methods:

• Generator-matrix-based adaptive MCMC was analyzed to understand path-dependent adaptation effects.
• A pretraining and shared-matrix strategy was proposed and validated.
• Reproducibility was quantified by measuring spread variability (SD) across multiple seeds and training lengths.
• Transferability of the pre-trained matrix across related DNA structures was assessed.

Main Results:

• On-the-fly learning in adaptive MCMC leads to severe run-to-run variability and sampler freezing.
• Short training durations result in degenerate, frozen samplers, while apparent overadaptation is an artifact of insufficient replication.
• The proposed shared-matrix approach reduced cross-run spread by 68% compared to independent learning.
• The pre-trained matrix demonstrated effective transferability across related DNA structures with a small transfer gap (<1 Å).
• Ensemble averaging of generator matrices was found to degrade performance.

Conclusions:

• Path-dependent adaptation in MCMC poses a significant challenge to reproducibility.
• Pretraining a generator matrix and sharing it as a fixed proposal kernel offers a robust framework for reproducible adaptive MCMC.
• The shared-matrix approach enhances reproducibility, maintains sampling quality, and provides effective transferability.
• Guidelines for training length selection and a framework for reproducible adaptive MCMC are established, validated in coarse-grained DNA systems.