Algebraic geometric comparison of probability distributions

dc.bibliographicCitation.volume2011-30
dc.contributor.authorKirály, Franz J.
dc.contributor.authorvon Bünau, Paul
dc.contributor.authorMeinecke, Frank C.
dc.contributor.authorBlythe, Duncan A.J.
dc.contributor.authorMüller, Klaus-Robert
dc.date.available2019-06-28T08:05:01Z
dc.date.issued2011
dc.description.abstractWe propose a novel algebraic framework for treating probability distributions represented by their cumulants such as the mean and covariance matrix. As an example, we consider the unsupervised learning problem of finding the subspace on which several probability distributions agree. Instead of minimizing an objective function involving the estimated cumulants, we show that by treating the cumulants as elements of the polynomial ring we can directly solve the problem, at a lower computational cost and with higher accuracy. Moreover, the algebraic viewpoint on probability distributions allows us to invoke the theory of Algebraic Geometry, which we demonstrate in a compact proof for an identifiability criterion.eng
dc.description.versionpublishedVersioneng
dc.formatapplication/pdf
dc.identifier.issn1864-7596
dc.identifier.urihttps://doi.org/10.34657/1948
dc.identifier.urihttps://oa.tib.eu/renate/handle/123456789/2257
dc.language.isoengeng
dc.publisherOberwolfach : Mathematisches Forschungsinstitut Oberwolfacheng
dc.relation.doihttps://doi.org/10.14760/OWP-2011-30
dc.relation.ispartofseriesOberwolfach Preprints (OWP), Volume 2011-30, ISSN 1864-7596eng
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.eng
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.ger
dc.subject.ddc510eng
dc.titleAlgebraic geometric comparison of probability distributionseng
dc.typereporteng
dc.typeTexteng
dcterms.bibliographicCitation.journalTitleOberwolfach Preprints (OWP)eng
tib.accessRightsopenAccesseng
wgl.contributorMFOeng
wgl.subjectMathematikeng
wgl.typeReport / Forschungsbericht / Arbeitspapiereng
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