Concentration inequalities under sub-Gaussian and sub-exponential conditions

Andreas Maurer, massimiliano pontil

Keywords: Statistical Learning Theory, Concentration Inequalities

Abstract: We prove analogues of the popular bounded difference inequality (also called McDiarmid's inequality) for functions of independent random variables under sub-gaussian and sub-exponential conditions. Applied to vector-valued concentration and the method of Rademacher complexities these inequalities allow an easy extension of uniform convergence results for PCA and linear regression to the case potentially unbounded input- and output variables.

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TL;DR: Concentration Inequalities Under Sub-Gaussian and Sub-Exponential Conditions