Noisy classification with 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.