Inference on covariance operators via concentration inequalities: k-sample tests, classification, and clustering via Rademacher complexities

TL;DR

This paper introduces a new method using concentration inequalities to analyze covariance operators, enabling non-asymptotic confidence sets and applications in k-sample testing, classification, and clustering for functional data.

Contribution

It presents a novel approach leveraging concentration inequalities for covariance operators, with practical algorithms for testing, classification, and clustering in functional data analysis.

Findings

Effective non-asymptotic confidence sets for covariance operators

Successful application to k-sample tests, classification, and clustering

Validated on simulated and phoneme datasets

Abstract

We propose a novel approach to the analysis of covariance operators making use of concentration inequalities. First, non-asymptotic confidence sets are constructed for such operators. Then, subsequent applications including a k sample test for equality of covariance, a functional data classifier, and an expectation-maximization style clustering algorithm are derived and tested on both simulated and phoneme data.