{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/108158"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/108158","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Bayesian high dimensional modeling with group structures","abstract":"U of I Only","abstract_html":"U of I Only","abstract_has_math":false,"creators":["Yang, Xinming"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Statistics","degree_department":null,"school":null,"contributors":["Narisetty, Naveen Naidu","Chen, Yuguo","Koyejo, Oluwasanmi","Liang, Feng"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-08-26T23:58:39Z","date_published":"2020-08-26T23:58:39Z","updated_at":"2026-07-22T22:24:47Z","subjects":["group variable selection","graphical models","sequential logistic regressions","spike and slab priors","Bayesian regularization"],"languages":["en"],"rights":["Copyright 2020 Xinming Yang"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/108158","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Narisetty, Naveen Naidu","Chen, Yuguo","Koyejo, Oluwasanmi","Liang, Feng"]},{"key":"dc:creator","label":"Author","values":["Yang, Xinming"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2020-08-26T23:58:39Z","2022-08-26T23:58:55Z","2020-05-06","2020-05"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Statistics"]},{"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":["group variable selection","graphical models","sequential logistic regressions","spike and slab priors","Bayesian regularization"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2020 Xinming Yang"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/108158"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["U of I Only","Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2022-05-01","The student, Xinming Yang, accepted the attached license on 2020-05-05 at 20:34.","The student, Xinming Yang, submitted this Dissertation for approval on 2020-05-05 at 20:54.","This Dissertation was approved for publication on 2020-05-06 at 18:17.","DSpace SAF Submission Ingestion Package generated from Vireo submission #15226 on 2020-08-25 at 17:29:47","Made available in DSpace on 2020-08-26T23:58:39Z (GMT). No. of bitstreams: 2 YANG-DISSERTATION-2020.pdf: 3544454 bytes, checksum: e3aa183dd42b7e93ee98fcce7520d4ee (MD5) LICENSE.txt: 4209 bytes, checksum: d42ae85ec45ea6f48b277cd30ef4b831 (MD5) Previous issue date: 2020-05-06","Embargo set by: Seth Robbins for item 115771 Lift date: 2022-08-26T23:58:55Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system","Group structures arise naturally in a variety of modern data applications and statistical problems in the high-dimensional data setting where the number of variables can greatly exceed the number of observations. The group structures are usually very informative as they express the inherent similarities among the variables and observations and it is thus desirable to take the prior group information into consideration in the construction of statistical models in pursuit of efficient statistical inference. In this dissertation, we propose methods for three statistical problems: linear regression, graphical model, and sequential logistic regressions when group structures are present at either the variable level or the observation level. We adopt the Bayesian framework and extend the spike-and-slab priors in the group setting to incorporate the group information. Our proposed hierarchical Bayesian models are well suited for sharing of similar sparsity patterns within the groups. For posterior computation, we propose EM algorithms and shotgun stochastic search algorithm which are more efficient than standard Markov chain Monte Carlo sampling algorithms. Compared to methods that simply ignore the grouping structure, our proposed methods that involve the group information can lead to better statistical inference results and the fitted models are more interpretable and provide more insights into the data. Further, we show that our methods are also advantageous theoretically or empirically in comparison with other group selection competitors due to the nonconvex regularization induced from our Bayesian modeling.","Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Bayesian high dimensional modeling with group structures"]}]}],"canonical_facts":{"dc:contributor":["Narisetty, Naveen Naidu","Chen, Yuguo","Koyejo, Oluwasanmi","Liang, Feng"],"dc:creator":["Yang, Xinming"],"dc:date":["2020-08-26T23:58:39Z","2022-08-26T23:58:55Z","2020-05-06","2020-05"],"dc:description":["U of I Only","Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2022-05-01","The student, Xinming Yang, accepted the attached license on 2020-05-05 at 20:34.","The student, Xinming Yang, submitted this Dissertation for approval on 2020-05-05 at 20:54.","This Dissertation was approved for publication on 2020-05-06 at 18:17.","DSpace SAF Submission Ingestion Package generated from Vireo submission #15226 on 2020-08-25 at 17:29:47","Made available in DSpace on 2020-08-26T23:58:39Z (GMT). No. of bitstreams: 2 YANG-DISSERTATION-2020.pdf: 3544454 bytes, checksum: e3aa183dd42b7e93ee98fcce7520d4ee (MD5) LICENSE.txt: 4209 bytes, checksum: d42ae85ec45ea6f48b277cd30ef4b831 (MD5) Previous issue date: 2020-05-06","Embargo set by: Seth Robbins for item 115771 Lift date: 2022-08-26T23:58:55Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system","Group structures arise naturally in a variety of modern data applications and statistical problems in the high-dimensional data setting where the number of variables can greatly exceed the number of observations. The group structures are usually very informative as they express the inherent similarities among the variables and observations and it is thus desirable to take the prior group information into consideration in the construction of statistical models in pursuit of efficient statistical inference. In this dissertation, we propose methods for three statistical problems: linear regression, graphical model, and sequential logistic regressions when group structures are present at either the variable level or the observation level. We adopt the Bayesian framework and extend the spike-and-slab priors in the group setting to incorporate the group information. Our proposed hierarchical Bayesian models are well suited for sharing of similar sparsity patterns within the groups. For posterior computation, we propose EM algorithms and shotgun stochastic search algorithm which are more efficient than standard Markov chain Monte Carlo sampling algorithms. Compared to methods that simply ignore the grouping structure, our proposed methods that involve the group information can lead to better statistical inference results and the fitted models are more interpretable and provide more insights into the data. Further, we show that our methods are also advantageous theoretically or empirically in comparison with other group selection competitors due to the nonconvex regularization induced from our Bayesian modeling.","Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/108158"],"dc:language":["en"],"dc:rights":["Copyright 2020 Xinming Yang"],"dc:subject":["group variable selection","graphical models","sequential logistic regressions","spike and slab priors","Bayesian regularization"],"dc:title":["Bayesian high dimensional modeling with group structures"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Statistics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:47Z"}