Noisy classification with boundary assumptions

TL;DR

This paper studies the challenge of classification with measurement errors, establishing minimax convergence rates under boundary assumptions using deconvolution classifiers.

Contribution

It introduces a framework for analyzing classification with measurement errors, deriving bounds on convergence rates based on margin and boundary smoothness assumptions.

Findings

Established lower and upper bounds on minimax rates

Developed a deconvolution classifier for this setting

Provided theoretical insights into boundary assumptions

Abstract

We address the problem of classification when data are collected from two samples with measurement errors. This problem turns to be an inverse problem and requires a specific treatment. In this context, we investigate the minimax rates of convergence using both a margin assumption, and a smoothness condition on the boundary of the set associated to the Bayes classifier. We establish lower and upper bounds (based on a deconvolution classifier) on these rates.