  Mutual information (MI) is an information-theoretic measure of dependency
between two random variables. Several methods to estimate MI, from samples of
two random variables with unknown underlying probability distributions have
been proposed in the literature. Recent methods realize parametric probability
distributions or critic as a neural network to approximate unknown density
ratios. The approximated density ratios are used to estimate different
variational lower bounds of MI. While these methods provide reliable estimation
when the true MI is low, they produce high variance estimates in cases of high
MI. We argue that the high variance characteristic is due to the uncontrolled
complexity of the critic's hypothesis space. In support of this argument, we
use the data-driven Rademacher complexity of the hypothesis space associated
with the critic's architecture to analyse generalization error bound of
variational lower bound estimates of MI. In the proposed work, we show that it
is possible to negate the high variance characteristics of these estimators by
constraining the critic's hypothesis space to Reproducing Hilbert Kernel Space
(RKHS), which corresponds to a kernel learned using Automated Spectral Kernel
Learning (ASKL). By analysing the aforementioned generalization error bounds,
we augment the overall optimisation objective with effective regularisation
term. We empirically demonstrate the efficacy of this regularization in
enforcing proper bias variance tradeoff on four variational lower bounds,
namely NWJ, MINE, JS and SMILE.
