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On $L^q$ Convergence of the Hamiltonian Monte Carlo
Published 21 Jan 2021 in math.CA, cs.DS, cs.LG, math.FA, and stat.ML | (2101.08688v2)
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.
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