Improved Concentration Bounds for Gaussian Quadratic Forms

For a wide class of monotonic functions \(f\), we develop a Chernoff-style concentration inequality for quadratic forms \(Q_f \sim \sum\limits_{i=1}^n f(\eta_i) (Z_i + \delta_i)^2\), where \(Z_i \sim N(0,1)\). The inequality is expressed in terms of traces that are rapid to compute, making it useful...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2019-11
Main Authors: Gallagher, Robert E, Aslett, Louis J M, Steinsaltz, David, Christ, Ryan R
Format: Article
Language:English
Subjects:
Quadratic forms
Queuing theory
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:For a wide class of monotonic functions \(f\), we develop a Chernoff-style concentration inequality for quadratic forms \(Q_f \sim \sum\limits_{i=1}^n f(\eta_i) (Z_i + \delta_i)^2\), where \(Z_i \sim N(0,1)\). The inequality is expressed in terms of traces that are rapid to compute, making it useful for bounding p-values in high-dimensional screening applications. The bounds we obtain are significantly tighter than those that have been previously developed, which we illustrate with numerical examples.
ISSN:2331-8422