P-Values for Classification in High-Dimensional Settings

• Activity Number: 320
• Type: Invited
• Date/Time: Tuesday, August 3, 2010 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Niki Zumbrunnen*+ and Lutz Dümbgen
• Companies: University of Bern and University of Bern
• Keywords: nonparametric ; regularization ; data-driven tuning parameters ; confidence region

Abstract

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.