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We introduce a notion of algorithmic stability of learning algorithms---that we term \emph{argument stability}---that captures stability of the hypothesis output by the learning algorithm in the normed space of functions from which hypotheses are selected.
Distribution-free inequalities for the deleted and holdout error estimates
Devroye, Luc and Wagner, Terry J · 1979
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Lugosi, Gábor and Pawlak, Miroslaw · 1994
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Optimum bounds for the distributions of martingales in Banach spaces
Pinelis, Iosif · 1994
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Boucheron, Stéphane, Lugosi, Gábor, and Massart, Pascal · 2013
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Ledoux, Michel and Talagrand, Michel · 2013
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Hardt, Moritz, Recht, Benjamin, and Singer, Yoram · 2015
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On equivalence of martingale tail bounds and deterministic regret inequalities
Rakhlin, Alexander and Sridharan, Karthik · 2015
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Pisier, Gilles · 2011
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Algorithm-dependent generalization bounds for multi-task learning
Liu, Tongliang, Tao, Dacheng, Song, Mingli, and Maybank, Stephen J · 2017
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