Abstract

July 1 - 11.50-12.40
S.Eguchi - Information Geometry of Bregman Divergences

The class of Bregman divergences and the application to statistical methods including PCA, ICA, Gaussian mixture and so forth have been proposed. It is shown that this class offers a special structure on the information geometry, which is in contrast with that associated with the alpha divergences. In the dual connections one is always the mixture connection in the class, which enables us to getting easily the empirical form of the divergence. Thus the objective function to be optimised becomes a linear functional of the empirical distribution. The structure determines the statistical performance of the proposed methods. We also apply this discussion to classification problems. By using the dual form for the optimisation problem to the empirical Bregman distance over a linear combination of weak learners we propose the class of U-boost including AdaBoost, and investigate the performance structure from the statistical point of view. [an error occurred while processing this directive]