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 $C^k$-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.
Hông Vân Lê, Diffeological statistical models,the Fisher metric and probabilistic mappings, Mathematics 2020, 8(2) 167 arXiv:1912.02090
Hông Vân Lê, Supervised learning with probabilistic morphisms and kernel mean embeddings, arXiv:2305.06348
In this paper I propose a generative model of supervised learning that unifies two approaches to supervised learning, using a concept of a correct loss function. Addressing two measurability problems, which have been ignored in statistical learning theory, I propose to use convergence in outer probability to characterize the consistency of a learning algorithm. Building upon these results, I extend a result due to Cucker-Smale, which addresses the learnability of a regression model, to the setting of a conditional probability estimation problem. Additionally, I present a variant of Vapnik-Stefanyuk’s regularization method for solving stochastic ill-posed problems, and using it to prove the generalizability of overparameterized supervised learning models.
Last revised on July 17, 2024 at 14:06:33. See the history of this page for a list of all contributions to it.