تقرير
HMC and underdamped Langevin united in the unadjusted convex smooth case
| العنوان: | HMC and underdamped Langevin united in the unadjusted convex smooth case |
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| المؤلفون: | Gouraud, Nicolaï, Bris, Pierre Le, Majka, Adrien, Monmarché, Pierre |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics Statistics |
| مصطلحات موضوعية: | Mathematics - Probability, Mathematics - Statistics Theory, 65C05 |
| الوصف: | We consider a family of unadjusted generalized HMC samplers, which includes standard position HMC samplers and discretizations of the underdamped Langevin process. A detailed analysis and optimization of the parameters is conducted in the Gaussian case, which shows an improvement from $1/\kappa$ to $1/\sqrt{\kappa}$ for the convergence rate in terms of the condition number $\kappa$ by using partial velocity refreshment, with respect to classical full refreshments. A similar effect is observed empirically for two related algorithms, namely Metropolis-adjusted gHMC and kinetic piecewise-deterministic Markov processes. Then, a stochastic gradient version of the samplers is considered, for which dimension-free convergence rates are established for log-concave smooth targets over a large range of parameters, gathering in a unified framework previous results on position HMC and underdamped Langevin and extending them to HMC with inertia. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2202.00977 |
| رقم الأكسشن: | edsarx.2202.00977 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |