研究报告:一个基于核测度的高维变量间距离的新框架

编辑: 陈亮君    发布时间:2019-12-16    次点击

A New Framework for Distance and Kernel-based Metrics in High Dimensions

一个基于核测度的高维变量间距离的新框架


报告人:张先扬教授  美国德州农工大学

时间:2019年12月23日上午11:30

地点:数学与信息学院201报告厅

联系人:夏强  教授


报告摘要:We present new metrics to quantify and test for (i) the equality of distributions and (ii) the independence between two high-dimensional random vectors. We show that the energy distance based on the usual Euclidean distance cannot completely characterize the homogeneity of two high-dimensional distributions in the sense that it only detects the equality of means and the traces of covariance matrices in the high-dimensional setup. We propose a new class of metrics which inherit the desirable properties of the energy distance/distance covariance in the low-dimensional setting and is capable of detecting the homogeneity of/ completely characterizing independence between the low-dimensional marginal distributions in the high dimensional setup. We further propose t-tests based on the new metrics to perform high-dimensional two-sample independence testing and study its asymptotic behavior under both high dimension low sample size (HDLSS) and high dimension medium sample size (HDMSS) setups. The computational complexity of the t-tests only grows linearly with the dimension and thus is scalable to very high dimensional data. We demonstrate the superior power behavior of the proposed tests for homogeneity of distributions and independence via both simulated and real datasets.


报告人简介:张先扬教授,2008年本科毕业于中国科学技术大学,2015年博士毕业于伊利诺伊大学香槟分校。目前供职于美国德州农工大学统计系,从事统计的理论和应用的研究工作。所涉及的研究领域包括高维数据分析、多重检验、函数型数据分析、时间序列和经济计量学等。先后在国际公认的统计top期刊----“四大天王”《The Annals of Statistics》、《Journal of the American Statistical Association》、《Biometrika》《Journal of the Royal Statistical Society, Series B》,以及计量经济学top期刊《Journal of Econometrics》发表论文11篇。


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