• Login
    View Item 
    •   Home
    • Research
    • Articles
    • View Item
    •   Home
    • Research
    • Articles
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of KAUSTCommunitiesIssue DateSubmit DateThis CollectionIssue DateSubmit Date

    My Account

    Login

    Quick Links

    Open Access PolicyORCID LibguideTheses and Dissertations LibguideSubmit an Item

    Statistics

    Display statistics

    Optimal projection of observations in a Bayesian setting

    • CSV
    • RefMan
    • EndNote
    • BibTex
    • RefWorks
    Thumbnail
    Name:
    1-s2.0-S0167947318300501-main.pdf
    Size:
    1.812Mb
    Format:
    PDF
    Description:
    Accepted Manuscript
    Download
    Type
    Article
    Authors
    Giraldi, Loic cc
    Le Maître, Olivier P.
    Hoteit, Ibrahim cc
    Knio, Omar cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Earth Fluid Modeling and Prediction Group
    Earth Science and Engineering Program
    Physical Science and Engineering (PSE) Division
    KAUST Grant Number
    CRG3-2156
    OSR-2016-RPP-3268
    Date
    2018-03-18
    Preprint Posting Date
    2017-09-19
    Online Publication Date
    2018-03-18
    Print Publication Date
    2018-08
    Permanent link to this record
    http://hdl.handle.net/10754/627354
    
    Metadata
    Show full item record
    Abstract
    Optimal 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.
    Citation
    Giraldi 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.
    Sponsors
    This work is supported by King Abdullah University of Science and Technology Awards CRG3-2156 and OSR-2016-RPP-3268.
    Publisher
    Elsevier BV
    Journal
    Computational Statistics & Data Analysis
    DOI
    10.1016/j.csda.2018.03.002
    arXiv
    1709.06606
    Additional Links
    http://www.sciencedirect.com/science/article/pii/S0167947318300501
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.csda.2018.03.002
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Physical Science and Engineering (PSE) Division; Earth Science and Engineering Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

    entitlement

     
    DSpace software copyright © 2002-2022  DuraSpace
    Quick Guide | Contact Us | KAUST University Library
    Open Repository is a service hosted by 
    Atmire NV
     

    Export search results

    The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

    By default, clicking on the export buttons will result in a download of the allowed maximum amount of items. For anonymous users the allowed maximum amount is 50 search results.

    To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

    After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.