Random Objects: Distance Profiles and Conformal Prediction
报告人： 周航（加利福尼亚大学戴维斯分校)
时间：2025-03-13 16:00-17:00
地点：智华楼四元厅-225
Abstract:
Random objects are complex random variables taking values in general metric spaces. Although such data are increasingly common in scientific research, current statistical methodology and theory remain limited. The primary challenge in analyzing such data lies in the absence of vector space operations, such as addition, subtraction, scalar multiplication, and inner products, which are fundamental tools in conventional statistical methodologies.
This talk explores object data with distance profiles and their application to conformal prediction. We introduce conditional profile average transport costs by comparing distance profiles through the optimal transport. A novel score function for random objects is proposed, enabling the construction of prediction sets using the split conformal algorithm. We develop a theoretical framework to establish uniform convergence rates for the local linear estimator involving function classes defined on metric spaces and the asymptotic conditional validity of the prediction sets. The practical utility of our proposed methodology is demonstrated through applications to network data from New York taxi trips and compositional data from brain imaging studies.
About the Speaker:
周航现为加利福尼亚大学戴维斯分校博士后研究员，即将入职北卡罗来纳大学教堂山分校统计系，担任助理教授（tenure-track assistant professor）。他于2022年在北京大学获得博士学位，导师为姚方教授。他的研究主要包括离散观测函数型数据分析、非欧数据的统计方法、机器学习的统计理论基础等。研究成果发表于AoS、JASA、Biometrika、IEEE TPAMI等期刊，以及ICML、NeurIPS、ACM KDD等会议。
k
Your participation is warmly welcomed!
欢迎扫码关注北大统计科学中心公众号，了解更多讲座信息!
