Sampling a probability distribution with known likelihood is a fundamental task in computational science and engineering. Aiming at multimodality, we propose a new sampling method that takes advantage of both birth-death process and exploration component. The main idea of this method is \textit{look before you leap}. We keep two sets of samplers, one at warmer temperature and one at original temperature. The former one serves as pioneer in exploring new modes and passing useful information to the other, while the latter one samples the target distribution after receiving the information. We derive a mean-field limit and show how the exploration process determines sampling efficiency. Moreover, we prove exponential asymptotic convergence under mild assumption. Finally, we test on experiments from previous literature and compared our methodology to previous ones.
翻译:针对已知似然概率分布的采样是计算科学与工程中的基础任务。为应对多模态问题,我们提出一种融合生灭过程与探索组件的新型采样方法。该方法的核心思想是"三思而后行"。我们维护两组采样器:一组处于较高温度,另一组保持原始温度。前者作为先锋探索新模态并将有用信息传递给后者,后者在接收信息后对目标分布进行采样。我们推导了平均场极限,阐明了探索过程如何决定采样效率。此外,在温和假设下证明了指数渐近收敛性。最后,我们在现有文献实验上进行测试,并将所提方法与已有方法进行了比较。