{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/11062"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/11062","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Exact Solution of Bayes and Minimax Change-Detection Problems","abstract":"The challenge of detecting a change in the distribution of data is a sequential decision problem that is relevant to many engineering solutions, including quality control and machine and process monitoring. This dissertation develops techniques for exact solution of change-detection problems with discrete time and discrete observations. Change-detection problems are classified as Bayes or minimax based on the availability of information on the change-time distribution. A Bayes optimal solution uses prior information about the distribution of the change time to minimize the expected cost, whereas a minimax optimal solution minimizes the cost under the worst-case change-time distribution. Both types of problems are addressed. The most important result of the dissertation is the development of a polynomial-time algorithm for the solution of important classes of Markov Bayes change-detection problems. Existing techniques for epsilon-exact solution of partially observable Markov decision processes have complexity exponential in the number of observation symbols. A new algorithm, called constellation induction, exploits the concavity and Lipschitz continuity of the value function, and has complexity polynomial in the number of observation symbols. It is shown that change-detection problems with a geometric change-time distribution and identically- and independently-distributed observations before and after the change are solvable in polynomial time. Also, change-detection problems on hidden Markov models with a fixed number of recurrent states are solvable in polynomial time. A detailed implementation and analysis of the constellation-induction algorithm are provided. Exact solution methods are also established for several types of minimax change-detection problems. Finite-horizon problems with arbitrary observation distributions are modeled as extensive-form games and solved using linear programs. Infinite-horizon problems with linear penalty for detection delay and identically- and independently-distributed observations can be solved in polynomial time via epsilon-optimal parameterization of a cumulative-sum procedure. Finally, the properties of policies for change-detection problems are described and analyzed. Simple classes of formal languages are shown to be sufficient for epsilon-exact solution of change-detection problems, and methods for finding minimally sized policy representations are described.","abstract_html":"The challenge of detecting a change in the distribution of data is a sequential decision problem that is relevant to many engineering solutions, including quality control and machine and process monitoring. This dissertation develops techniques for exact solution of change-detection problems with discrete time and discrete observations. Change-detection problems are classified as Bayes or minimax based on the availability of information on the change-time distribution. A Bayes optimal solution uses prior information about the distribution of the change time to minimize the expected cost, whereas a minimax optimal solution minimizes the cost under the worst-case change-time distribution. Both types of problems are addressed. The most important result of the dissertation is the development of a polynomial-time algorithm for the solution of important classes of Markov Bayes change-detection problems. Existing techniques for epsilon-exact solution of partially observable Markov decision processes have complexity exponential in the number of observation symbols. A new algorithm, called constellation induction, exploits the concavity and Lipschitz continuity of the value function, and has complexity polynomial in the number of observation symbols. It is shown that change-detection problems with a geometric change-time distribution and identically- and independently-distributed observations before and after the change are solvable in polynomial time. Also, change-detection problems on hidden Markov models with a fixed number of recurrent states are solvable in polynomial time. A detailed implementation and analysis of the constellation-induction algorithm are provided. Exact solution methods are also established for several types of minimax change-detection problems. Finite-horizon problems with arbitrary observation distributions are modeled as extensive-form games and solved using linear programs. Infinite-horizon problems with linear penalty for detection delay and identically- and independently-distributed observations can be solved in polynomial time via epsilon-optimal parameterization of a cumulative-sum procedure. Finally, the properties of policies for change-detection problems are described and analyzed. Simple classes of formal languages are shown to be sufficient for epsilon-exact solution of change-detection problems, and methods for finding minimally sized policy representations are described.","abstract_has_math":false,"creators":["Isom, Joshua D."],"institution":"University of Illinios at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Chemical Engineering","degree_department":null,"school":null,"contributors":["Braatz, Richard D.","Meyn, Sean P.","LaBarre, Robert E.","Rao, Christopher V."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2009,"date_issued":"2009-04-20T15:01:24Z","date_published":"2009-04-20T15:01:24Z","updated_at":"2026-07-22T22:24:42Z","subjects":["change detection","Stochastic optimal control","Formal languages","Cumulative sum (CUSUM)","Bayes","Minimax","partially observable Markov decision process"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["Dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Chemical Engineering in the Graduate College of the University of Illinois at Urbana-Champaign, 2009"],"render_values":[{"text":"Dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Chemical Engineering in the Graduate College of the University of Illinois at Urbana-Champaign, 2009","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/11062","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Braatz, Richard D.","Meyn, Sean P.","LaBarre, Robert E.","Rao, Christopher V."]},{"key":"dc:creator","label":"Author","values":["Isom, Joshua D."