- Title Information
- Title
- Riemannian Langevin Equation and Its Applications in Random Matrix Theory and Gibbs Sampling Problems
- Type of Resource (primo)
- dissertations
- Name:
Personal
- Name Part
- Yu, Tianmin
- Role
- Role Term:
Text
- creator
- Name:
Personal
- Name Part
- Menon, Govind
- Role
- Role Term:
Text
- Advisor
- Name:
Personal
- Name Part
- Darbon, Jerome
- Role
- Role Term:
Text
- Reader
- Name:
Personal
- Name Part
- Shenfeld, Yair
- Role
- Role Term:
Text
- Reader
- Name:
Corporate
- Name Part
- Brown University. Department of Applied Mathematics
- Role
- Role Term:
Text
- sponsor
- Origin Information
- Copyright Date
- 2024
- Physical Description
- Extent
- 9, 197 p.
- digitalOrigin
- born digital
- Note:
thesis
- Thesis (Ph. D.)--Brown University, 2024
- Genre (aat)
- theses
- 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.
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/01400410")
- Topic
- Applied mathematics
- Language
- Language Term (ISO639-2B)
- English
- Record Information
- Record Content Source (marcorg)
- RPB
- Record Creation Date
(encoding="iso8601")
- 20240505