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Sampling from Non-smooth Distributions Through Langevin Diffusion
Methodology and Computing in Applied Probability ( IF 0.9 ) Pub Date : 2020-07-17 , DOI: 10.1007/s11009-020-09809-7
Tung Duy Luu , Jalal Fadili , Christophe Chesneau

In this paper, we propose proximal splitting-type algorithms for sampling from distributions whose densities are not necessarily smooth nor log-concave. Our approach brings together tools from, on the one hand, variational analysis and non-smooth optimization, and on the other hand, stochastic diffusion equations, and in particular the Langevin diffusion. We establish in particular consistency guarantees of our algorithms seen as discretization schemes in this context. These algorithms are then applied to compute the exponentially weighted aggregates for regression problems involving non-smooth penalties that are commonly used to promote some notion of simplicity/complexity. Some popular penalties are detailed and implemented on some numerical experiments.



中文翻译:

通过Langevin扩散从非平滑分布中采样

在本文中,我们提出了一种近端分裂类型算法,用于从密度不一定平滑或对数凹的分布中进行采样。我们的方法一方面汇集了变量分析和非平滑优化工具,另一方面汇集了随机扩散方程,尤其是Langevin扩散。在这种情况下,我们特别建立了算法的一致性保证,这些算法被视为离散化方案。然后将这些算法应用于计算涉及非光滑惩罚的回归问题的指数加权聚合,这些非光滑惩罚通常用于促进简单性/复杂性的某种概念。一些流行的惩罚措施进行了详细说明,并在一些数值实验中实施。

更新日期:2020-07-17
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