HMC, an Algorithms in Data Mining, the Functional Analysis approach

2021/02/04 by Soumyadip Ghosh, Ghosh, Soumyadip, Yingdong Lu +3
Engineering · Mathematics · #68W40 28A33 70H05 #Computation (stat.CO) #Dynamical Systems (math.DS) #F.2 #FOS: Computer and information sciences #FOS: Mathematics #Fault Detection and Control Systems #Functional Analysis (math.FA) #Machine Learning (cs.LG) #Markov Chains and Monte Carlo Methods #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2102.02691

openalex publication_date 2021/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main purpose of this paper is to facilitate the communication between the Analytic, Probabilistic and Algorithmic communities. We present a proof of convergence of the Hamiltonian (Hybrid) Monte Carlo algorithm from the point of view of the Dynamical Systems, where the evolving objects are densities of probability distributions and the tool are derived from the Functional Analysis.

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