Moreau-Yosida 正则化 Metropolis 调整朗之万算法的最优缩放结果
Optimal Scaling Results for Moreau-Yosida Metropolis-adjusted Langevin Algorithms
AI总结：
本文研究了一类基于Moreau-Yosida包络、用邻近映射构建提议机制的MCMC方法的最优缩放问题，该方法适配可微与不可微目标、稳定性强，可替代MALA，研究还给出了实现指导。
摘要：
我们研究了近期提出的一类马尔可夫链蒙特卡洛（MCMC）方法，这类方法用邻近映射而非梯度来构建提议机制，可同时适用于可微与不可微目标分布。已被证明这类方法对广泛的目标分布都具备稳定性，是 Metropolis 调整朗之万算法（MALA）的有效替代方案，且已在成像领域得到广泛应用。其更优的稳定性是通过为目标分布构建依赖参数 $\lambda$ 的 Moreau-Yosida 包络来实现的。本文研究了这类涵盖 MALA 的算法的最优缩放问题，并给出了这些方法的实际实现指导。
英文摘要：
We consider a recently proposed class of MCMC methods which uses proximity maps instead of gradients to build proposal mechanisms which can be employed for both differentiable and non-differentiable targets. These methods have been shown to be stable for a wide class of targets, making them a valuable alternative to Metropolis-adjusted Langevin algorithms (MALA); and have found wide application in imaging contexts. The wider stability properties are obtained by building the Moreau-Yosida envelope for the target of interest, which depends on a parameter $λ$. In this work, we investigate the optimal scaling problem for this class of algorithms, which encompasses MALA, and provide practical guidelines for the implementation of these methods.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
