State estimation and inference in time-varying dynamic systems

This thesis addresses the problem of state estimation and inference in time-varying dynamic systems from noisy, incomplete measurements collected over time. Specifically, the first part of thesis develops efficient estimators for switching linear dynamic systems ({SLDS}). SLDS model may represent a large class of dynamic systems, including those that have nonlinearity or switching behavior, using conditionally linear models. However, the computational complexity of implementing an optimal SLDS estimator grows exponentially with time. Even when using approximate SLDS estimators, the required computational complexity may be incompatible with the available resources if the state variable is high-dimensional or if the number of linear models considered in SLDS is large. Hence, thesis focuses on finding model reduction algorithms that can provide optimal estimates constrained by computational resources. The second part of thesis focuses on learning the causal structure of a multivariate system from observational data. When observations of the system variables are collected from multiple domains such that the exogenous variables' distributions are distinct, the underlying causal structure may be detected by testing causal structure invariance between domains. For a linear causal structure with additive Gaussian noise, this thesis analytically quantifies the impact of limited observational data, including a finite number of samples and measurement noise, on the inferred structure via testing causal invariance. Moreover, learning if and how the variation of an external variable affects a dynamic system based on observational data is important for the analysis, prediction, and control of the system. This thesis thus proposes a method to detect external drivers of a dynamic system given state observations and a set of candidate drivers over time, such that the impact of each candidate on each spatial and temporal mode of the dynamic system is quantified. Assuming the observed system variables are correlated via an underlying differential equation that governs their evolution, the focus of the third part of this thesis is on data-driven learning of time-varying dynamic systems given state observations. A major challenge in learning the dynamic system from data is the requirement that the dynamics must not change over a sufficiently long time window so that a unique solution can be found for the inverse problem. Under violation of this assumption, classical algorithms would perform poorly. To address this limitation, this thesis incorporates a Bayesian prior into the inference framework and enables inferring dynamics using a few observations.

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

2023

Author dc:creator

• Karimi, Parisa

Contributors dc:contributor

• Kamalabadi, Farzad
• Zhao, Zhizhen
• Shomorony, Ilan
• Waldrop, Lara

• Statistical Inference
• Estimation Theory
• Machine Learning
• Dynamic Systems

Statement dc:rights

• Copyright 2023 Parisa Karimi

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/120237

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F120237