This is the program for the 2010 Joint Statistical Meetings in Vancouver, British Columbia.

Abstract Details

Activity Number: 320
Type: Invited
Date/Time: Tuesday, August 3, 2010 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract - #306014
Title: P-Values for Classification in High-Dimensional Settings
Author(s): Niki Zumbrunnen*+ and Lutz Dümbgen
Companies: University of Bern and University of Bern
Address: Alpeneggstrasse 22, Bern, International, 3012, Switzerland
Keywords: nonparametric ; regularization ; data-driven tuning parameters ; confidence region

Let (X,Y) be a random variable consisting of an observed feature vector X and an unobserved class label Y=1,2,...,L with unknown joint distribution. In addition, let D be a training data set consisting of n completely observed independent copies of (X,Y). Instead of providing point predictors (classifiers) for Y, we construct for each b=1,2,...,L a p-value pi_b(X,D) for the null hypothesis that Y=b, treating Y temporarily as a fixed parameter, i.e. we construct a prediction region for Y with a certain confidence. Any reasonable classifier can be modified to yield nonparametric p-values. For classifiers and p-values involving tuning parameters, we propose data-driven choices. One example are nearest neighbor classifiers. A second example is multicategory logistic regression , where we use regularization terms to deal with high-dimensional feature vectors X.

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