Adaptive tuning of Hamiltonian Monte Carlo methods

2025-06-04

AI Summary

HMC performance critically depends on hyperparameters such as integrator type and step size; existing tuning methods often rely on heuristics or incur additional computational overhead, leading to resonance, low sampling accuracy, or sampler failure. To address this, we propose ATune: an adaptive tuning framework that leverages trajectory statistics during the burn-in phase for automated, diagnostic-driven selection of both integrator and hyperparameters—achieved without extra computational cost. ATune introduces a trust-based randomized interval to avoid pathological parameter configurations and theoretically establishes that Generalized HMC (GHMC) is better suited than standard HMC for high-performance sampling. Integrated into the HaiCS software package, ATune is compatible with mainstream Bayesian inference frameworks. Empirical evaluation on real-world tasks—including cancer drug resistance modeling, cell adhesion analysis, and influenza dynamics—demonstrates that ATune consistently outperforms heuristic HMC and NUTS in stability, efficiency, and estimation accuracy.

Technology Category

• Machine Learning: Auto ML and Hyperparameter Tuning
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

With the recently increased interest in probabilistic models, the efficiency of an underlying sampler becomes a crucial consideration. A Hamiltonian Monte Carlo (HMC) sampler is one popular option for models of this kind. Performance of HMC, however, strongly relies on a choice of parameters associated with an integration method for Hamiltonian equations, which up to date remains mainly heuristic or introduce time complexity. We propose a novel computationally inexpensive and flexible approach (we call it Adaptive Tuning or ATune) that, by analyzing the data generated during a burning stage of an HMC simulation, detects a system specific splitting integrator with a set of reliable HMC hyperparameters, including their credible randomization intervals, to be readily used in a production simulation. The method automatically eliminates those values of simulation parameters which could cause undesired extreme scenarios, such as resonance artifacts, low accuracy or poor sampling. The new approach is implemented in the in-house software package extsf{HaiCS}, with no computational overheads introduced in a production simulation, and can be easily incorporated in any package for Bayesian inference with HMC. The tests on popular statistical models using original HMC and generalized Hamiltonian Monte Carlo (GHMC) reveal the superiority of adaptively tuned methods in terms of stability, performance and accuracy over conventional HMC tuned heuristically and coupled with the well-established integrators. We also claim that the generalized formulation of HMC, i.e. GHMC, is preferable for achieving high sampling performance. The efficiency of the new methodology is assessed in comparison with state-of-the-art samplers, e.g. the No-U-Turn-Sampler (NUTS), in real-world applications, such as endocrine therapy resistance in cancer, modeling of cell-cell adhesion dynamics and influenza epidemic outbreak.

Problem

• Adaptively tunes HMC parameters to improve sampling efficiency
• Automatically detects optimal integrators and hyperparameters for HMC
• Enhances stability and accuracy compared to heuristic HMC tuning

Innovation

• Adaptive Tuning (ATune) for HMC parameters
• Automated detection of splitting integrator
• No computational overhead in production