Description
- Abstract:
- The Riemannian Langevin Equation is a natural extension of Langevin equation on Riemannian manifolds. As a stochastic relaxation of gradient flow, Riemannian Langevin equation serves as a model of stochastic gradient descent which appears to be the core algorithm in machine learning, on the theoretical side also reveals more information about underlying geometric structure. This dissertation contains the applications of Riemannian Langevin Equation in different areas including random matrix theory, Gibbs sampling problems, conic programming and deep linear network. In each problem, Riemannian Langevin Equation turns out to be a powerful tool to connect optimization problem with geometric insight in a probabilistic manner.
- Notes:
- Thesis (Ph. D.)--Brown University, 2024
Citation
Yu, Tianmin,
"Riemannian Langevin Equation and Its Applications in Random Matrix Theory and Gibbs Sampling Problems"
(2024).
Applied Mathematics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://repository.library.brown.edu/studio/item/bdr:cpjek7g7/
Relations
Collection:
-
Applied Mathematics Theses and Dissertations
Theses and Dissertations for the Applied Mathematics department....