The paper presents a new copula based method for measuring dependence between random variables. Our approach extends the Maximum Mean Discrepancy to the copula of the joint distribution. We prove that this approach has several advantageous properties. Similarly to Shannon mutual information, the proposed dependence measure is invariant to any strictly increasing transformation of the marginal variables. This is important in many applications, for example in feature selection. The estimator is consistent, robust to outliers, and uses rank statistics only. We derive upper bounds on the convergence rate and propose independence tests too. We illustrate the theoretical contributions through a series of experiments in feature selection and low-dimensional embedding of distributions.
Deep Learning with Kernels through RKHM and the Perron-Frobenius Operator
NTT Network Service Systems Laboratories（NTT网络服务系统研究所）；RIKEN AIP（理化学研究所革新智能统合研究中心）；Keio University（庆应义塾大学）；Aix-Marseille University（艾克斯-马赛大学）；CNRS（法国国家科学研究中心）；LIS（信息科学实验室）
Copula-Stein Discrepancy: A Generator-Based Stein Operator for Archimedean Dependence
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana, USA（路易斯安那州拉法叶大学数学系）；Department of Statistics, formerly of Presidency College, Kolkata, India（加德满都大学统计系）
A2 Copula-Driven Spatial Bayesian Neural Network For Modeling Non-Gaussian Dependence: A Simulation Study
Department of Mathematics, University of Louisiana at Lafayette（数学系，路易斯安那州立大学拉斐特分校）；Department of Physical Sciences & Mathematics, West Liberty University（物理科学与数学系，韦斯特利比大学）；Department of Mathematics and Statistics, Minnesota State University（数学与统计学系，明尼苏达州立大学）；Department of Statistics, formerly of Presidency College, Kolkata, India（统计学系，原加尔各答 Presidency College）；Department of Kinesiology, University of Louisiana at Lafayette（运动科学系，路易斯安那州立大学拉斐特分校）；Department of Mathematics and Statistics, Texas Tech University（数学与统计学系，德克萨斯技术大学）；The Office of Vice President for Research, Innovation, and Economic Development, University of Louisiana at Lafayette（研究、创新与经济发展副总监办公室，路易斯安那州立大学拉斐特分校）
Department of Mathematics, University of Louisiana at Lafayette（路易斯安那州拉法叶大学数学系）；Department of Statistics, formerly of Presidency College（统计系，原为 Presidency College）
Cross-LKTCN: Modern Convolution Utilizing Cross-Variable Dependency for Multivariate Time Series Forecasting Dependency for Multivariate Time Series Forecasting
VARSHAP: Addressing Global Dependency Problems in Explainable AI with Variance-Based Local Feature Attribution
Faculty of Computing and Telecommunications（计算机与电信学院）；Poznan University of Technology（波兹南技术大学）；Faculty of Mathematics, Informatics and Mechanics（数学、信息学与力学学院）；University of Warsaw（华沙大学）；MIM Solutuions Research Institute（MIM解决方案研究所）
Patient-specific Conditional Joint Models of Shape, Image Features and Clinical Indicators
Massachusetts General Hospital（麻省总医院）；Harvard Medical School（哈佛医学院）；German Centre for Neurodegenerative Diseases (DZNE)（德国神经退行性疾病中心）；Erasmus MC - University Medical Center Rotterdam（伊拉斯谟医学中心——鹿特丹大学医学中心）
