Abstract
We present dimension-free convergence and discretization error bounds for the unadjusted Hamiltonian Monte Carlo algorithm applied to high-dimensional probability distributions of mean-field type. These bounds require the discretization step to be sufficiently small, but do not require strong convexity of either the unary or pairwise potential terms present in the mean-field model. To handle high dimensionality, our proof uses a particlewise coupling that is contractive in a complementary particlewise metric.
Funding Statement
N. B.-R. was supported by the National Science Foundation under Grant No. DMS-1816378 and the Alexander von Humboldt Foundation. K. S. was supported by Bonn International Graduate School of Mathematics. Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) im Rahmen der Exzellenzstrategie des Bundes und der Länder - GZ 2047/1, Projekt-ID 390685813.
Acknowledgments
The authors would like to thank Andreas Eberle for his insights and advice during the development of this work.
Citation
Nawaf Bou-Rabee. Katharina Schuh. "Convergence of unadjusted Hamiltonian Monte Carlo for mean-field models." Electron. J. Probab. 28 1 - 40, 2023. https://doi.org/10.1214/23-EJP970
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