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