On the Geometry of Mixtures of Prescribed Distributions

Frank Nielsen; Richard Nock

ICASSP 2018accepted0 citations

On the Geometry of Mixtures of Prescribed Distributions

Abstract

We consider the space of w-mixtures that are finite statistical mixtures sharing the same prescribed component distributions, like Gaussian mixture models sharing the same components. The information geometry induced by the Kullback-Leibler (KL) divergence yields a dually flat space where the KL divergence between two w-mixtures amounts to a Bregman divergence for the negative Shannon entropy generator, called the Shannon information. Furthermore, we prove that the skew Jensen-Shannon statistical divergence between w-mixtures amount to skew Jensen divergences on their parameters and state several divergence inequalities between w-mixtures and their closures.

BibTeX

@inproceedings{icassp2018_onthegeometryofm,
  title = {On the Geometry of Mixtures of Prescribed Distributions},
  author = {Frank Nielsen and Richard Nock},
  booktitle = {ICASSP 2018},
  year = {2018}
}