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Statistical Consistency of Ranking Methods in A Rank-Differentiable Probability Space
Yanyan Lan · Jiafeng Guo · Xueqi Cheng · Tie-Yan Liu

Wed Dec 05 07:00 PM -- 12:00 AM (PST) @ Harrah’s Special Events Center 2nd Floor #None

This paper is concerned with the statistical consistency of ranking methods. Recently, it was proven that many commonly used pairwise ranking methods are inconsistent with the weighted pairwise disagreement loss (WPDL), which can be viewed as the true loss of ranking, even in a low-noise setting. This result is interesting but also surprising, given that the pairwise ranking methods have been shown very effective in practice. In this paper, we argue that the aforementioned result might not be conclusive, depending on what kind of assumptions are used. We give a new assumption that the labels of objects to rank lie in a rank-differentiable probability space (RDPS), and prove that the pairwise ranking methods become consistent with WPDL under this assumption. What is especially inspiring is that RDPS is actually not stronger than but similar to the low-noise setting. Our studies provide theoretical justifications of some empirical findings on pairwise ranking methods that are unexplained before, which bridge the gap between theory and applications.

Author Information

Yanyan Lan (Tsinghua University)
Jiafeng Guo
Xueqi Cheng (ICT)
Tie-Yan Liu (Microsoft Research Asia)

Tie-Yan Liu is an assistant managing director of Microsoft Research Asia, leading the machine learning research area. He is very well known for his pioneer work on learning to rank and computational advertising, and his recent research interests include deep learning, reinforcement learning, and distributed machine learning. Many of his technologies have been transferred to Microsoft’s products and online services (such as Bing, Microsoft Advertising, Windows, Xbox, and Azure), and open-sourced through Microsoft Cognitive Toolkit (CNTK), Microsoft Distributed Machine Learning Toolkit (DMTK), and Microsoft Graph Engine. He has also been actively contributing to academic communities. He is an adjunct/honorary professor at Carnegie Mellon University (CMU), University of Nottingham, and several other universities in China. He has published 200+ papers in refereed conferences and journals, with over 17000 citations. He has won quite a few awards, including the best student paper award at SIGIR (2008), the most cited paper award at Journal of Visual Communications and Image Representation (2004-2006), the research break-through award (2012) and research-team-of-the-year award (2017) at Microsoft Research, and Top-10 Springer Computer Science books by Chinese authors (2015), and the most cited Chinese researcher by Elsevier (2017). He has been invited to serve as general chair, program committee chair, local chair, or area chair for a dozen of top conferences including SIGIR, WWW, KDD, ICML, NIPS, IJCAI, AAAI, ACL, ICTIR, as well as associate editor of ACM Transactions on Information Systems, ACM Transactions on the Web, and Neurocomputing. Tie-Yan Liu is a fellow of the IEEE, and a distinguished member of the ACM.

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