A0411
Title: Nonparametric estimation via variance-reduced sketching
Authors: Yuehaw Khoo - University of Chicago (United States)
Yifan Peng - University of Chicago (United States)
Daren Wang - University of Notre Dame (United States) [presenting]
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. A new framework is introduced, called variance-reduced sketching (VRS), specifically designed to estimate density functions and nonparametric regression functions in higher dimensions with a reduced curse of dimensionality. The framework conceptualizes multivariable functions as infinite-size matrices and facilitates a new sketching technique motivated by numerical linear algebra literature to reduce the variance in estimation problems. The robust numerical performance of VRS is demonstrated through a series of simulated experiments and real-world data applications. Notably, VRS shows remarkable improvement over existing neural network estimators and classical kernel methods in numerous density estimation and nonparametric regression models. Additionally, theoretical justifications are offered for VRS to support its ability to deliver nonparametric estimation with a reduced curse of dimensionality.
