Latent Structure Estimation for Panel Data and Theoretical Guarantees for Stochastic Optimization

The past two decades have witnessed a dramatic growth of research interest in statistics, optimization, and machine learning. Despite the widespread use of machine learning techniques and optimization algorithms, many of these surprisingly lack fundamental theoretical grounding. The central theme of this work is adopting tools from statistics to bridge the gap between theory and application in machine learning and optimization. In this thesis, we investigate several fundamental problems arising from machine learning and optimization under modern regimes, and we develop theoretical guarantees that align closely with practical experience in these fields. The first contribution of this thesis is developing efficient unsupervised learning paradigms with the guarantees of quality and correctness for the estimation of patterns from panel data. The remaining part of this work focuses on understanding the foundations of stochastic optimization from both statistical and computational aspects. Our work capitalizes on the cross-fertilization among statistics, machine learning, and optimization, thereby further improves our theoretical understanding of machine learning techniques and optimization algorithms under the statistical setting.

Department dc:contributor.department

Statistics

Year dc:date.issued

2022

Author dc:creator

• Yu, Lu

Advisors dc:contributor.advisor

• Volgushev, Stanislav
• Erdogdu, Murat

Handle dc:identifier.uri

http://hdl.handle.net/1807/125108

OAI identifier oai:identifier

oai:utoronto.scholaris.ca:1807/125108