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Sparse Learning-to-Rank via an Efficient Primal-Dual Algorithm
June 2013 (vol. 62 no. 6)
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.
Index Terms:
Prediction algorithms,Optimization,Machine learning algorithms,Vectors,Computational modeling,Support vector machines,Accuracy,Fenchel duality,Learning-to-rank,sparse models,ranking algorithm
Citation:
Hanjiang Lai, Yan Pan, Cong Liu, Liang Lin, Jie Wu, "Sparse Learning-to-Rank via an Efficient Primal-Dual Algorithm," IEEE Transactions on Computers, vol. 62, no. 6, pp. 1221-1233, June 2013, doi:10.1109/TC.2012.62
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