Statistical Analysis of Bipartite and Multipartite Ranking by Convex Risk Minimization

• Activity Number: 532
• Type: Contributed
• Date/Time: Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Kazuki Uematsu*+ and Yoonkyung Lee
• Companies: The Ohio State University and The Ohio State University
• Keywords: Bipartite Ranking ; Consistency ; Convex Risk Minimization ; Multipartite Ranking ; Ordinal Regression

Abstract

There has been growing interest in the problem of ranking in machine learning and data mining for information retrieval and web search. As a special type of the problem, bipartite or multipartite ranking aims to learn a function which can rank instances using covariates in accordance with their ordered categorical responses such as movie ratings. We examine the theoretical relationship between a class of bipartite ranking loss criteria and the associated best ranking functions in the framework of convex risk minimization. The result illuminates the parallel between ranking and classification and suggests a notion of consistency. We further extend it to multipartite ranking by considering appropriate extensions of the ranking loss criteria based on AUC. The study provides a new perspective on ordinal regression and the proportional odds model for handling ordered categorical responses.