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dc.contributor.authorGiraldi, Loic
dc.contributor.authorLe Maître, Olivier P.
dc.contributor.authorHoteit, Ibrahim
dc.contributor.authorKnio, Omar
dc.date.accessioned2018-03-19T09:05:22Z
dc.date.available2018-03-19T09:05:22Z
dc.date.issued2018-03-18
dc.identifier.citationGiraldi L, Le Maître OP, Hoteit I, Knio OM (2018) Optimal projection of observations in a Bayesian setting. Computational Statistics & Data Analysis. Available: http://dx.doi.org/10.1016/j.csda.2018.03.002.
dc.identifier.issn0167-9473
dc.identifier.doi10.1016/j.csda.2018.03.002
dc.identifier.urihttp://hdl.handle.net/10754/627354
dc.description.abstractOptimal dimensionality reduction methods are proposed for the Bayesian inference of a Gaussian linear model with additive noise in presence of overabundant data. Three different optimal projections of the observations are proposed based on information theory: the projection that minimizes the Kullback–Leibler divergence between the posterior distributions of the original and the projected models, the one that minimizes the expected Kullback–Leibler divergence between the same distributions, and the one that maximizes the mutual information between the parameter of interest and the projected observations. The first two optimization problems are formulated as the determination of an optimal subspace and therefore the solution is computed using Riemannian optimization algorithms on the Grassmann manifold. Regarding the maximization of the mutual information, it is shown that there exists an optimal subspace that minimizes the entropy of the posterior distribution of the reduced model; a basis of the subspace can be computed as the solution to a generalized eigenvalue problem; an a priori error estimate on the mutual information is available for this particular solution; and that the dimensionality of the subspace to exactly conserve the mutual information between the input and the output of the models is less than the number of parameters to be inferred. Numerical applications to linear and nonlinear models are used to assess the efficiency of the proposed approaches, and to highlight their advantages compared to standard approaches based on the principal component analysis of the observations.
dc.description.sponsorshipThis work is supported by King Abdullah University of Science and Technology Awards CRG3-2156 and OSR-2016-RPP-3268.
dc.publisherElsevier BV
dc.relation.urlhttp://www.sciencedirect.com/science/article/pii/S0167947318300501
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Computational Statistics & Data Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computational Statistics & Data Analysis, 14 March 2018. DOI: 10.1016/j.csda.2018.03.002. © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectOptimal dimensionality reduction
dc.subjectOptimal data reduction
dc.subjectGaussian linear model
dc.subjectInformation theory
dc.titleOptimal projection of observations in a Bayesian setting
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentEarth Fluid Modeling and Prediction Group
dc.contributor.departmentEarth Science and Engineering Program
dc.contributor.departmentPhysical Science and Engineering (PSE) Division
dc.identifier.journalComputational Statistics & Data Analysis
dc.eprint.versionPost-print
dc.contributor.institutionLIMSI, CNRS, Université Paris-Saclay, France
dc.identifier.arxivid1709.06606
kaust.personGiraldi, Loic
kaust.personHoteit, Ibrahim
kaust.personKnio, Omar
kaust.grant.numberCRG3-2156
kaust.grant.numberOSR-2016-RPP-3268
refterms.dateFOA2020-03-14T00:00:00Z
dc.date.published-online2018-03-18
dc.date.published-print2018-08
dc.date.posted2017-09-19


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