{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/105221"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/105221","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Variational approximation for importance sampling and statistical inference on social influence","abstract":"Monte Carlo methods are widely used in statistical computing area to solve different problems. Social network analysis plays an importance role in many fields. In this dissertation, we focus on improving the efficiency of importance sampling, detecting the degrees of influence in networks, and exploring properties of generalized Erd\\H{o}s-R\\'enyi model. In the first part of the thesis, we propose an importance sampling algorithm with proposal distribution obtained from variational approximation. This method combines the strength of both importance sampling and the variational method. On one hand, this method avoids the bias from variational approximation. On the other hand, variational approximation provides a way to design the proposal distribution for the importance sampling algorithm. Theoretical justification of the proposed method is provided. Numerical results show that using variational approximation as the proposal can improve the performance of importance sampling and sequential importance sampling. In the second part of the thesis, we propose a sequential hypothesis testing procedure to detect the degrees of influence in a network. We build a multivariate Bernoulli model to represent the status of each node in the network with different degrees of influence. A double bootstrap strategy is used to resolve the uncertainty from by estimating nuisance parameters in hypothesis testing. Theoretical justification of the proposed method is provided to show that the hypothesis testing is powerful for larger networks. Simulation studies show that our method can preserve the levels and improve the powers in hypothesis testing. We also apply our proposed method on two real network data to explore the degree of influence for various features. In the third part of the thesis, we propose a random graph model for undirected networks with small-world properties, namely with a high clustering coefficient and a low average path length. We generalize the regular Erd\\H{o}s-R\\'enyi dyadic random graph by considering higher-order motif, which is triadic graph. We show some properties of our proposed model, analyze the probability of multi-edges, and compare the local clustering coefficient with ER model. In addition, we also provide some conditions about phase transition including connectivity threshold and the existence of giant components.","abstract_html":"Monte Carlo methods are widely used in statistical computing area to solve different problems. Social network analysis plays an importance role in many fields. In this dissertation, we focus on improving the efficiency of importance sampling, detecting the degrees of influence in networks, and exploring properties of generalized Erd\\H{o}s-R\\'enyi model. In the first part of the thesis, we propose an importance sampling algorithm with proposal distribution obtained from variational approximation. This method combines the strength of both importance sampling and the variational method. On one hand, this method avoids the bias from variational approximation. On the other hand, variational approximation provides a way to design the proposal distribution for the importance sampling algorithm. Theoretical justification of the proposed method is provided. Numerical results show that using variational approximation as the proposal can improve the performance of importance sampling and sequential importance sampling. In the second part of the thesis, we propose a sequential hypothesis testing procedure to detect the degrees of influence in a network. We build a multivariate Bernoulli model to represent the status of each node in the network with different degrees of influence. A double bootstrap strategy is used to resolve the uncertainty from by estimating nuisance parameters in hypothesis testing. Theoretical justification of the proposed method is provided to show that the hypothesis testing is powerful for larger networks. Simulation studies show that our method can preserve the levels and improve the powers in hypothesis testing. We also apply our proposed method on two real network data to explore the degree of influence for various features. In the third part of the thesis, we propose a random graph model for undirected networks with small-world properties, namely with a high clustering coefficient and a low average path length. We generalize the regular Erd\\H{o}s-R\\'enyi dyadic random graph by considering higher-order motif, which is triadic graph. We show some properties of our proposed model, analyze the probability of multi-edges, and compare the local clustering coefficient with ER model. In addition, we also provide some conditions about phase transition including connectivity threshold and the existence of giant components.","abstract_has_math":false,"creators":["Su, Xiao"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Statistics","degree_department":null,"school":null,"contributors":["Chen, Yuguo","Liang, Feng","Narisetty, Naveen Naidu","Simpson, Douglas G."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-08-23T20:47:34Z","date_published":"2019-08-23T20:47:34Z","updated_at":"2026-07-22T22:24:44Z","subjects":["f-divergence","Importance sampling","Monte Carlo","Variational inference","Social influence","Sequential hypothesis testing","Double bootstrap","Multivariate Bernoulli model","Hyper-graph","Phase transition"],"languages":["en"],"rights":["Copyright 2019 Xiao Su"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/105221","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Chen, Yuguo","Liang, Feng","Narisetty, Naveen Naidu","Simpson, Douglas G."]