Bayes Multiple Decision Functions in Classification

• Activity Number: 347
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Wensong Wu*+ and Edsel Aldea Pena
• Companies: Florida International University and University of South Carolina
• Keywords: classification ; Bayesian ; Decision Thoery ; Generalized Linear Models ; False Positive Rate ; high dimension data

Abstract

In this presentation we consider a two-class classification problem, where the goal is to predict the class membership of M units based on the values of high-dimensional predictor variables as well as both the values of the predictor variables and the class membership of other N independent units. We consider a Bayesian and decision-theoretic framework, and develop a general form of Bayes multiple decision function (BMDF) with respect to a class of cost-weighted loss functions. In particular, the loss function pairs such as the proportions of false positives and false negatives, and (1-sensitivity) and (1-specificity), are considered, and the cost weights are customer-determined. An efficient algorithm of finding the BMDF is provided based upon posterior expectations. The result is applicable to the general classification models, but particular generalized linear regression models are investigated, where the predictor variables and the link functions are to be chosen from a finite class. The results will be illustrated via simulations and on a real medical data set.