A Convex Algorithm for Mixed Linear Regression

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dc.contributor.advisorHand, Paul Een_US
dc.creatorJoshi, Babhruen_US
dc.date.accessioned2017-08-01T15:18:04Zen_US
dc.date.available2017-08-01T15:18:04Zen_US
dc.date.created2016-12en_US
dc.date.issued2017-03-22en_US
dc.date.submittedDecember 2016en_US
dc.date.updated2017-08-01T15:18:04Zen_US
dc.description.abstractMixed linear regression is a high dimensional affine space clustering problem where the goal is to find the parameters of multiple affine spaces that best fit a collection of points. We introduce a convex 2nd order cone program (based on l1/fused lasso) which allows us to reformulate the mixed linear regression as an Rd clustering problem. The convex program is parameter free and does not require prior knowledge of the number of clusters, which is more tractable while clustering in Rd. In the noiseless case, we prove that the convex program recovers the regression coefficients exactly under narrow technical conditions of well-separation and balance. We demonstrate numerical performance on BikeShare data and music tone perception data.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationJoshi, Babhru. "A Convex Algorithm for Mixed Linear Regression." (2017) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/95962">https://hdl.handle.net/1911/95962</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/95962en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectmixed linear regressionen_US
dc.subjectmixed regressionen_US
dc.subjectmixture modelen_US
dc.subjectfused lassoen_US
dc.titleA Convex Algorithm for Mixed Linear Regressionen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentComputational and Applied Mathematicsen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Artsen_US
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