Multiplicative updates for the LASSO

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    Abstract

    Multiplicative updates have proven useful for non-negativity constrained optimization. Presently, we demonstrate how multiplicative updates also can be used for unconstrained optimization. This is for instance useful when estimating the least absolute shrinkage and selection operator (LASSO), i.e. least squares minimization with $L_1$-norm regularization, since the multiplicative updates (MU) can efficiently exploit the structure of the problem traditionally solved using quadratic programming (QP). We derive an algorithm based on MU for the LASSO and compare the performance to Matlabs standard QP solver as well as the basis pursuit denoising algorithm (BP) which can be obtained from www.sparselab.stanford.edu. The algorithms were tested on three benchmark bio-informatic datasets: A small scale data set where the number of observations is larger than the number of variables estimated ($M
    Original languageEnglish
    Title of host publication2007 IEEE International Workshop on MACHINE LEARNING FOR SIGNAL PROCESSING : MLSP2007
    PublisherIEEE
    Publication date2007
    Pages33-38
    ISBN (Print)978-1-4244-1565-6
    DOIs
    Publication statusPublished - 2007
    Event2007 IEEE International Workshop on Machine Learning for Signal Processing - Thessaloniki, Greece
    Duration: 27 Aug 200729 Aug 2007
    http://mlsp2007.conwiz.dk/

    Workshop

    Workshop2007 IEEE International Workshop on Machine Learning for Signal Processing
    CountryGreece
    CityThessaloniki
    Period27/08/200729/08/2007
    Internet address

    Bibliographical note

    Copyright: 2007 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE

    Keywords

    • Basis Pursuit Denoising (BPD)
    • Least Absolute Shrinkage and Selection Operator (LASSO)
    • Multiplicative Updates

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