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

Soumyadip Ghosh, Yingdong Lu, Tomasz Nowicki

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.