AdaBoost and robust one-bit compressed sensing

TL;DR

This paper analyzes the robustness of AdaBoost in one-bit compressed sensing with adversarial errors, providing theoretical bounds and insights into its performance under heavy-tailed features and overparameterization.

Contribution

It establishes prediction error bounds for AdaBoost in robust one-bit compressed sensing, connecting it to max-ell-1 margin classifiers and explaining its resilience to adversarial noise.

Findings

AdaBoost achieves favorable error bounds in robust one-bit compressed sensing.

Heavy-tailed feature distributions can be handled with minimal assumptions.

Interpolating adversarial noise may not harm classification performance.

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-$\ell_1$-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.