{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/115520"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/115520","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"System identification for the bar model: Algorithms, consistency and sample complexity","abstract":"Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2024-05-01","abstract_html":"Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2024-05-01","abstract_has_math":false,"creators":["Xie, Xiaotian"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Industrial Engineering","degree_department":null,"school":null,"contributors":["Beck, Carolyn L.","Srikant, Rayadurgam","Sowers, Richard B.","Varshney, Lav R.","Katselis, Dimitrios"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-05","date_published":"2022-05","updated_at":"2026-07-22T22:24:54Z","subjects":["System identification","Network inference","Sample complexity","Concentration inequalities"],"languages":["en","eng"],"rights":["Copyright 2022 Xiaotian Xie"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/115520","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Beck, Carolyn L.","Srikant, Rayadurgam","Sowers, Richard B.","Varshney, Lav R.","Katselis, Dimitrios"]},{"key":"dc:creator","label":"Author","values":["Xie, Xiaotian"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2022-05","2022-04-20"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Industrial Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["System identification","Network inference","Sample complexity","Concentration inequalities"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2022 Xiaotian Xie"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/115520"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2024-05-01","The student, Xiaotian Xie, accepted the attached license on 2022-04-01 at 14:09.","The student, Xiaotian Xie, submitted this Dissertation for approval on 2022-04-01 at 14:26.","This Dissertation was approved for publication on 2022-04-20 at 16:05.","DSpace SAF Submission Ingestion Package generated from Vireo submission #17571 on 2022-11-11 at 11:55:54","System identification has been extensively studied in the context of linear state-space models with continuous state variables. In this thesis, we focus on system identification problems in dynamical systems where the state takes values in a discrete set. If the state vector has p components and each component of the vector can take on two values, then the number of possible states is 2^p, thus leading to a combinatorial explosion in the number of parameters to be identified. To overcome this difficulty, we consider a recently introduced structured dynamical system model, called the Bernoulli Autoregressive (BAR) Model, which consists of (p^2+p) parameters. For this model, we first consider two estimators of the system parameters: a maximum likelihood (ML) estimator and a variant of the ML estimator which leads to closed-form expressions for the estimated parameters. We prove that both of these estimators are consistent in the sense that the estimates converge to the true parameter values when the number of observations goes to infinity. Then, we consider the sample complexity of the closed-form estimator. Using concentration results for random matrices and Lipschitz functions, we derive a bound on the probability that the estimates deviate from the true parameter values by a certain amount, and use the bound to show that the sample complexity is polynomial in p. Finally, building upon the tools used to study the closed-form estimator, we derive new concentration inequalities for vector-valued Lipschitz functions of Markov processes and use them to improve sample complexity results for other estimation problems beyond the BAR model."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["System identification for the bar model: Algorithms, consistency and sample complexity"]}]}],"canonical_facts":{"dc:contributor":["Beck, Carolyn L.","Srikant, Rayadurgam","Sowers, Richard B.","Varshney, Lav R.","Katselis, Dimitrios"],"dc:creator":["Xie, Xiaotian"],"dc:date":["2022-05","2022-04-20"],"dc:description":["Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2024-05-01","The student, Xiaotian Xie, accepted the attached license on 2022-04-01 at 14:09.","The student, Xiaotian Xie, submitted this Dissertation for approval on 2022-04-01 at 14:26.","This Dissertation was approved for publication on 2022-04-20 at 16:05.","DSpace SAF Submission Ingestion Package generated from Vireo submission #17571 on 2022-11-11 at 11:55:54","System identification has been extensively studied in the context of linear state-space models with continuous state variables. In this thesis, we focus on system identification problems in dynamical systems where the state takes values in a discrete set. If the state vector has p components and each component of the vector can take on two values, then the number of possible states is 2^p, thus leading to a combinatorial explosion in the number of parameters to be identified. To overcome this difficulty, we consider a recently introduced structured dynamical system model, called the Bernoulli Autoregressive (BAR) Model, which consists of (p^2+p) parameters. For this model, we first consider two estimators of the system parameters: a maximum likelihood (ML) estimator and a variant of the ML estimator which leads to closed-form expressions for the estimated parameters. We prove that both of these estimators are consistent in the sense that the estimates converge to the true parameter values when the number of observations goes to infinity. Then, we consider the sample complexity of the closed-form estimator. Using concentration results for random matrices and Lipschitz functions, we derive a bound on the probability that the estimates deviate from the true parameter values by a certain amount, and use the bound to show that the sample complexity is polynomial in p. Finally, building upon the tools used to study the closed-form estimator, we derive new concentration inequalities for vector-valued Lipschitz functions of Markov processes and use them to improve sample complexity results for other estimation problems beyond the BAR model."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/115520"],"dc:language":["en","eng"],"dc:rights":["Copyright 2022 Xiaotian Xie"],"dc:subject":["System identification","Network inference","Sample complexity","Concentration inequalities"],"dc:title":["System identification for the bar model: Algorithms, consistency and sample complexity"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Industrial Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:54Z"}