Hamiltonian Monte Carlo (HMC), as a classical machine learning algorithm, leverages its constructed Hamiltonian system to achieve high sampling efficiency. However, traditional momentum updating strategies in the Hamiltonian system suffer from limitations such as insufficient adaptation to new sampling regions and instability in maintaining optimal momentum for stable sampling. To address these issues, we propose an Adaptive Partial Momentum Hamiltonian Monte Carlo (APMHMC), capable of handling complex sampling scenarios more stably and efficiently. Specifically, we design an adaptive momentum updating strategy that dynamically adjusts the degree of momentum updates based on current sampling efficiency. This adaptive approach ensures that momentum adjustments are tailored to the current sampling needs, thereby promoting rapid adaptation to new regions while maintaining stable and efficient sampling. To fully utilize computational resources, we introduce a more efficient parallel sampling method and incorporate gradient-based hyperparameter optimization. Inspired by the variational inference principles, we fully exploit the merit of sampling stability of APMHMC to propose a scalable contrastive divergence as the objective function for hyperparameter optimization. We extensively evaluate the performance of APMHMC through numerous simulation experiments, including sampling from 2D distributions, Bayesian compressed sensing, and training Variational Autoencoders. The experimental results demonstrate that our method exhibits better sampling performance than alternative baselines.

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Adaptive Partial Momentum Hamiltonian Monte Carlo

  • Fangkai Zhao,
  • Bing He,
  • Fangmei Chen,
  • Fasheng Wang

摘要

Hamiltonian Monte Carlo (HMC), as a classical machine learning algorithm, leverages its constructed Hamiltonian system to achieve high sampling efficiency. However, traditional momentum updating strategies in the Hamiltonian system suffer from limitations such as insufficient adaptation to new sampling regions and instability in maintaining optimal momentum for stable sampling. To address these issues, we propose an Adaptive Partial Momentum Hamiltonian Monte Carlo (APMHMC), capable of handling complex sampling scenarios more stably and efficiently. Specifically, we design an adaptive momentum updating strategy that dynamically adjusts the degree of momentum updates based on current sampling efficiency. This adaptive approach ensures that momentum adjustments are tailored to the current sampling needs, thereby promoting rapid adaptation to new regions while maintaining stable and efficient sampling. To fully utilize computational resources, we introduce a more efficient parallel sampling method and incorporate gradient-based hyperparameter optimization. Inspired by the variational inference principles, we fully exploit the merit of sampling stability of APMHMC to propose a scalable contrastive divergence as the objective function for hyperparameter optimization. We extensively evaluate the performance of APMHMC through numerous simulation experiments, including sampling from 2D distributions, Bayesian compressed sensing, and training Variational Autoencoders. The experimental results demonstrate that our method exhibits better sampling performance than alternative baselines.