A wavelet-based filtering approach to functional bipartite ranking

It is the purpose of this paper to investigate the bipartite ranking task from the perspective of functional data analysis (FDA). Precisely, given a collection of independent copies of a (possibly sampled) random curve X = (X(t))
_tϵ[0,1]
taking its values in a function space X, with a locally smooth autocorrelation structure and to which a binary label Y ϵ {-1, +1} is randomly assigned, the goal is to learn a scoring functions: X → R with optimal ROC curve. Based on nonlinear wavelet-based approximation, it is shown how to select compact finite dimensional representations of the input curves in order to build accurate ranking rules, using recent advances in the ranking problem for multivariate data with binary feedback.