Tokyo Research
INCOLLECTION
On the f-divergences between hyperboloid and Poincaré distributions
Lecture Notes in Computer Science | pages 176--185, 2023
Author
Nielsen, Frank and Okamura, Kazuki
Abstract
Hyperbolic geometry has become popular in machine learning due to its capacity to embed discrete hierarchical graph structures with low distortions into continuous spaces for further downstream processing. It is thus becoming important to consider statistical models and inference methods for data sets grounded in hyperbolic spaces. In this work, we study the statistical f-divergences between two kinds of hyperbolic distributions: The Poincaré distributions and the related hyperboloid distributions. By exhibiting maximal invariants of group actions, we show how these f-divergences can be expressed as functions of canonical terms.
Related Members
Frank Nielsen