AdaBoost and robust one-bit compressed sensing
Geoffrey ChinotETH Zürich, Switzerland
Felix KuchelmeisterETH Zürich, Switzerland
Matthias LöfflerETH Zürich, Switzerland
Sara van de GeerETH Zürich, Switzerland
This paper studies binary classification in robust one-bit compressed sensing with adversarial errors. It is assumed that the model is overparametrized 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 this article
Geoffrey Chinot, Felix Kuchelmeister, Matthias Löffler, Sara van de Geer, AdaBoost and robust one-bit compressed sensing. Math. Stat. Learn. 5 (2022), no. 1/2, pp. 117–158DOI 10.4171/MSL/31