2019/05/10 by Evgenii Chzhen, Chzhen, Evgenii
Computer Science · Mathematics · #Advanced Statistical Methods and Models #FOS: Mathematics #Machine Learning and Algorithms #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1905.04039
openalex publication_date 2019/05/10 · openalex created_date 2023/08/08 · openalex updated_date 2026/07/28
We study the minimax settings of binary classification with F-score under the β-smoothness assumptions on the regression function η(x) = ℙ(Y = 1|X = x) for x ∈ ℝd. We 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.