The DOI matches its Crossref record; 27 of the 27 references it cites were found in a registry or an index.
Ranking and Empirical Minimization of U-statistics
Open accessAbstract
The problem of ranking/ordering instances, instead of simply classifying them, has recently gained much attention in machine learning. In this paper we formulate the ranking problem in a rigorous statistical framework. The goal is to learn a ranking rule for deciding, among two instances, which one is “better,” with minimum ranking risk. Since the natural estimates of the risk are of the form of a U-statistic, results of the theory of U-processes are required for investigating the consistency of empirical risk minimizers. We establish, in particular, a tail inequality for degenerate U-processes, and apply it for showing that fast rates of convergence may be achieved under specific noise assumptions, just like in classification. Convex risk minimization methods are also studied.
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Cites
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Self-citationA Class of Statistics with Asymptotically Normal Distribution
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On the mathematical foundations of learning
Cucker, F., & Smale, S. (2001) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-01-00923-5 · Cited by 1,545
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Convexity, Classification, and Risk Bounds
Bartlett, P. L., Jordan, M. I., & McAuliffe, J. D. (2006) · Journal of the American Statistical Association · doi:10.1198/016214505000000907 · Cited by 1,037
Statistical behavior and consistency of classification methods based on convex risk minimization
Zhang, T. (2004) · The Annals of Statistics · doi:10.1214/aos/1079120130 · Cited by 711
Optimal aggregation of classifiers in statistical learning
Tsybakov, A. B. (2004) · The Annals of Statistics · doi:10.1214/aos/1079120131 · Cited by 582
Adapting ranking SVM to document retrieval
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Cited by
A Theoretical Analysis of NDCG Type Ranking Measures
Wang, Y., Wang, L., Li, Y., He, D., Liu, T.-Y., & Chen, W. (2013) · arXiv · doi:10.48550/arxiv.1304.6480 · Cited by 351
Distribution-free, Risk-controlling Prediction Sets
Bates, S., Angelopoulos, A., Lei, L., Malik, J., & Jordan, M. (2021) · Journal of the ACM · doi:10.1145/3478535 · Cited by 144
“We consider the problem of uncertainty quantification for learning a ranking rule [see, e.g., 57].”
Background
Metadata
- Authors
- Clémençon, S., Lugosi, G., & Vayatis, N.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2008-04-01
- Volume
- 36
- Issue
- 2
- Pages
- 844-874
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W1978810924
- Cited by
- 275
- References
- 27
- FWCI
- 12.42
- Type
- journal article
- Language
- en
- Open access
- bronze
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