Gaussian Processes and the Kullback-Leibler divergence have been deeply studied in Statistics and Machine Learning. This paper marries these two concepts and introduce the local Kullback-Leibler divergence to learn about intervals where two Gaussian Processes differ the most. We address subtleties entailed in the estimation of local divergences and the corresponding interval of local maximum divergence as well. The estimation performance and the numerical efficiency of the proposed method are showcased via a Monte Carlo simulation study. In a medical research context, we assess the potential of the devised tools in the analysis of electrocardiogram signals.

翻译：高斯过程与Kullback-Leibler散度在统计学与机器学习领域中已得到深入研究。本文融合这两个概念，引入局部Kullback-Leibler散度，用以识别两个高斯过程差异最大的区间。我们同时探讨了局部散度估计及其对应局部最大差异区间估计中所涉及的细微问题。通过蒙特卡洛模拟研究，验证了所提方法的估计性能与数值效率。在医学研究背景下，我们评估了所设计工具在心电图信号分析中的潜力。