Lagrangian Inference for Ranking Problems

Abstract

Understanding ranking orders of different items is of great importance in many applications such as sports, online game, and recommendation, among many others. This paper provides a novel approach to inferring the ranking systems. In particular, the paper aims to answer questions like, is item A better than item B? Is item A among the top 10 items? Such inference problems are challenging as they involve combinatorial structures. The key technical innovation is a new Lagrangian inference framework with new bootstrap tools. Strong theoretical guarantees are provided showing the optimality of the proposed method. A novel application of inferring movies’ ranking using a large-scale data set is provided to demonstrate the applicability of the proposed method.