Articles producció científica> Enginyeria Química

Bayesian estimation of information-theoretic metrics for sparsely sampled distributions

  • Identification data

    Identifier: imarina:9386996
    Authors:
    Piga, AngeloFont-Pomarol, LlucSales-Pardo, MartaGuimera, Roger
    Abstract:
    Estimating the Shannon entropy of a discrete distribution from which we have only observed a small sample is challenging. Estimating other information-theoretic metrics, such as the Kullback-Leibler divergence between two sparsely sampled discrete distributions, is even harder. Here, we propose a fast, semi-analytical estimator for sparsely sampled distributions. Its derivation is grounded in probabilistic considerations and uses a hierarchical Bayesian approach to extract as much information as possible from the few observations available. Our approach provides estimates of the Shannon entropy with precision at least comparable to the benchmarks we consider, and most often higher; it does so across diverse distributions with very different properties. Our method can also be used to obtain accurate estimates of other information-theoretic metrics, including the notoriously challenging Kullback-Leibler divergence. Here, again, our approach has less bias, overall, than the benchmark estimators we consider.
  • Others:

    Author, as appears in the article.: Piga, Angelo; Font-Pomarol, Lluc; Sales-Pardo, Marta; Guimera, Roger
    Department: Enginyeria Química
    URV's Author/s: Font Pomarol, Lluc / Guimera Manrique, Roger / Piga, Angelo / Sales Pardo, Marta
    Keywords: Bayesian estimation Entropy estimation Inferenc Information theor Information theory Kullback-leibler divergence Kullback–leibler divergence Shannon entropy Sparse sampling
    Abstract: Estimating the Shannon entropy of a discrete distribution from which we have only observed a small sample is challenging. Estimating other information-theoretic metrics, such as the Kullback-Leibler divergence between two sparsely sampled discrete distributions, is even harder. Here, we propose a fast, semi-analytical estimator for sparsely sampled distributions. Its derivation is grounded in probabilistic considerations and uses a hierarchical Bayesian approach to extract as much information as possible from the few observations available. Our approach provides estimates of the Shannon entropy with precision at least comparable to the benchmarks we consider, and most often higher; it does so across diverse distributions with very different properties. Our method can also be used to obtain accurate estimates of other information-theoretic metrics, including the notoriously challenging Kullback-Leibler divergence. Here, again, our approach has less bias, overall, than the benchmark estimators we consider.
    Thematic Areas: Applied mathematics Astronomia / física Ciência da computação Ciências biológicas i Ciências biológicas ii Direito Economia Engenharias i Engenharias ii Engenharias iii Engenharias iv General mathematics General physics and astronomy Geociências Interdisciplinar Matemática / probabilidade e estatística Materiais Mathematical physics Mathematics (all) Mathematics (miscellaneous) Mathematics, applied Mathematics, interdisciplinary applications Physics Physics and astronomy (all) Physics and astronomy (miscellaneous) Physics, mathematical Physics, multidisciplinary Química Statistical and nonlinear physics
    licence for use: https://creativecommons.org/licenses/by/3.0/es/
    Author's mail: marta.sales@urv.cat lluc.fonti@estudiants.urv.cat lluc.fonti@estudiants.urv.cat roger.guimera@urv.cat
    Author identifier: 0000-0002-8140-6525 0000-0002-3597-4310
    Record's date: 2024-10-19
    Papper version: info:eu-repo/semantics/publishedVersion
    Link to the original source: https://www.sciencedirect.com/science/article/pii/S0960077924001152?via%3Dihub
    Papper original source: Chaos Solitons & Fractals. 180 114564-
    APA: Piga, Angelo; Font-Pomarol, Lluc; Sales-Pardo, Marta; Guimera, Roger (2024). Bayesian estimation of information-theoretic metrics for sparsely sampled distributions. Chaos Solitons & Fractals, 180(), 114564-. DOI: 10.1016/j.chaos.2024.114564
    Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
    Article's DOI: 10.1016/j.chaos.2024.114564
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2024
    Publication Type: Journal Publications
  • Keywords:

    Applied Mathematics,Mathematical Physics,Mathematics (Miscellaneous),Mathematics, Applied,Mathematics, Interdisciplinary Applications,Physics,Physics and Astronomy (Miscellaneous),Physics, Mathematical,Physics, Multidisciplinary,Statistical and Nonlinear Physics
    Bayesian estimation
    Entropy estimation
    Inferenc
    Information theor
    Information theory
    Kullback-leibler divergence
    Kullback–leibler divergence
    Shannon entropy
    Sparse sampling
    Applied mathematics
    Astronomia / física
    Ciência da computação
    Ciências biológicas i
    Ciências biológicas ii
    Direito
    Economia
    Engenharias i
    Engenharias ii
    Engenharias iii
    Engenharias iv
    General mathematics
    General physics and astronomy
    Geociências
    Interdisciplinar
    Matemática / probabilidade e estatística
    Materiais
    Mathematical physics
    Mathematics (all)
    Mathematics (miscellaneous)
    Mathematics, applied
    Mathematics, interdisciplinary applications
    Physics
    Physics and astronomy (all)
    Physics and astronomy (miscellaneous)
    Physics, mathematical
    Physics, multidisciplinary
    Química
    Statistical and nonlinear physics
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