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<p>Subsampling plays a crucial role in enhancing the efficiency of Markov chain Monte Carlo (MCMC) algorithms. This paper presents a subsampling-based MCMC algorithm aimed at addressing the computational complexity challenges of traditional MCMC methods on large-scale datasets. The proposed approach significantly reduces computational costs by approximating the full data likelihood function using only a subset of the full data in each iteration. The subsampling process is guided by the fidelity to the full data, which is measured by the energy distance. The resulting algorithm, termed the energy distance-based subsampling MCMC (EDSS-MCMC), offers a flexible approach while maintaining the simplicity of the standard MCMC algorithm. Additionally, we provide an analysis of the invariant distribution generated by the EDSS-MCMC algorithm and quantify the total variation norm between this distribution and the target distribution. Numerical experiments demonstrate the outstanding performance of the proposed algorithm on large-scale datasets. Compared with the standard MCMC algorithm and other subsampling MCMC algorithms, the EDSS-MCMC algorithm exhibits advantages in terms of accuracy and computational speed. Therefore, the proposed algorithm holds practical significance in tasks involving large-scale dataset analysis and machine learning.</p>

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Energy distance-based subsampling Markov chain Monte Carlo

  • 期刊论文

  • 发表日期：

    2025年3月27日

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  • Sumin Wang,
  • Fasheng Sun,
  • Min-Qian Liu

摘要

Subsampling plays a crucial role in enhancing the efficiency of Markov chain Monte Carlo (MCMC) algorithms. This paper presents a subsampling-based MCMC algorithm aimed at addressing the computational complexity challenges of traditional MCMC methods on large-scale datasets. The proposed approach significantly reduces computational costs by approximating the full data likelihood function using only a subset of the full data in each iteration. The subsampling process is guided by the fidelity to the full data, which is measured by the energy distance. The resulting algorithm, termed the energy distance-based subsampling MCMC (EDSS-MCMC), offers a flexible approach while maintaining the simplicity of the standard MCMC algorithm. Additionally, we provide an analysis of the invariant distribution generated by the EDSS-MCMC algorithm and quantify the total variation norm between this distribution and the target distribution. Numerical experiments demonstrate the outstanding performance of the proposed algorithm on large-scale datasets. Compared with the standard MCMC algorithm and other subsampling MCMC algorithms, the EDSS-MCMC algorithm exhibits advantages in terms of accuracy and computational speed. Therefore, the proposed algorithm holds practical significance in tasks involving large-scale dataset analysis and machine learning.