  The data for many classification problems, such as pattern and speech
recognition, follow mixture distributions. To quantify the optimum performance
for classification tasks, the Shannon mutual information is a natural
information-theoretic metric, as it is directly related to the probability of
error. The mutual information between mixture data and the class label does not
have an analytical expression, nor any efficient computational algorithms. We
introduce a variational upper bound, a lower bound, and three estimators, all
employing pair-wise divergences between mixture components. We compare the new
bounds and estimators with Monte Carlo stochastic sampling and bounds derived
from entropy bounds. To conclude, we evaluate the performance of the bounds and
estimators through numerical simulations.

Signal Processing