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

TL;DR

This paper introduces a functional analysis approach to prove the convergence of the Hamiltonian Monte Carlo algorithm, aiming to bridge analytic, probabilistic, and algorithmic communities in data mining.

Contribution

It provides a novel convergence proof of HMC using dynamical systems and functional analysis, enhancing theoretical understanding of the algorithm.

Findings

Proof of convergence of HMC from a dynamical systems perspective

Application of functional analysis to probabilistic density evolution

Bridging communities in data mining through theoretical insights

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.