Hông Vân Lê is a Vietnamese-Czech mathematician with research in differential geometry (especially contact geometry, symplectic geometry and special holonomy manifolds), information geometry and mathematics of machine learning.
The following treatment of information geometry (and Fisher metric in particular) is using diffeological spaces (motivated by singular statistical models, including from machine learning)
Hông Vân Lê, Natural differentiable structures on statistical models and the Fisher metric, Information Geometry (2022) arXiv:2208.06539 doi
Hông Vân Lê, Diffeological statistical models and diffeological Hausdorff measures, video yt, slides pdf
Hông Vân Lê, Alexey A. Tuzhilin, Nonparametric estimations and the diffeological Fisher metric, In: Barbaresco F., Nielsen F. (eds) Geometric Structures of Statistical Physics, Information Geometry, and Learning, p. 120–138, SPIGL 2020. Springer Proceedings in Mathematics & Statistics 361, doi
In this paper, first, we survey the concept of diffeological Fisher metric and its naturality, using functorial language of probability morphisms, and slightly extending Lê’s theory in (Le2020) to include weakly -diffeological statistical models. Then we introduce the resulting notions of the diffeological Fisher distance, the diffeological Hausdorff–Jeffrey measure and explain their role in classical and Bayesian nonparametric estimation problems in statistics.
Last revised on April 7, 2023 at 12:05:35. See the history of this page for a list of all contributions to it.