AdaBoost and robust one-bit compressed sensing
Abstract
This paper studies binary classification in robust one-bit compressed sensing with adversarial errors. It is assumed that the model is overparameterized and that the parameter of interest is effectively sparse. AdaBoost is considered, and, through its relation to the max--margin-classifier, prediction error bounds are derived. The developed theory is general and allows for heavy-tailed feature distributions, requiring only a weak moment assumption and an anti-concentration condition. Improved convergence rates are shown when the features satisfy a small deviation lower bound. In particular, the results provide an explanation why interpolating adversarial noise can be harmless for classification problems. Simulations illustrate the presented theory.
Cite
@article{arxiv.2105.02083,
title = {AdaBoost and robust one-bit compressed sensing},
author = {Geoffrey Chinot and Felix Kuchelmeister and Matthias Löffler and Sara van de Geer},
journal= {arXiv preprint arXiv:2105.02083},
year = {2021}
}
Comments
40 pages, 4 figures, code available at https://github.com/Felix-127/Adaboost-and-robust-one-bit-compressed-sensing, extended results to features that satisfy weak-moment and anti-concentration assumption