11:30 am–12:30 pm
Jones 303 5747 S. Ellis Ave.
Ping-Shou Zhong
Professor
University of Illinois Chicago
Title: On the Adaptivity and Scalability of Kernel Methods for Testing and Prediction
Abstract: Kernel methods are widely used for prediction and hypothesis testing. In this talk, I will introduce two approaches that enhance the scalability and adaptivity of kernel methods. In the first part, we introduce a new family of adaptive, distribution-free tests of independence based on binary expansion coefficients. By characterizing independence through cross-covariances of multiscale interaction terms, the proposed method is applicable in a general setting and does not require the reproducing kernel Hilbert space assumption. The resulting tests admit an explicit kernel representation, enabling efficient computation while reducing sensitivity to kernel choice. In the second part, we propose an informative sub-data selection method for large-scale kernel learning. This method identifies a representative subset of observations, enabling model training on a substantially reduced yet informative sample. The approach provides a principled form of data reduction and integrates naturally with existing kernel approximation and sketching techniques.