PAC-Bayesian High Dimensional Bipartite Ranking

Benjamin Guedj (1) , Sylvain Robbiano (2)

1 MODAL - MOdel for Data Analysis and Learning
2 Department of Statistical Science

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.

Mots clés: Bipartite Ranking; High Dimension and Sparsity; PAC-Bayesian Aggregation; MCMC; Supervised Statistical Learning

Domaines: Machine Learning [stat.ML]; Théorie [stat.TH]; Statistiques [math.ST]

Benjamin Guedj, Sylvain Robbiano. PAC-Bayesian High Dimensional Bipartite Ranking. Journal of Statistical Planning and Inference, 2018, ⟨10.1016/j.jspi.2017.10.010⟩. ⟨hal-01226472⟩