تقرير
Coupling and Convergence for Hamiltonian Monte Carlo
| العنوان: | Coupling and Convergence for Hamiltonian Monte Carlo |
|---|---|
| المؤلفون: | Bou-Rabee, Nawaf, Eberle, Andreas, Zimmer, Raphael |
| المصدر: | Ann. Appl. Probab., Volume 30, Number 3 (2020), 1209-1250 |
| سنة النشر: | 2018 |
| المجموعة: | Mathematics Statistics |
| مصطلحات موضوعية: | Mathematics - Probability, Statistics - Computation, Statistics - Machine Learning, 60J05, 65P10, 65C05 |
| الوصف: | Based on a new coupling approach, we prove that the transition step of the Hamiltonian Monte Carlo algorithm is contractive w.r.t. a carefully designed Kantorovich (L1 Wasserstein) distance. The lower bound for the contraction rate is explicit. Global convexity of the potential is not required, and thus multimodal target distributions are included. Explicit quantitative bounds for the number of steps required to approximate the stationary distribution up to a given error are a direct consequence of contractivity. These bounds show that HMC can overcome diffusive behaviour if the duration of the Hamiltonian dynamics is adjusted appropriately. Comment: 50 pages, 8 figures, extended the coupling approach to include corresponding results under a Foster-Lyapunov condition |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1214/19-AAP1528 |
| URL الوصول: | http://arxiv.org/abs/1805.00452 |
| رقم الأكسشن: | edsarx.1805.00452 |
| قاعدة البيانات: | arXiv |
كن أول من يترك تعليقا!