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20191104 潘文亮:Ball Covariance: A Generic Measure of Dependence in Banach Space
时间:2019-10-31

报告时间:2019年11月4日16:00-17:00

报告地点:明德主楼1016


报告题目:Ball Covariance: A Generic Measure of Dependence in Banach Space

报告摘要:Technological advances in science and engineering have led to the routine collection of large and complex data objects, where the dependence structure among those objects is often of great interest. Those complex objects (e.g, different brain subcortical structures) often reside in some Banach spaces, and hence their relationship cannot be well characterized by most of the existing measures of dependence such as correlation coefficients developed in Hilbert spaces. To overcome the limitations of the existing measures, we propose Ball Covariance as a generic measure of dependence between two random objects in two possibly different Banach spaces.  Our Ball Covariance possesses the following attractive properties: (i)  It is nonparametric and model-free, which make the proposed measure robust to model mis-specification; (ii) It is nonnegative and equal to zero if and only if two random objects in two separable Banach spaces are independent; (iii)  Empirical Ball Covariance is easy to compute and can be used as a test statistic of independence. We present both theoretical and numerical results to reveal the potential power of the Ball Covariance in detecting dependence. Also importantly, we analyze two real datasets to demonstrate the usefulness of Ball Covariance in the complex dependence detection.

报告人简介:潘文亮副教授,硕士生导师,2016年毕业于中山大学统计科学系,获理学博士, 2019年7月受聘中山大学副教授职位。曾于2014-2016年在美国北卡罗莱纳大学教堂山分校留学。 主要从事统计学习和数据挖掘算法、医学图像数据分析、度量空间的非参数方法、统计学和数据科学的应用等领域的研究。目前已在统计学顶级杂志Annals of Statistics, Journal of the American Statistical Association,国际医学图像顶级会议Information Processing in Medical Imaging等发表了学术论文十余篇。主持国家自然科学基金青年基金、广东省纵向协同和博士启动项目,参与国家自然科学基金面上项目两项。