#### Authors

Luis E. Ortiz, David McAllester

#### Abstract

This paper gives distribution-free concentration inequalities for the miss- ing mass and the error rate of histogram rules. Negative association meth- ods can be used to reduce these concentration problems to concentration questions about independent sums. Although the sums are independent, they are highly heterogeneous. Such highly heterogeneous independent sums cannot be analyzed using standard concentration inequalities such as Hoeffding’s inequality, the Angluin-Valiant bound, Bernstein’s in- equality, Bennett’s inequality, or McDiarmid’s theorem.