## The Annals of Applied Probability

### Bounding the generalization error of convex combinations of classifiers: balancing the dimensionality and the margins

#### Abstract

A problem of bounding the generalization error of a classifier %\break $f\in \conv(\mathcal{H})$, where $\mathcal{H}$ is a "base" class of functions (classifiers), is considered. This problem frequently occurs in computer learning, where efficient algorithms that combine simple classifiers into a complex one (such as boosting and bagging) have attracted a lot of attention. Using Talagrand's concentration inequalities for empirical processes, we obtain new sharper bounds on the generalization error of combined classifiers that take into account both the empirical distribution of "classification margins" and an "approximate dimension" of the classifiers, and study the performance of these bounds in several experiments with learning algorithms.

#### Article information

Source
Ann. Appl. Probab., Volume 13, Number 1 (2003), 213-252.

Dates
First available in Project Euclid: 16 January 2003

https://projecteuclid.org/euclid.aoap/1042765667

Digital Object Identifier
doi:10.1214/aoap/1042765667

Mathematical Reviews number (MathSciNet)
MR1951998

Zentralblatt MATH identifier
1073.62535

Subjects
Primary: 62G05: Estimation
Secondary: 62G20: Asymptotic properties 60F15: Strong theorems

#### Citation

Koltchinskii, Vladimir; Panchenko, Dmitriy; Lozano, Fernando. Bounding the generalization error of convex combinations of classifiers: balancing the dimensionality and the margins. Ann. Appl. Probab. 13 (2003), no. 1, 213--252. doi:10.1214/aoap/1042765667. https://projecteuclid.org/euclid.aoap/1042765667

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• ALBUQUERQUE, NEW MEXICO 87131-1141 E-MAIL: vlad@math.unm.edu panchenk@math.unm.edu F. LOZANO DEPARTMENT OF ELECTRONIC ENGINEERING UNIVERSIDAD JAVERIANA BOGOTA COLOMBIA E-MAIL: fernando.lozano@javeriana.edu.co