%0 Journal Article
%T Generalised Pinsker Inequalities
%A Mark D. Reid
%A Robert C. Williamson
%J Mathematics
%D 2009
%I arXiv
%X We generalise the classical Pinsker inequality which relates variational divergence to Kullback-Liebler divergence in two ways: we consider arbitrary f-divergences in place of KL divergence, and we assume knowledge of a sequence of values of generalised variational divergences. We then develop a best possible inequality for this doubly generalised situation. Specialising our result to the classical case provides a new and tight explicit bound relating KL to variational divergence (solving a problem posed by Vajda some 40 years ago). The solution relies on exploiting a connection between divergences and the Bayes risk of a learning problem via an integral representation.
%U http://arxiv.org/abs/0906.1244v1