Concentration inequalities under sub-Gaussian and sub-exponential conditions

Part of Advances in Neural Information Processing Systems 34 pre-proceedings (NeurIPS 2021)

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Andreas Maurer, Massimiliano Pontil


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.