提出一种新采样方法，能在有孔的非凸空间中高效采样。
Sampling with Shielded Langevin Monte Carlo Using Navigation Potentials
- 利用导航势函数设计带防护的采样路径
- 在2D高斯混合与MIMO检测中表现优于无约束采样
- 适合处理含障碍物的复杂分布采样问题
我们提出屏蔽式Langevin蒙特卡洛（shielded LMC），一种受导航函数启发的约束采样方法，可对定义在穿孔支撑集上的非归一化目标分布进行采样。即在凸集内存在凸洞的非凸空间中采样，这构成了一个新颖且具有挑战性的约束采样问题。该方法结合空间自适应温度与排斥性漂移，确保样本始终位于可行区域内。在二维高斯混合模型和多输入多输出（MIMO）符号检测任务上的实验表明，该方法相较于无约束情形具有显著优势。
原文摘要 · Abstract (English)
We introduce shielded Langevin Monte Carlo (LMC), a constrained sampler inspired by navigation functions, capable of sampling from unnormalized target distributions defined over punctured supports. In other words, this approach samples from non-convex spaces defined as convex sets with convex holes. This defines a novel and challenging problem in constrained sampling. To do so, the sampler incorporates a combination of a spatially adaptive temperature and a repulsive drift to ensure that samples remain within the feasible region. Experiments on a 2D Gaussian mixture and multiple-input multiple-output (MIMO) symbol detection showcase the advantages of the proposed shielded LMC in contrast to unconstrained cases.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。