Skip to Main content Skip to Navigation
Journal articles

Bregman divergences based on optimal design criteria and simplicial measures of dispersion

Abstract : In previous work the authors defined the k-th order simplicial distance between probability distributions which arises naturally from a measure of dispersion based on the squared volume of random simplices of dimension k. This theory is embedded in the wider theory of divergences and distances between distributions which includes Kullback-Leibler, Jensen-Shannon, Jeffreys-Bregman divergence and Bhattacharyya distance. A general construction is given based on defining a directional derivative of a function φ from one distribution to the other whose concavity or strict concavity influences the properties of the resulting divergence. For the normal distribution these divergences can be expressed as matrix formula for the (multivariate) means and covariances. Optimal experimental design criteria contribute a range of functionals applied to non-negative, or positive definite, information matrices. Not all can distinguish normal distributions but sufficient conditions are given. The k-th order simplicial distance is revisited from this aspect and the results are used to test empirically the identity of means and covariances.
Complete list of metadatas

Cited literature [25 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01866846
Contributor : Luc Pronzato <>
Submitted on : Monday, September 3, 2018 - 4:29:09 PM
Last modification on : Tuesday, May 26, 2020 - 6:50:35 PM
Document(s) archivé(s) le : Tuesday, December 4, 2018 - 6:41:00 PM

Files

Stat_Papers_PWZ.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01866846, version 1

Collections

Citation

Luc Pronzato, Henry Wynn, Anatoly Zhigljavsky. Bregman divergences based on optimal design criteria and simplicial measures of dispersion. Statistical Papers, Springer Verlag, 2019, 60, pp.195-214. ⟨hal-01866846⟩

Share

Metrics

Record views

292

Files downloads

125