Random projections for Bayesian regression

dc.contributor.authorGeppert, Leo N.
dc.contributor.authorIckstadt, Katja
dc.contributor.authorMunteanu, Alexander
dc.contributor.authorSohler, Christian
dc.date.accessioned2018-10-12T08:35:55Z
dc.date.available2018-10-12T08:35:55Z
dc.date.issued2014-04
dc.description.abstractThis article introduces random projections applied as a data reduction technique for Bayesian regression analysis. We show sufficient conditions under which the entire d -dimensional distribution is preserved under random projections by reducing the number of data points from n to k element of O(poly(d/epsilon)) in the case n >> d . Under mild assumptions, we prove that evaluating a Gaussian likelihood function based on the projected data instead of the original data yields a (1+ O(epsilon))-approximation in the l_2-Wasserstein distance. Our main result states that the posterior distribution of a Bayesian linear regression is approximated up to a small error depending on only an epsilon-fraction of its defining parameters when using either improper non-informative priors or arbitrary Gaussian priors. Our empirical evaluations involve different simulated settings of Bayesian linear regression. Our experiments underline that the proposed method is able to recover the regression model while considerably reducing the total run-time.en
dc.identifier.urihttp://hdl.handle.net/2003/37174
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-19170
dc.language.isoende
dc.relation.ispartofseriesTechnical report / Sonderforschungsbereich Verfügbarkeit von Information durch Analyse unter Ressourcenbeschränkung;4/2014
dc.subject.ddc004
dc.titleRandom projections for Bayesian regressionen
dc.typeTextde
dc.type.publicationtypereportde
dcterms.accessRightsopen access
eldorado.secondarypublicationfalsede

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