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Title: Algebraic geometric comparison of probability distributions
Authors: Király, Franz J.von Bünau, PaulMeinecke, Frank C.Blythe, Duncan A. J.Müller, Klaus-Robert
Publishers Version: https://doi.org/10.14760/OWP-2011-30
Issue Date: 2011
Published in: Oberwolfach Preprints (OWP), Volume 2011-30, ISSN 1864-7596
Publisher: Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach
Abstract: We 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.
DDC: 510
License: This 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.
Dieses 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.
Appears in Collections:Mathematik



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