  We are concerned with obtaining novel concentration inequalities for the
missing mass, i.e. the total probability mass of the outcomes not observed in
the sample. We not only derive - for the first time - distribution-free
Bernstein-like deviation bounds with sublinear exponents in deviation size for
missing mass, but also improve the results of McAllester and Ortiz (2003)
andBerend and Kontorovich (2013, 2012) for small deviations which is the most
interesting case in learning theory. It is known that the majority of standard
inequalities cannot be directly used to analyze heterogeneous sums i.e. sums
whose terms have large difference in magnitude. Our generic and intuitive
approach shows that the heterogeneity issue introduced in McAllester and Ortiz
(2003) is resolvable at least in the case of missing mass via regulating the
terms using our novel thresholding technique.
