PAC-Bayesian high dimensional bipartite ranking

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Journal of Statistical Planning and Inference, ISSN: 0378-3758, Vol: 196, Page: 70-86

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Guedj, Benjamin; Robbiano, Sylvain
Elsevier BV
Mathematics; Decision Sciences; Statistics - Machine Learning; Mathematics - Statistics Theory
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article description
This paper is devoted to the bipartite ranking problem, a classical statistical learning task, in a high dimensional setting. We propose a scoring and ranking strategy based on the PAC-Bayesian approach. We consider nonlinear additive scoring functions, and we derive non-asymptotic risk bounds under a sparsity assumption. In particular, oracle inequalities in probability holding under a margin condition assess the performance of our procedure, and prove its minimax optimality. An MCMC-flavored algorithm is proposed to implement our method, along with its behavior on synthetic and real-life datasets.