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Issue No. 06 - June (2013 vol. 62)
ISSN: 0018-9340
pp: 1221-1233
Hanjiang Lai , Sun Yat-sen University, Guangzhou
Yan Pan , Sun Yat-sen University, Guangzhou
Cong Liu , Sun Yat-sen University, Guangzhou
Liang Lin , Sun Yat-sen University, Guangzhou
Jie Wu , Temple University, Philadelphia
Learning-to-rank for information retrieval has gained increasing interest in recent years. Inspired by the success of sparse models, we consider the problem of sparse learning-to-rank, where the learned ranking models are constrained to be with only a few nonzero coefficients. We begin by formulating the sparse learning-to-rank problem as a convex optimization problem with a sparse-inducing $(\ell_1)$ constraint. Since the $(\ell_1)$ constraint is nondifferentiable, the critical issue arising here is how to efficiently solve the optimization problem. To address this issue, we propose a learning algorithm from the primal dual perspective. Furthermore, we prove that, after at most $(O({1\over \epsilon } ))$ iterations, the proposed algorithm can guarantee the obtainment of an $(\epsilon)$-accurate solution. This convergence rate is better than that of the popular subgradient descent algorithm. i.e., $(O({1\over \epsilon^2} ))$. Empirical evaluation on several public benchmark data sets demonstrates the effectiveness of the proposed algorithm: 1) Compared to the methods that learn dense models, learning a ranking model with sparsity constraints significantly improves the ranking accuracies. 2) Compared to other methods for sparse learning-to-rank, the proposed algorithm tends to obtain sparser models and has superior performance gain on both ranking accuracies and training time. 3) Compared to several state-of-the-art algorithms, the ranking accuracies of the proposed algorithm are very competitive and stable.
Prediction algorithms, Optimization, Machine learning algorithms, Vectors, Computational modeling, Support vector machines, Accuracy, Fenchel duality, Learning-to-rank, sparse models, ranking algorithm

C. Liu, Y. Pan, H. Lai, L. Lin and J. Wu, "Sparse Learning-to-Rank via an Efficient Primal-Dual Algorithm," in IEEE Transactions on Computers, vol. 62, no. , pp. 1221-1233, 2013.
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