DIMENSION REDUCTION USING INVERSE SPLINE REGRESSION

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dc.contributor.advisorSmith, Paul J.en_US
dc.contributor.advisorDolgopyat, Dmitryen_US
dc.contributor.authorNam, Kijoengen_US
dc.contributor.departmentMathematical Statisticsen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2014-10-11T05:50:17Z
dc.date.available2014-10-11T05:50:17Z
dc.date.issued2014en_US
dc.description.abstractIn high-dimensional data analysis, we often want to reduce the number of predictors without eliminating variables which are related to the response of interest. Inverse regression methods use the response variable when performing dimension reduction so that information regarding the relation between the covariates and the response is not lost. However, it is common to assume that the inverse regression function is linear or to use some other ad hoc approach. Instead, we propose a new dimension reduction method which models the inverse regression function as a spline. We develop asymptotics for our approach and demonstrate its performance through simulations and several data sets commonly found in the machine learning literature. We show that its performance is better than existing inverse regression based methods, especially when the dimension reduction space is a nonlinear manifold such as the Swiss roll example of Roweis and Saul (2000).en_US
dc.identifierhttps://doi.org/10.13016/M2F88G
dc.identifier.urihttp://hdl.handle.net/1903/15776
dc.language.isoenen_US
dc.subject.pqcontrolledStatisticsen_US
dc.subject.pquncontrolledAsymptoticsen_US
dc.subject.pquncontrolledHigh-dimensional dataen_US
dc.subject.pquncontrolledInverse regression methodsen_US
dc.titleDIMENSION REDUCTION USING INVERSE SPLINE REGRESSIONen_US
dc.typeDissertationen_US

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