Electronic Journal of Statistics

Query-dependent ranking and its asymptotic properties

Ben Dai and Junhui Wang

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Statist., Volume 13, Number 1 (2019), 465-488.

Dates
Received: September 2018
First available in Project Euclid: 12 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1549962032

Digital Object Identifier
doi:10.1214/19-EJS1531

Subjects
Primary: 62F07: Ranking and selection 62G20: Asymptotic properties
Secondary: 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20] 62P30: Applications in engineering and industry

Keywords
Empirical process ranking $U$-process local smoothing margin loss SVM

Rights
Creative Commons Attribution 4.0 International License.

Citation

Dai, Ben; Wang, Junhui. Query-dependent ranking and its asymptotic properties. Electron. J. Statist. 13 (2019), no. 1, 465--488. doi:10.1214/19-EJS1531. https://projecteuclid.org/euclid.ejs/1549962032


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