Minimax semi-supervised set-valued approach to multi-class classification

We study supervised and semi-supervised algorithms in the set-valued classification framework with controlled expected size. While former methods can use only n labeled samples, latter are able to make of N additional unlabeled data. obtain minimax rates convergence under α-margin assumption a β-Hölder condition on conditional distribution labels. Our analysis implies that if no further is made, there method outperforms estimator proposed this work – best achievable rate for any O(n−1/2), even margin extremely favorable; contrary, developed achieve faster O((n/logn)−(1+α)β/(2β+d)) provided sufficiently many samples available. also show smoothness assumption, sample cannot improve convergence. Finally, numerical supports our theory emphasizes relevance assumptions we required from an empirical perspective.