Approximation of Densities on Riemannian Manifolds

Abstract : Finding an approximate probability distribution best representing a sample on a measure space is one of the most basic operations in statistics. Many procedures were designed for that purpose when the underlying space is a finite dimensional Euclidean space. In applications, however, such a simple setting may not be adapted and one has to consider data living on a Riemannian manifold. The lack of unique generalizations of the classical distributions, along with theoretical and numerical obstructions require several options to be considered. The present work surveys some possible extensions of well known families of densities to the Riemannian setting, both for parametric and non-parametric estimation.
Complete list of metadatas

Cited literature [49 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02002521
Contributor : Alice Le Brigant <>
Submitted on : Thursday, January 31, 2019 - 5:37:39 PM
Last modification on : Monday, July 15, 2019 - 6:27:14 PM
Long-term archiving on : Wednesday, May 1, 2019 - 7:04:52 PM

File

entropy-21-00043-v2.pdf
Files produced by the author(s)

Identifiers

Données associées

Collections

Citation

Alice Le Brigant, Stéphane Puechmorel. Approximation of Densities on Riemannian Manifolds. Entropy, MDPI, 2019, 21 (1), pp.43. ⟨10.3390/e21010043⟩. ⟨hal-02002521⟩

Share

Metrics

Record views

38

Files downloads

26