Optimal rates for F-score binary classification

Abstract

We study the minimax settings of binary classification with F-score under the βsmoothness assumptions on the regression function ηWe propose a classification procedure which under the α-margin assumption achieves the rate O(n −(1+α)β/(2β+d) ) for the excess F-score. In this context, the Bayes optimal classifier for the F-score can be obtained by thresholding the aforementioned regression function η on some level θ * to be estimated. The proposed procedure is performed in a semi-supervised manner, that is, for the estimation of the regression function we use a labeled dataset of size n ∈ N and for the estimation of the optimal threshold θ * we use an unlabeled dataset of size N ∈ N. Interestingly, the value of N ∈ N does not affect the rate of convergence, which indicates that it is "harder" to estimate the regression function η than the optimal threshold θ * . This further implies that the binary classification with F-score behaves similarly to the standard settings of binary classification. Finally, we show that the rates achieved by the proposed procedure are optimal in the minimax sense up to a constant factor.