Minimax semi-supervised confidence sets for multi-class classification

Abstract : In this work we study the semi-supervised framework of confidence set classification with controlled expected size in minimax settings. We obtain semi-supervised minimax rates of convergence under the margin assumption and a Hölder condition on the regression function. Besides, we show that if no further assumptions are made, there is no supervised method that outperforms the semi-supervised estimator proposed in this work. We establish that the best achievable rate for any supervised method is n^{−1/2} , even if the margin assumption is extremely favorable. On the contrary, semi-supervised estimators can achieve faster rates of convergence provided that sufficiently many unlabeled samples are available. We additionally perform numerical evaluation of the proposed algorithms empirically confirming our theoretical findings.
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https://hal-upec-upem.archives-ouvertes.fr/hal-02112918
Contributor : Evgenii Chzhen <>
Submitted on : Saturday, April 27, 2019 - 11:53:45 AM
Last modification on : Thursday, July 18, 2019 - 3:00:05 PM

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  • HAL Id : hal-02112918, version 1
  • ARXIV : 1904.12527

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Evgenii Chzhen, Christophe Denis, Mohamed Hebiri. Minimax semi-supervised confidence sets for multi-class classification. 2019. ⟨hal-02112918⟩

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