Boosting the margin: a new explanation for the effectiveness of voting methods

TLDR

Boosting classifiers often maintain or reduce test error even as model size grows and training error reaches zero. The paper investigates how the distribution of training‑example margins explains boosting’s robustness to overfitting. The authors adapt support‑vector‑classifier and small‑weight neural‑network analyses to relate margin distributions to test error, and compare this explanation to bias‑variance decompositions. The study demonstrates theoretically and experimentally that boosting markedly increases training‑example margins, accounting for its low test error.

Abstract

One of the surprising recurring phenomena observed in experiments with boosting is that the test error of the generated classifier usually does not increase as its size becomes very large, and often is observed to decrease even after the training error reaches zero. In this paper, we show that this phenomenon is related to the distribution of margins of the training examples with respect to the generated voting classification rule, where the margin of an example is simply the difference between the number of correct votes and the maximum number of votes received by any incorrect label. We show that techniques used in the analysis of Vapnik’s support vector classifiers and of neural networks with small weights can be applied to voting methods to relate the margin distribution to the test error. We also show theoretically and experimentally that boosting is especially effective at increasing the margins of the training examples. Finally, we compare our explanation to those based on the bias-variance decomposition.