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2009-04-20T15:01:24Z","2009-04-20"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation / Thesis","text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Chemical 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 Illinios at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["change detection","Stochastic optimal control","Formal languages","Cumulative sum (CUSUM)","Bayes","Minimax","partially observable Markov decision process"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["Dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Chemical Engineering in the Graduate College of the University of Illinois at Urbana-Champaign, 2009","http://hdl.handle.net/2142/11062"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The challenge of detecting a change in the distribution of data is a sequential decision problem that is relevant to many engineering solutions, including quality control and machine and process monitoring. This dissertation develops techniques for exact solution of change-detection problems with discrete time and discrete observations. Change-detection problems are classified as Bayes or minimax based on the availability of information on the change-time distribution. A Bayes optimal solution uses prior information about the distribution of the change time to minimize the expected cost, whereas a minimax optimal solution minimizes the cost under the worst-case change-time distribution. Both types of problems are addressed. The most important result of the dissertation is the development of a polynomial-time algorithm for the solution of important classes of Markov Bayes change-detection problems. Existing techniques for epsilon-exact solution of partially observable Markov decision processes have complexity exponential in the number of observation symbols. A new algorithm, called constellation induction, exploits the concavity and Lipschitz continuity of the value function, and has complexity polynomial in the number of observation symbols. It is shown that change-detection problems with a geometric change-time distribution and identically- and independently-distributed observations before and after the change are solvable in polynomial time. Also, change-detection problems on hidden Markov models with a fixed number of recurrent states are solvable in polynomial time. A detailed implementation and analysis of the constellation-induction algorithm are provided. Exact solution methods are also established for several types of minimax change-detection problems. Finite-horizon problems with arbitrary observation distributions are modeled as extensive-form games and solved using linear programs. Infinite-horizon problems with linear penalty for detection delay and identically- and independently-distributed observations can be solved in polynomial time via epsilon-optimal parameterization of a cumulative-sum procedure. Finally, the properties of policies for change-detection problems are described and analyzed. Simple classes of formal languages are shown to be sufficient for epsilon-exact solution of change-detection problems, and methods for finding minimally sized policy representations are described.","Submitted by Joshua Isom (isom@illinois.edu) on 2009-04-20T12:37:43Z No. of bitstreams: 1 Isom_Dissertation.pdf: 1602473 bytes, checksum: a6875120eacc078be87b3149f535c839 (MD5)","Approved for entry into archive by Sarah Shreeves(sshreeve@illinois.edu) on 2009-04-20T15:01:24Z (GMT) No. of bitstreams: 1 Isom_Dissertation.pdf: 1602473 bytes, checksum: a6875120eacc078be87b3149f535c839 (MD5)","Made available in DSpace on 2009-04-20T15:01:24Z (GMT). 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A Bayes optimal solution uses prior information about the distribution of the change time to minimize the expected cost, whereas a minimax optimal solution minimizes the cost under the worst-case change-time distribution. Both types of problems are addressed. The most important result of the dissertation is the development of a polynomial-time algorithm for the solution of important classes of Markov Bayes change-detection problems. Existing techniques for epsilon-exact solution of partially observable Markov decision processes have complexity exponential in the number of observation symbols. A new algorithm, called constellation induction, exploits the concavity and Lipschitz continuity of the value function, and has complexity polynomial in the number of observation symbols. It is shown that change-detection problems with a geometric change-time distribution and identically- and independently-distributed observations before and after the change are solvable in polynomial time. Also, change-detection problems on hidden Markov models with a fixed number of recurrent states are solvable in polynomial time. A detailed implementation and analysis of the constellation-induction algorithm are provided. Exact solution methods are also established for several types of minimax change-detection problems. Finite-horizon problems with arbitrary observation distributions are modeled as extensive-form games and solved using linear programs. Infinite-horizon problems with linear penalty for detection delay and identically- and independently-distributed observations can be solved in polynomial time via epsilon-optimal parameterization of a cumulative-sum procedure. Finally, the properties of policies for change-detection problems are described and analyzed. Simple classes of formal languages are shown to be sufficient for epsilon-exact solution of change-detection problems, and methods for finding minimally sized policy representations are described.","Submitted by Joshua Isom (isom@illinois.edu) on 2009-04-20T12:37:43Z No. of bitstreams: 1 Isom_Dissertation.pdf: 1602473 bytes, checksum: a6875120eacc078be87b3149f535c839 (MD5)","Approved for entry into archive by Sarah Shreeves(sshreeve@illinois.edu) on 2009-04-20T15:01:24Z (GMT) No. of bitstreams: 1 Isom_Dissertation.pdf: 1602473 bytes, checksum: a6875120eacc078be87b3149f535c839 (MD5)","Made available in DSpace on 2009-04-20T15:01:24Z (GMT). No. of bitstreams: 1 Isom_Dissertation.pdf: 1602473 bytes, checksum: a6875120eacc078be87b3149f535c839 (MD5) Previous issue date: 2009-04-20","unpublished"],"dc:identifier":["Dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Chemical Engineering in the Graduate College of the University of Illinois at Urbana-Champaign, 2009","http://hdl.handle.net/2142/11062"],"dc:subject":["change detection","Stochastic optimal control","Formal languages","Cumulative sum (CUSUM)","Bayes","Minimax","partially observable Markov decision process"],"dc:title":["Exact Solution of Bayes and Minimax Change-Detection Problems"],"dc:type":["Dissertation / Thesis","text"],"thesis:degree_discipline":["Chemical Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinios at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:42Z"}