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dc.contributor.advisorDong, Yuexiao
dc.creatorChen, Chen
dc.date.accessioned2022-05-26T18:25:14Z
dc.date.available2022-05-26T18:25:14Z
dc.date.issued2022
dc.identifier.urihttp://hdl.handle.net/20.500.12613/7778
dc.description.abstractSolution-path convex clustering is combined with concave penalties by Ma and Huang (2017) to reduce clustering bias. Their method was introduced in the setting of single-response regression to handle heterogeneity. Such heterogeneity may come from either the regression intercepts or the regression slopes. The procedure, realized by the alternating direction method of multipliers (ADMM) algorithm, can simultaneously identify the grouping structure of observations and estimate regression coefficients. In the first part of our work, we extend this procedure to multi-response regression. We propose models to solve cases with heterogeneity in either the regression intercepts or the regression slopes. We combine the existing gadgets of the ADMM algorithm and group-wise concave penalties to find solutions for the model. Our work improves model performance in both clustering accuracy and estimation accuracy. We also demonstrate the necessity of such extension through the fact that by utilizing information in multi-dimensional space, the performance can be greatly improved. In the second part, we introduce robust solutions to our proposed work. We introduce two approaches to handle outliers or long-tail distributions. The first is to replace the squared loss with robust loss, among which are absolute loss and Huber loss. The second is to characterize and remove outliers' effects by a mean-shift vector. We demonstrate that these robust solutions outperform the squared loss based method when outliers are present, or the underlying distribution is long-tailed.
dc.format.extent90 pages
dc.language.isoeng
dc.publisherTemple University. Libraries
dc.relation.ispartofTheses and Dissertations
dc.rightsIN COPYRIGHT- This Rights Statement can be used for an Item that is in copyright. Using this statement implies that the organization making this Item available has determined that the Item is in copyright and either is the rights-holder, has obtained permission from the rights-holder(s) to make their Work(s) available, or makes the Item available under an exception or limitation to copyright (including Fair Use) that entitles it to make the Item available.
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectStatistics
dc.subjectK-means clustering
dc.subjectOptimization
dc.subjectPenalized estimation
dc.subjectRobust solution
dc.subjectSubgroup detection
dc.titleA Concave Pairwise Fusion Approach to Clustering of Multi-Response Regression and Its Robust Extensions
dc.typeText
dc.type.genreThesis/Dissertation
dc.contributor.committeememberTang, Cheng Yong
dc.contributor.committeememberChitturi, Pallavi
dc.contributor.committeememberShen, Cencheng
dc.description.departmentStatistics
dc.relation.doihttp://dx.doi.org/10.34944/dspace/7750
dc.ada.noteFor Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.edu
dc.description.degreePh.D.
dc.identifier.proqst14830
dc.creator.orcid0000-0003-1175-3027
dc.date.updated2022-05-11T16:10:09Z
refterms.dateFOA2022-05-26T18:25:14Z
dc.identifier.filenameChen_temple_0225E_14830.pdf


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