  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.
