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An extension of McDiarmid's inequality

Published 17 Nov 2015 in cs.LG, math.PR, math.ST, and stat.TH | (1511.05240v4)

Abstract: We generalize McDiarmid's inequality for functions with bounded differences on a high probability set, using an extension argument. Those functions concentrate around their conditional expectations. We further extend the results to concentration in general metric spaces.

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References (14)
  1. B. Bollobás. The chromatic number of random graphs. Combinatorica, 8(1):49–55, 1988.
  2. O. Bousquet and A. Elisseeff. Algorithmic stability and generalization performance. In Proc. of NIPS (2001).
  3. Concentration of multivariate polynomials and its applications. Combinatorica, 20:417–434, 2000.
  4. M. D. Kirszbraun. Uber die zusammenziehende und lipschitzsche transformationen. Fund. Math, 22:77–108, 1934.
  5. A. Kontorovich. Concentration in unbounded metric spaces and algorithmic stability. In Proc. of ICML (2014).
  6. S. Kutin. Extensions to McDiarmid’s inequality when differences are bounded with high probability. Technical report, 2002.
  7. Michel Ledoux. Isoperimetry and Gaussian analysis. Springer Berlin Heidelberg, 1996.
  8. C. McDiarmid. On the method of bounded differences. Surveys in Combinatorics, 141:148–188, 1989.
  9. C. McDiarmid. Concentration. Probabilistic Methods for Algorithmic Discrete Mathematics, 16:195–248, 1998.
  10. E. J. McShane. Extension of range of functions. Bull. Amer. Math. Soc., 40(1):837–842, 1934.
  11. W. Schudy and M. Sviridenko. Concentration and moment inequalities for polynomials of independent random variables. In Proc. of SODA (2012).
  12. V. H. Vu. On the concentration of multivariate polynomials with small expectation. Random Structures and Algorithms, 16:344–363, 2000.
  13. V. H. Vu. Concentration of non-Lipschitz functions and applications. Random Structures and Algorithms, 20:262–316, 2002.
  14. L. Warnke. On the method of typical bounded differences. Combinatorics, Probability and Computing, pages 1–31, 8 2015.
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