From the 1 of 6 linked papers with an AI index.
6 papers
Estimating conditional expectation
Hông Vân Lê
In this paper, we consider the problem of estimating conditional expectations as an ill-posed inverse problem. We propose a solution based on a generalization of Vapnik's theorem \…
Empirical Hodge Laplacians: Spectral Convergence and Harmonic Forms from Point Clouds
Hông Vân Lê
The paper builds empirical Hodge Laplacians from uniformly sampled point clouds on a smooth manifold and proves they converge to the true Hodge Laplacian, enabling consistent recov…
Batch learning equals online learning in Bayesian supervised learning
Hông Vân Lê
In this paper we study Bayesian supervised learning models proposed by Lê in \cite{Le2025}. Using functoriality of probabilistic morphisms, we prove that sequential and batch Baye…
Probabilistic morphisms and Bayesian supervised learning
Hông Vân Lê
In this paper, we develop category theory of Markov kernels to study categorical aspects of Bayesian inversions. As a result, we present a unified model for Bayesian supervised lea…
Categorical and geometric methods in statistical, manifold, and machine learning
Hông Vân Lê, Hà Quang Minh, Frederic Protin +1
We present and discuss applications of the category of probabilistic morphisms, initially developed in \cite{Le2023}, as well as some geometric methods to several classes of proble…
Unital -algebras and the real homotopy type of -connected compact manifolds of dimension
Domenico Fiorenza, Hông Vân Lê
We encode the real homotopy type of an -dimensional -connected compact manifold , into a minimal unital -structure on , obtained…