### Abstract

This paper describes an efficient reduction of the learning problem of ranking to binary classification. The reduction is randomized and guarantees a pairwise misranking regret bounded by that of the binary classifier, improving on a recent result of Balcan et al. (2007) which ensures only twice that upper-bound. Moreover, our reduction applies to a broader class of ranking loss functions, admits a simple proof, and the expected time complexity of our algorithm in terms of number of calls to a classifier or preference function is also improved from Ω(n^{2}) to O(nlogn). In addition, when the top k ranked elements only are required (k ≪ n), as in many applications in information extraction or search engine design, the time complexity of our algorithm can be further reduced to O(k log k+n). Our reduction and algorithm are thus practical for realistic applications where the number of points to rank exceeds several thousands. Much of our results also extend beyond the bipartite case previously studied. To further complement them, we also derive lower bounds for any deterministic reduction of ranking to binary classification, proving that randomization is necessary to achieve our reduction guarantees.

Original language | English (US) |
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Title of host publication | 21st Annual Conference on Learning Theory, COLT 2008 |

Pages | 87-97 |

Number of pages | 11 |

State | Published - 2008 |

Event | 21st Annual Conference on Learning Theory, COLT 2008 - Helsinki, Finland Duration: Jul 9 2008 → Jul 12 2008 |

### Other

Other | 21st Annual Conference on Learning Theory, COLT 2008 |
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Country | Finland |

City | Helsinki |

Period | 7/9/08 → 7/12/08 |

### Fingerprint

### ASJC Scopus subject areas

- Education

### Cite this

*21st Annual Conference on Learning Theory, COLT 2008*(pp. 87-97)

**An efficient reduction of ranking to classification.** / Ailon, Nir; Mohri, Mehryar.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*21st Annual Conference on Learning Theory, COLT 2008.*pp. 87-97, 21st Annual Conference on Learning Theory, COLT 2008, Helsinki, Finland, 7/9/08.

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TY - GEN

T1 - An efficient reduction of ranking to classification

AU - Ailon, Nir

AU - Mohri, Mehryar

PY - 2008

Y1 - 2008

N2 - This paper describes an efficient reduction of the learning problem of ranking to binary classification. The reduction is randomized and guarantees a pairwise misranking regret bounded by that of the binary classifier, improving on a recent result of Balcan et al. (2007) which ensures only twice that upper-bound. Moreover, our reduction applies to a broader class of ranking loss functions, admits a simple proof, and the expected time complexity of our algorithm in terms of number of calls to a classifier or preference function is also improved from Ω(n2) to O(nlogn). In addition, when the top k ranked elements only are required (k ≪ n), as in many applications in information extraction or search engine design, the time complexity of our algorithm can be further reduced to O(k log k+n). Our reduction and algorithm are thus practical for realistic applications where the number of points to rank exceeds several thousands. Much of our results also extend beyond the bipartite case previously studied. To further complement them, we also derive lower bounds for any deterministic reduction of ranking to binary classification, proving that randomization is necessary to achieve our reduction guarantees.

AB - This paper describes an efficient reduction of the learning problem of ranking to binary classification. The reduction is randomized and guarantees a pairwise misranking regret bounded by that of the binary classifier, improving on a recent result of Balcan et al. (2007) which ensures only twice that upper-bound. Moreover, our reduction applies to a broader class of ranking loss functions, admits a simple proof, and the expected time complexity of our algorithm in terms of number of calls to a classifier or preference function is also improved from Ω(n2) to O(nlogn). In addition, when the top k ranked elements only are required (k ≪ n), as in many applications in information extraction or search engine design, the time complexity of our algorithm can be further reduced to O(k log k+n). Our reduction and algorithm are thus practical for realistic applications where the number of points to rank exceeds several thousands. Much of our results also extend beyond the bipartite case previously studied. To further complement them, we also derive lower bounds for any deterministic reduction of ranking to binary classification, proving that randomization is necessary to achieve our reduction guarantees.

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