Concentration in unbounded metric spaces and algorithmic stability

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

8 Scopus citations


We prove an extension of McDiarmid's inequality for metric spaces with unbounded diame-ter. To this end, we introduce the notion of the subgaussian diameter, which is a distribution- dependent refinement of the metric diameter. Our technique provides an alternative approach to that of Kutin and Niyogi's method of weakly difference-bounded functions, and yields non- trivial, dimension-free results in some interesting cases where the former does not. As an application, we give apparently the first generalization bound in the algorithmic stability setting that holds for unbounded loss functions. This yields a novel risk bound for some regularized metric regression algorithms. We give two extensions of the basic concentration result. The first enables one to replace the independence assumption by appropriate strong mixing. The second generalizes the subgaussian technique to other Orlicz norms.

Original languageEnglish
Title of host publication31st International Conference on Machine Learning, ICML 2014
PublisherInternational Machine Learning Society (IMLS)
Number of pages11
ISBN (Electronic)9781634393973
StatePublished - 1 Jan 2014
Event31st International Conference on Machine Learning, ICML 2014 - Beijing, China
Duration: 21 Jun 201426 Jun 2014


Conference31st International Conference on Machine Learning, ICML 2014

ASJC Scopus subject areas

  • Artificial Intelligence
  • Computer Networks and Communications
  • Software


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