caa a22 4500 605478252 CHVBK 20210128100404.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s10994-015-5491-2 doi (NATIONALLICENCE)springer-10.1007/s10994-015-5491-2 Geist Matthieu IMS - MaLIS Research Group and UMI 2958 (GeorgiaTech-CNRS), CentraleSupélec, Metz, France aut Soft-max boosting [Elektronische Daten] [Matthieu Geist] The standard multi-class classification risk, based on the binary loss, is rarely directly minimized. This is due to (1) the lack of convexity and (2) the lack of smoothness (and even continuity). The classic approach consists in minimizing instead a convex surrogate. In this paper, we propose to replace the usually considered deterministic decision rule by a stochastic one, which allows obtaining a smooth risk (generalizing the expected binary loss, and more generally the cost-sensitive loss). Practically, this (empirical) risk is minimized by performing a gradient descent in the function space linearly spanned by a base learner (a.k.a. boosting). We provide a convergence analysis of the resulting algorithm and experiment it on a bunch of synthetic and real-world data sets (with noiseless and noisy domains, compared to convex and non-convex boosters). The Author(s), 2015 Multi-class classification nationallicence Boosting nationallicence Binary loss nationallicence Noise-tolerant learning nationallicence Machine Learning Springer US; http://www.springer-ny.com 100/2-3(2015-09-01), 305-332 0885-6125 100:2-3<305 2015 100 10994 https://doi.org/10.1007/s10994-015-5491-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10994-015-5491-2 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Geist Matthieu IMS - MaLIS Research Group and UMI 2958 (GeorgiaTech-CNRS), CentraleSupélec, Metz, France aut NATIONALLICENCE 773 0- Machine Learning Springer US; http://www.springer-ny.com 100/2-3(2015-09-01), 305-332 0885-6125 100:2-3<305 2015 100 10994