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Bennett, G. (1962) Probability Inequalities for the Sum of Independent Random Variables. Journal of the American Statistical Association, 57, 33-45.

has been cited by the following article:

• TITLE: Error Analysis of ERM Algorithm with Unbounded and Non-Identical Sampling

  AUTHORS: Weilin Nie, Cheng Wang

  KEYWORDS: Learning Theory, ERM, Non-Identical, Unbounded Sampling, Covering Number

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.4 No.1, January 27, 2016

  ABSTRACT: A standard assumption in the literature of learning theory is the samples which are drawn independently from an identical distribution with a uniform bounded output. This excludes the common case with Gaussian distribution. In this paper we extend these assumptions to a general case. To be precise, samples are drawn from a sequence of unbounded and non-identical probability distributions. By drift error analysis and Bennett inequality for the unbounded random variables, we derive a satisfactory learning rate for the ERM algorithm.