Graphical models for high-dimensional stochastic processes: Estimation and inference

Using tools to extract knowledge from data is one of the most essential practices in academia and industry. Conversely, a graphical model represents the distribution of data by a graph – a flexible yet efficient tool to drive insights into potentially complex and high-dimensional systems. It has, therefore, been widely applied to many disciplines, including but not limited to artificial intelligence, biology, social science, and finance. Data, oftentimes, are collected sequentially or in a non-i.i.d. fashion. Such scenarios pose challenges in obtaining faithful estimates and establishing statistical guarantees. However, when data exhibit temporal structure, recovering underlying graphs becomes possible. This thesis is motivated by the pressing needs to develop methodologies to understand complex biological systems like brain networks from neuroimaging with guarantees. It develops methodologies to estimate both directed and undirected graphs from potentially nonlinear and nonstationary multivariate stochastic processes. It also presents novel approaches to make adaptive inferences under changing environments, which can be applied to adjust any statistical or machine learning model in the deployment phase. In terms of theory, we focus on graph recovery, convergence guarantees, statistical error bounds, and identification of the distributions.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Electrical & Computer Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2024

Author dc:creator

• Tsai, Katherine

Contributors dc:contributor

• Koyejo, Sanmi
• Kolar, Mladen
• Raginsky, Maxim
• Srikant, Rayadurgam
• Shomorony, Ilan

• Stochastic Process
• Network Estimation
• Integrative Analysis
• Distribution Shift

Statement dc:rights

• Copyright 2024 Katherine Tsai

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/127141

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F127141