  We investigate adaptive mixture methods that linearly combine outputs of $m$
constituent filters running in parallel to model a desired signal. We use
"Bregman divergences" and obtain certain multiplicative updates to train the
linear combination weights under an affine constraint or without any
constraints. We use unnormalized relative entropy and relative entropy to
define two different Bregman divergences that produce an unnormalized
exponentiated gradient update and a normalized exponentiated gradient update on
the mixture weights, respectively. We then carry out the mean and the
mean-square transient analysis of these adaptive algorithms when they are used
to combine outputs of $m$ constituent filters. We illustrate the accuracy of
our results and demonstrate the effectiveness of these updates for sparse
mixture systems.
