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2019 Query-dependent ranking and its asymptotic properties
Ben Dai, Junhui Wang
Electron. J. Statist. 13(1): 465-488 (2019). DOI: 10.1214/19-EJS1531


Ranking, also known as learning to rank in machine learning community, is to rank a number of items based on their relevance to a specific query. In literature, most ranking methods use a uniform ranking function to evaluate the relevance, which completely ignores the heterogeneity among queries. To admit different ranking functions for various queries, a general $U$-process formulation for query-dependent ranking is developed. It allows to incorporate neighborhood structure among queries via various forms of smoothing weights to improve the ranking performance. One of its salient features is its capability of producing reasonable rankings for novel queries that are absent in the training set, which is commonly encountered in practice but often neglected in the literature. The proposed method is implemented via an inexact alternating direction method of multipliers (ADMM) for each query parallelly. Its asymptotic risk bound is established, showing that it achieves desirable ranking accuracy at a fast rate for any query including the novel ones. Furthermore, simulated examples and a real application to the Yahoo! challenge dataset also support the advantage of the query-dependent ranking method against existing competitors.


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Ben Dai. Junhui Wang. "Query-dependent ranking and its asymptotic properties." Electron. J. Statist. 13 (1) 465 - 488, 2019.


Received: 1 September 2018; Published: 2019
First available in Project Euclid: 12 February 2019

zbMATH: 07021711
MathSciNet: MR3910859
Digital Object Identifier: 10.1214/19-EJS1531

Primary: 62F07 , 62G20
Secondary: 62H30 , 62P30

Keywords: $U$-process , empirical process , local smoothing , margin loss , ranking , SVM


Vol.13 • No. 1 • 2019
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