Abstract #300636

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JSM 2003 Abstract #300636
Activity Number: 155
Type: Invited
Date/Time: Monday, August 4, 2003 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract - #300636
Title: An Oracle Inequality for the Classification Problem
Author(s): Sara van de Geer*+
Companies: Leiden University
Address: Niels Borhweg 1, Leiden, , 2333 CA, Netherlands
Keywords: adaptation ; classification ; empirical risk ; oracle inequality ; penalty ; regression
Abstract:

Suppose one has an observations of the form (X,Y), where X is an instance and Y is a (0,1)-label. The aim is to use this training set to predict the label at a given instance. Classical examples are object recognition in images, speech recognition, and so on. The optimal classifier is Bayes rule, which predicts the most likely label given the value of X. Using the training set, we want to get as close as possible to Bayes rule. How well this can be done depends on how much the probability of the label given X differs from 1/2. We call this the margin behavior. Generally, the margin behavior is not known, so that the problem is to construct an estimator which is adaptive to the margin as well as to model complexity. We will consider a situation where it is possible to apply a penalized empirical risk estimator which is adaptive up to log n terms. Because empirical risk minimization is computationally hard, we will also discuss some alternative loss functions, such as support vector machine loss.

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