تقرير
Subgradient Langevin Methods for Sampling from Non-smooth Potentials
| العنوان: | Subgradient Langevin Methods for Sampling from Non-smooth Potentials |
|---|---|
| المؤلفون: | Habring, Andreas, Holler, Martin, Pock, Thomas |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics Statistics |
| مصطلحات موضوعية: | Mathematics - Optimization and Control, Statistics - Computation, 65C40, 65C05, 68U10, 65C60, G.3, G.1.6 |
| الوصف: | This paper is concerned with sampling from probability distributions $\pi$ on $\mathbb{R}^d$ admitting a density of the form $\pi(x) \propto e^{-U(x)}$, where $U(x)=F(x)+G(Kx)$ with $K$ being a linear operator and $G$ being non-differentiable. Two different methods are proposed, both employing a subgradient step with respect to $G\circ K$, but, depending on the regularity of $F$, either an explicit or an implicit gradient step with respect to $F$ can be implemented. For both methods, non-asymptotic convergence proofs are provided, with improved convergence results for more regular $F$. Further, numerical experiments are conducted for simple 2D examples, illustrating the convergence rates, and for examples of Bayesian imaging, showing the practical feasibility of the proposed methods for high dimensional data. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2308.01417 |
| رقم الأكسشن: | edsarx.2308.01417 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |