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

Tsai, Katherine

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

Description

Title

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

Author(s)

Tsai, Katherine

Issue Date

2024-10-01

Director of Research (if dissertation) or Advisor (if thesis)

• Koyejo, Sanmi
• Kolar, Mladen

Doctoral Committee Chair(s)

Koyejo, Sanmi

Committee Member(s)

• Raginsky, Maxim
• Srikant, Rayadurgam
• Shomorony, Ilan

Department of Study

Electrical & Computer Eng

Discipline

Electrical & Computer Engr

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

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

Language

eng

Abstract

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.

Graduation Semester

2024-12

Type of Resource

Thesis

Handle URL

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

Copyright and License Information

Copyright 2024 Katherine Tsai

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