Speaker: Daren Wang
University of Notre Dame
Will give a Graduate Student Seminar entitled:
Nonparametric Density 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, we introduce a new framework called Variance-Reduced Sketching (VRS), specifically designed to estimate density functions in higher dimensions with a reduced curse of dimensionality. Our framework conceptualizes multivariable functions as infinite-size matrices/tensors, facilitating a new matrix/tensor-based bias-variance tradeoff in various nonparametric contexts. We demonstrate the robust numerical performance of VRS 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 models. Additionally, we will discuss theoretical guarantees for VRS to support its ability to deliver density estimation with a reduced curse of dimensionality.
Date: 09-05-2024
Time: 2:00 pm
Location: 258 Hurley Bldg
Originally published at math.nd.edu.