Show simple item record Wu, Q Guinney, J Maggioni, M Mukherjee, S 2011-06-21T17:32:26Z 2010-08-01
dc.identifier.citation Journal of Machine Learning Research, 2010, 11 pp. 2175 - 2198
dc.identifier.issn 1532-4435
dc.description.abstract The problems of dimension reduction and inference of statistical dependence are addressed by the modeling framework of learning gradients. The models we propose hold for Euclidean spaces as well as the manifold setting. The central quantity in this approach is an estimate of the gradient of the regression or classification function. Two quadratic forms are constructed from gradient estimates: the gradient outer product and gradient based diffusion maps. The first quantity can be used for supervised dimension reduction on manifolds as well as inference of a graphical model encoding dependencies that are predictive of a response variable. The second quantity can be used for nonlinear projections that incorporate both the geometric structure of the manifold as well as variation of the response variable on the manifold. We relate the gradient outer product to standard statistical quantities such as covariances and provide a simple and precise comparison of a variety of supervised dimensionality reduction methods. We provide rates of convergence for both inference of informative directions as well as inference of a graphical model of variable dependencies. © 2010.
dc.format.extent 2175 - 2198
dc.language.iso en_US en_US
dc.relation.ispartof Journal of Machine Learning Research
dc.title Learning gradients: Predictive models that infer geometry and statistical dependence
dc.title.alternative en_US
dc.type Journal Article
dc.description.version Version of Record en_US 2010-8-0 en_US
duke.description.endpage 2198 en_US
duke.description.issue en_US
duke.description.startpage 2175 en_US
duke.description.volume 11 en_US
dc.relation.journal Journal of Machine Learning Research en_US
pubs.organisational-group /Duke
pubs.organisational-group /Duke/Trinity College of Arts & Sciences
pubs.organisational-group /Duke/Trinity College of Arts & Sciences/Mathematics
pubs.publication-status Published
pubs.volume 11
dc.identifier.eissn 1533-7928

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