# Optimal rates for F-score binary classification

Abstract : We study the minimax settings of binary classification with F-score under the $\beta$-smoothness assumptions on the regression function $\eta(x) = \mathbb{P}(Y = 1|X = x)$ for $x \in \mathbb{R}^d$. We propose a classification procedure which under the $\alpha$-margin assumption achieves the rate $O(n^{−(1+\alpha)\beta/(2\beta+d)})$ 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 $\eta$ on some level $\theta^*$ 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 $n \in \mathbb{N}$ and for the estimation of the optimal threshold $\theta^*$ we use an unlabeled dataset of size $N \in \mathbb{N}$. Interestingly, the value of $N \in \mathbb{N}$ does not affect the rate of convergence, which indicates that it is "harder" to estimate the regression function $\eta$ than the optimal threshold $\theta^*$. 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.

Cited literature [26 references]

https://hal-upec-upem.archives-ouvertes.fr/hal-02123314
Contributor : Evgenii Chzhen <>
Submitted on : Wednesday, May 8, 2019 - 12:40:53 AM
Last modification on : Thursday, March 19, 2020 - 12:26:03 PM
Document(s) archivé(s) le : Thursday, October 10, 2019 - 11:58:46 AM

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• HAL Id : hal-02123314, version 1
• ARXIV : 1905.04039

### Citation

Evgenii Chzhen. Optimal rates for F-score binary classification. 2019. ⟨hal-02123314⟩

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