caa a22 4500 467939357 CHVBK 20180406153007.0 cr unu---uuuuu 170328e20060701xx s 000 0 eng 10.1007/s10444-004-7634-z doi (NATIONALLICENCE)springer-10.1007/s10444-004-7634-z Learning theory: stability is sufficient for generalization and necessary and sufficient for consistency of empirical risk minimization [Elektronische Daten] [Sayan Mukherjee, Partha Niyogi, Tomaso Poggio, Ryan Rifkin] Solutions of learning problems by Empirical Risk Minimization (ERM) - and almost-ERM when the minimizer does not exist - need to be consistent, so that they may be predictive. They also need to be well-posed in the sense of being stable, so that they might be used robustly. We propose a statistical form of stability, defined as leave-one-out (LOO) stability. We prove that for bounded loss classes LOO stability is (a) sufficient for generalization, that is convergence in probability of the empirical error to the expected error, for any algorithm satisfying it and, (b) necessary and sufficient for consistency of ERM. Thus LOO stability is a weak form of stability that represents a sufficient condition for generalization for symmetric learning algorithms while subsuming the classical conditions for consistency of ERM. In particular, we conclude that a certain form of well-posedness and consistency are equivalent for ERM. Springer, 2006 stability nationallicence inverse problems nationallicence generalization nationallicence consistency nationallicence empirical risk minimization nationallicence uniform Glivenko-Cantelli nationallicence Mukherjee Sayan Center for Biological and Computational Learning, Artificial Intelligence Laboratory, and McGovern Institute, USA aut Niyogi Partha Department of Computer Science and Statistics, University of Chicago, 60637, Chicago, IL, USA aut Poggio Tomaso Center for Biological and Computational Learning, Artificial Intelligence Laboratory, and McGovern Institute, USA aut Rifkin Ryan Center for Biological and Computational Learning, Artificial Intelligence Laboratory, and McGovern Institute, USA aut Advances in Computational Mathematics Kluwer Academic Publishers 25/1-3(2006-07-01), 161-193 1019-7168 25:1-3<161 2006 25 10444 https://doi.org/10.1007/s10444-004-7634-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10444-004-7634-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Mukherjee Sayan Center for Biological and Computational Learning, Artificial Intelligence Laboratory, and McGovern Institute, USA aut NATIONALLICENCE 700 1- Niyogi Partha Department of Computer Science and Statistics, University of Chicago, 60637, Chicago, IL, USA aut NATIONALLICENCE 700 1- Poggio Tomaso Center for Biological and Computational Learning, Artificial Intelligence Laboratory, and McGovern Institute, USA aut NATIONALLICENCE 700 1- Rifkin Ryan Center for Biological and Computational Learning, Artificial Intelligence Laboratory, and McGovern Institute, USA aut NATIONALLICENCE 773 0- Advances in Computational Mathematics Kluwer Academic Publishers 25/1-3(2006-07-01), 161-193 1019-7168 25:1-3<161 2006 25 10444 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer