Adaptive Mixture Methods Based on Bregman Divergences

TL;DR

This paper introduces adaptive mixture algorithms based on Bregman divergences, providing new multiplicative update rules for combining filter outputs, with analysis and validation of their effectiveness in sparse systems.

Contribution

It develops novel adaptive mixture methods using Bregman divergences with multiplicative updates and provides their mean and mean-square transient analysis.

Findings

Effective in sparse mixture systems

Accurate transient analysis results

Demonstrated improved adaptive filtering performance

Abstract

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.