HMC, an example of Functional Analysis applied to Algorithms in Data Mining. The convergence in Lp

Soumyadip Ghosh, Yingdong Lu, Tomasz Nowicki

Abstract: We establish $L_q$ convergence for Hamiltonian Monte Carlo algorithms. More specifically, under mild conditions for the associated Hamiltonian motion, we show that the outputs of the algorithms converge (strongly for $2\le q<\infty$ and weakly for $1<q<2$) to the desired target distribution.