Issue No. 06 - June (2013 vol. 62)
ISSN: 0018-9340
pp: 1221-1233
Cong Liu , Sun Yat-sen University, Guangzhou
Yan Pan , Sun Yat-sen University, Guangzhou
Hanjiang Lai , Sun Yat-sen University, Guangzhou
Liang Lin , Sun Yat-sen University, Guangzhou
Jie Wu , Temple University, Philadelphia
ABSTRACT
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
Cong Liu, Yan Pan, Hanjiang Lai, Liang Lin, Jie Wu, "Sparse Learning-to-Rank via an Efficient Primal-Dual Algorithm", IEEE Transactions on Computers, vol. 62, no. , pp. 1221-1233, June 2013, doi:10.1109/TC.2012.62