  We show that the variational representations for f-divergences currently used
in the literature can be tightened. This has implications to a number of
methods recently proposed based on this representation. As an example
application we use our tighter representation to derive a general f-divergence
estimator based on two i.i.d. samples and derive the dual program for this
estimator that performs well empirically. We also point out a connection
between our estimator and MMD.
