Title:
Data-Adaptive Kernel Methods for Distributional Inference
Date:
Wednesday, June 10, 2026
Time:
10:00 AM – 12:00 PM EDT
Location:
Groseclose 304 and Microsoft Teams
Meeting Link:
https://teams.microsoft.com/meet/286033428872136?p=uHeI8ONCjhgJctRlwM
Yijin Ni
Ph.D. Candidate in Statistics
H. Milton Stewart School of Industrial and Systems Engineering
Georgia Institute of Technology
Advisor/Chairperson:
Dr. Xiaoming Huo, H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology
Committee:
Dr. Xiaoming Huo, H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology
Dr. Wenjing Liao, School of Mathematics, Georgia Institute of Technology
Dr. Yajun Mei, H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology
Dr. Lizhen Xu, Scheller College of Business, Georgia Institute of Technology
Dr. Yao Xie, H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology
Abstract:
Kernel-based discrepancy measures, especially maximum mean discrepancy, provide flexible nonparametric tools for comparing probability distributions. Their practical performance, however, depends critically on the choice of kernel. In many applications, the kernel is selected or optimized using data, but such adaptivity introduces a statistical cost that must be controlled in order to preserve valid inference. This dissertation develops theory and methodology for data-adaptive kernel inference, with a focus on valid and powerful two-sample testing in both batch and sequential settings.
The first part establishes a uniform concentration framework for kernel-based two-sample statistics. This theory provides finite-sample control for kernel discrepancy and dependence measures optimized over transformation or kernel classes, including energy distance, distance covariance, maximum mean discrepancy, and the Hilbert–Schmidt independence criterion. These bounds provide a foundation for statistically valid data-adaptive inference.
The second part applies this framework to batch two-sample testing. Kernel selection is formulated as a model selection problem, leading to a complexity-penalized MMD criterion that accounts for the cost of optimizing over rich kernel families. This approach enables data-driven kernel selection over continuous kernel classes while maintaining Type I error control and improving test power.
The third part extends adaptive kernel methodology to sequential testing. A predictable-bandwidth sequential kernel two-sample test is developed, where the bandwidth is updated using only past observations. This construction preserves anytime-valid Type I error control while adapting to the signal structure of the alternative distribution. The resulting test achieves detection performance comparable to an oracle procedure that knows the best bandwidth in advance.
Together, these results show how kernel methods can be made adaptive without sacrificing statistical validity. The dissertation provides a unified framework for complexity-controlled kernel selection in modern distributional inference.