报告人： 陈雅清 (Rutgers University）
地点：Room 1114, Sciences Building No. 1
We propose new tools for the geometric exploration of data objects taking values in a general separable metric space. For a random object, we first introduce the concept of depth profiles. Specifically, the depth profile of a point in a metric space is the distribution of distances between the very point and the random object. Depth profiles can be harnessed to define transport ranks based on optimal transport, which capture the centrality and outlyingness of each element in the metric space with respect to the probability measure induced by the random object. We study the properties of transport ranks and show that they provide an effective device for detecting and visualizing patterns in samples of random objects. In particular, we establish the theoretical guarantees for the estimation of the depth profiles and the transport ranks for a wide class of metric spaces, followed by practical illustrations on distributional data comprising a sample of age-at-death distributions for different countries and compositional data for electricity generation for the U.S. states.
About the Speaker:
Yaqing Chen is an Assistant Professor in the Department of Statistics at Rutgers University. Before joining Rutgers, she completed her Ph.D. in Statistics in 2020 and was a postdoctoral scholar, both under the supervision of Professor Hans-Georg Müller, in the Department of Statistics at the University of California, Davis (UC Davis). Prior to that, she received a Bachelor of Science in Mathematics and Applied Mathematics from Peking University in 2015.
Her research mainly focuses on developing statistical methods for metric space valued data or non-Euclidean data, including but not limited to distributions and distributional time series, networks, compositional data and also time-varying non-Euclidean data. She is also interested in functional or longitudinal data analysis. In addition to theoretical and methodological challenges, she is also interested in various interdisciplinary applications and collaborations such as brain imaging, child growth and development, aging and longevity.
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