},{"key":"dc:creator","label":"Author","values":["Su, Xiao"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019-08-23T20:47:34Z","2021-08-24T09:15:16Z","2019-04-19","2019-05"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"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":["f-divergence","Importance sampling","Monte Carlo","Variational inference","Social influence","Sequential hypothesis testing","Double bootstrap","Multivariate Bernoulli model","Hyper-graph","Phase transition"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2019 Xiao Su"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/105221"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Monte Carlo methods are widely used in statistical computing area to solve different problems. Social network analysis plays an importance role in many fields. In this dissertation, we focus on improving the efficiency of importance sampling, detecting the degrees of influence in networks, and exploring properties of generalized Erd\\H{o}s-R\\'enyi model. In the first part of the thesis, we propose an importance sampling algorithm with proposal distribution obtained from variational approximation. This method combines the strength of both importance sampling and the variational method. On one hand, this method avoids the bias from variational approximation. On the other hand, variational approximation provides a way to design the proposal distribution for the importance sampling algorithm. Theoretical justification of the proposed method is provided. Numerical results show that using variational approximation as the proposal can improve the performance of importance sampling and sequential importance sampling. In the second part of the thesis, we propose a sequential hypothesis testing procedure to detect the degrees of influence in a network. We build a multivariate Bernoulli model to represent the status of each node in the network with different degrees of influence. A double bootstrap strategy is used to resolve the uncertainty from by estimating nuisance parameters in hypothesis testing. Theoretical justification of the proposed method is provided to show that the hypothesis testing is powerful for larger networks. Simulation studies show that our method can preserve the levels and improve the powers in hypothesis testing. We also apply our proposed method on two real network data to explore the degree of influence for various features. In the third part of the thesis, we propose a random graph model for undirected networks with small-world properties, namely with a high clustering coefficient and a low average path length. We generalize the regular Erd\\H{o}s-R\\'enyi dyadic random graph by considering higher-order motif, which is triadic graph. We show some properties of our proposed model, analyze the probability of multi-edges, and compare the local clustering coefficient with ER model. In addition, we also provide some conditions about phase transition including connectivity threshold and the existence of giant components.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2021-05-01","The student, Xiao Su, accepted the attached license on 2019-04-18 at 03:00.","The student, Xiao Su, submitted this Dissertation for approval on 2019-04-18 at 03:24.","This Dissertation was approved for publication on 2019-04-19 at 10:04.","DSpace SAF Submission Ingestion Package generated from Vireo submission #13734 on 2019-08-22 at 16:23:09","Made available in DSpace on 2019-08-23T20:47:34Z (GMT). No. of bitstreams: 3 SU-DISSERTATION-2019.pdf: 979381 bytes, checksum: e3362dc81848eff410226c572163c33d (MD5) LICENSE.txt: 4204 bytes, checksum: fe35e46cf59db81ab4974d2c7911dad4 (MD5) PROQUEST_LICENSE.txt: 4550 bytes, checksum: 052d312c1fce0fd64374c74e645b9aaa (MD5) Previous issue date: 2019-04-19","Embargo set by: Seth Robbins for item 112342 Lift date: 2021-08-23T20:47:38Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system","Embargo set by: Seth Robbins for item 112342 Lift date: 2021-08-23T20:48:32Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system","Limited Restriction Lifted for Item 112342 on 2021-08-24T09:15:16Z."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Variational approximation for importance sampling and statistical inference on social influence"]}]}],"canonical_facts":{"dc:contributor":["Chen, Yuguo","Liang, Feng","Narisetty, Naveen Naidu","Simpson, Douglas G."],"dc:creator":["Su, Xiao"],"dc:date":["2019-08-23T20:47:34Z","2021-08-24T09:15:16Z","2019-04-19","2019-05"],"dc:description":["Monte Carlo methods are widely used in statistical computing area to solve different problems. Social network analysis plays an importance role in many fields. In this dissertation, we focus on improving the efficiency of importance sampling, detecting the degrees of influence in networks, and exploring properties of generalized Erd\\H{o}s-R\\'enyi model. In the first part of the thesis, we propose an importance sampling algorithm with proposal distribution obtained from variational approximation. This method combines the strength of both importance sampling and the variational method. On one hand, this method avoids the bias from variational approximation. On the other hand, variational approximation provides a way to design the proposal distribution for the importance sampling algorithm. Theoretical justification of the proposed method is provided. Numerical results show that using variational approximation as the proposal can improve the performance of importance sampling and sequential importance sampling. In the second part of the thesis, we propose a sequential hypothesis testing procedure to detect the degrees of influence in a network. We build a multivariate Bernoulli model to represent the status of each node in the network with different degrees of influence. A double bootstrap strategy is used to resolve the uncertainty from by estimating nuisance parameters in hypothesis testing. Theoretical justification of the proposed method is provided to show that the hypothesis testing is powerful for larger networks. Simulation studies show that our method can preserve the levels and improve the powers in hypothesis testing. We also apply our proposed method on two real network data to explore the degree of influence for various features. In the third part of the thesis, we propose a random graph model for undirected networks with small-world properties, namely with a high clustering coefficient and a low average path length. We generalize the regular Erd\\H{o}s-R\\'enyi dyadic random graph by considering higher-order motif, which is triadic graph. We show some properties of our proposed model, analyze the probability of multi-edges, and compare the local clustering coefficient with ER model. In addition, we also provide some conditions about phase transition including connectivity threshold and the existence of giant components.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2021-05-01","The student, Xiao Su, accepted the attached license on 2019-04-18 at 03:00.","The student, Xiao Su, submitted this Dissertation for approval on 2019-04-18 at 03:24.","This Dissertation was approved for publication on 2019-04-19 at 10:04.","DSpace SAF Submission Ingestion Package generated from Vireo submission #13734 on 2019-08-22 at 16:23:09","Made available in DSpace on 2019-08-23T20:47:34Z (GMT). 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