The probability of error of classification methods based on convex combinations of simple base classifiers by "boosting" algorithms is investigated. The main result of the paper is that certain regularized boosting algorithms provide Bayes-risk consistent classifiers under the sole assumption that the Bayes classifier may be approximated by a convex combination of the base classifiers. Nonasymptotic distribution-free bounds are also developed which offer interesting new insight into how boosting works and help explain its success in practical classification problems.
"On the Bayes-risk consistency of regularized boosting methods." Ann. Statist. 32 (1) 30 - 55, February 2004. https://doi.org/10.1214/aos/1079120129