AdaBoost and robust one-bit compressed sensing
This work addresses robust classification in overparameterized, sparse settings for applications like signal processing, but it is incremental as it builds on existing AdaBoost and margin theory.
The paper tackles binary classification in robust one-bit compressed sensing with adversarial errors, deriving prediction error bounds for AdaBoost and showing that interpolating adversarial noise can be harmless, with improved convergence rates under certain feature conditions.
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.