5月15日 | 张先扬:A New Framework for Distance and Kernel-based Metrics in High Dimensions

时间:2020-05-12浏览:60设置

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

Abstract: 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 setting. We propose a new class of metrics that 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 testing/ 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.


Bio: Xianyang Zhang is currently an Associate Professor of Statistics at Texas A&M University. He obtained his Ph.D. in statistics from the University of Illinois at Urbana Champaign in 2013. His research interests include high-dimensional statistics, multiple testing, functional data analysis, time series, and applications in econometrics and genomics. He currently serves as an associate editor for Biometrics and Journal of Multivariate Analysis.


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