## The Annals of Statistics

### Generalization bounds for averaged classifiers

#### Abstract

We study a simple learning algorithm for binary classification. Instead of predicting with the best hypothesis in the hypothesis class, that is, the hypothesis that minimizes the training error, our algorithm predicts with a weighted average of all hypotheses, weighted exponentially with respect to their training error. We show that the prediction of this algorithm is much more stable than the prediction of an algorithm that predicts with the best hypothesis. By allowing the algorithm to abstain from predicting on some examples, we show that the predictions it makes when it does not abstain are very reliable. Finally, we show that the probability that the algorithm abstains is comparable to the generalization error of the best hypothesis in the class.

#### Article information

Source
Ann. Statist., Volume 32, Number 4 (2004), 1698-1722.

Dates
First available in Project Euclid: 4 August 2004

https://projecteuclid.org/euclid.aos/1091626184

Digital Object Identifier
doi:10.1214/009053604000000058

Mathematical Reviews number (MathSciNet)
MR2089139

Zentralblatt MATH identifier
1045.62056

Subjects
Primary: 62C12: Empirical decision procedures; empirical Bayes procedures

#### Citation

Freund, Yoav; Mansour, Yishay; Schapire, Robert E. Generalization bounds for averaged classifiers. Ann. Statist. 32 (2004), no. 4, 1698--1722. doi:10.1214/009053604000000058. https://projecteuclid.org/euclid.aos/1091626184

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