We introduce a generalized formulation of mutual information (MI) based on the extended Bregman divergence, a framework that subsumes the generalized S-Bregman (GSB) divergence family. The GSB divergence unifies two important classes of statistical distances, namely the S-divergence and the Bregman exponential divergence (BED), thereby encompassing several widely used subfamilies, including the power divergence (PD), density power divergence (DPD), and S-Hellinger distance (S-HD). In parametric inference, minimum divergence estimators are well known to balance robustness with high asymptotic efficiency relative to the maximum likelihood estimator. However, nonparametric tests based on such statistical distances have been relatively less explored. In this paper, we construct a class of consistent and robust nonparametric two-sample tests for the equality of two absolutely continuous distributions using the generalized MI. We establish the asymptotic normality of the proposed test statistics under the null and contiguous alternatives. The robustness properties of the generalized MI are rigorously studied through the influence function and the breakdown point, demonstrating that stability of the generalized MI translates into stability of the associated tests. Extensive simulation studies show that divergences beyond the PD family often yield superior robustness under contamination while retaining high asymptotic power. A data-driven scheme for selecting optimal tuning parameters is also proposed. Finally, the methodology is illustrated with applications to real data.
A Bayesian Nonparametric Estimation of Mutual Information
互信息是一种广泛使用的信息理论度量，用于量化变量之间的关联量。它被广泛应用于许多应用中，如图像配准，电机故障诊断，模式识别，数据挖掘和独立性测试。本文的主要目标是提供一个有效的估计的互信息的方法的基础上Al Labadi等。等（2021）。通过各种示例探索估计量，并将其与Berrett et al.（2019）的频率论对应物进行比较。结果表明，该方法具有良好的性能，具有较小的均方误差。
Nonparametric Empirical Bayes Estimation on Heterogeneous Data
University of Kansas（堪萨斯大学）；San Francisco State University（旧金山州立大学）；Emory University（埃默里大学）；University of Southern California（南加州大学）；Zhejiang University（浙江大学）
Topological Effective Connectivity Modeling in Brain Networks
King Abdullah University of Science Technology（阿卜杜拉国王科技大学）；Department of Statistics, University of Wisconsin-Madison（威斯康星大学麦迪逊分校统计系）；Statistics Program, King Abdullah University of Science and Technology（阿卜杜拉国王科技大学统计学项目）
CISPA Helmholtz Center for Information Security（CISPA亥姆霍兹信息安全中心）；University College London（伦敦大学学院）；Inria（法国国家信息与自动化研究所）；Gatsby Computational Neuroscience Unit（盖茨计算神经科学单元）；University of Adelaide（阿德莱德大学）
