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Learning to Rank with Pairwise Regularized Least-Squares

Tapio Pahikkala, Evgeni Tsivtsivadze, Antti Airola, Jorma Boberg, Tapio Salakoski, Learning to Rank with Pairwise Regularized Least-Squares. In: Thorsten Joachims, Hang Li, Tie-Yan Liu, ChengXiang Zhai (Eds.), SIGIR 2007 Workshop on Learning to Rank for Information Retrieval, 27-33, 2007.

Abstract:

Learning preference relations between objects of interest is one of the key problems in machine learning. Our approach for addressing this task is based on pairwise comparisons for estimation of overall ranking. In this paper, we propose a simple preference learning algorithm based on regularized least squares and describe it within the kernel methods framework. Our algorithm, that we call RankRLS, minimizes a regularized least-squares approximation of a ranking error function that counts the number of incorrectly ranked pairs of data points. We consider both primal and dual versions of the algorithm. The primal version is preferable when the dimensionality of the feature space is smaller than the number of training data points and the dual one is preferable in the opposite case. We show that both versions of RankRLS can be trained as efficiently as the corresponding versions of standard regularized least-squares regression, despite the fact that the number of training data point pairs under consideration grows quadratically with respect to the number of individual points. As a representative example of a case where the data points outnumber features we choose the Letor dataset. For the opposite case, we choose the parse ranking task. We show that on the Letor dataset the primal RankRLS performs comparably to RankSVM and RankBoost algorithms that are used as baselines. Moreover, we show that the dual RankRLS notably outperforms the standard regularized least-squares regression in parse ranking. We suggest that the main advantage of RankRLS is the computational efficiency both in the primal and the dual versions, especially since the efficient implementation of the latter is not straightforward, for example, for the support vector machines.

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BibTeX entry:

@INPROCEEDINGS{inpPaTsAiBoSa07a,
  title = {Learning to Rank with Pairwise Regularized Least-Squares},
  booktitle = {SIGIR 2007 Workshop on Learning to Rank for Information Retrieval},
  author = {Pahikkala, Tapio and Tsivtsivadze, Evgeni and Airola, Antti and Boberg, Jorma and Salakoski, Tapio},
  editor = {Joachims, Thorsten and Li, Hang and Liu, Tie-Yan and Zhai, ChengXiang},
  pages = {27-33},
  year = {2007},
  keywords = {Information retrieval, Ranking, Regularized least-squares, Machine learning},
}

Belongs to TUCS Research Unit(s): Turku BioNLP Group

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