12:30–1:30 pm Searle 240A
Tuesday, March, 19, 2024, at 12:30 PM, in Searle 240A, 5735 S. Ellis Avenue
CAM & Stats Student Seminar
Yifan Peng, Committee on Computational and Applied Mathematics, University of Chicago
"Nonparametric Estimation via Variance-Reduced Sketching"
Abstract
Nonparametric models are of great interest in various scientific and engineering disciplines. Classical kernel methods, while numerically robust and statistically sound in low-dimensional settings, become inadequate in higher-dimensional settings due to the curse of dimensionality. In this talk, I would introduce a new framework for nonparametric estimation problem with a reduced curse of dimensionality. This framework conceptualizes multivariable functions as infinite-size matrices/tensors, and facilitates a new sketching technique motivated by numerical linear algebra literature to reduce the variance in estimation problems. Robust numerical performance of the new method is demonstrated through a series of simulated experiments and real-world data applications. Notably, it shows remarkable improvement over existing neural network estimators and classical kernel methods in numerous nonparametric problems. Additionally, theoretical justifications for the method is provided to support its ability to deliver nonparametric estimation with a reduced curse of dimensionality.