HMC, an Algorithms in Data Mining, the Functional Analysis approach
This work provides a theoretical convergence proof for the HMC algorithm, which is relevant for researchers and practitioners in data mining and machine learning who rely on Monte Carlo methods.
This paper aims to bridge communication between analytic, probabilistic, and algorithmic communities by presenting a proof of convergence for the Hamiltonian (Hybrid) Monte Carlo algorithm. The proof is approached from the perspective of Dynamical Systems, treating evolving objects as probability distribution densities and utilizing tools from Functional Analysis.
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.