Statistical Consistency of Multipartite Ranking

• Activity Number: 611
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Yoonkyung Lee*+ and Kazuki Uematsu
• Companies: The Ohio State University and Ohio State University
• Keywords: Ranking ; Consistency ; Ordinal response ; Convex risk

Abstract

Statistical consistency in multipartite ranking is investigated as an extension of bipartite ranking. We consider the consistency of ranking algorithms through minimization of the theoretical risk which combines pairwise ranking errors of ordinal categories. The extension shows that for a certain class of convex loss functions including exponential loss, the optimal ranking function can be represented as a ratio of weighted likelihood of upper categories to lower categories, where the weights are given by the misranking costs. This result also bridges traditional ranking methods such as proportional odds model in statistics with algorithmic ranking methods in machine learning. We illustrate our findings with simulation study and real data analysis.