PAC-Bayesian High Dimensional Bipartite Ranking
This addresses ranking in high-dimensional data for statistical learning, but it is incremental as it builds on existing PAC-Bayesian and sparsity frameworks.
The paper tackles the high-dimensional bipartite ranking problem by proposing a PAC-Bayesian scoring strategy with nonlinear additive functions, deriving non-asymptotic risk bounds under sparsity and proving minimax optimality with oracle inequalities.
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.