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Bayesian estimation of information-theoretic metrics for sparsely sampled distributions

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  • Piga, Angelo
  • Font-Pomarol, Lluc
  • Sales-Pardo, Marta
  • Guimerà, 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.

Suggested Citation

  • Piga, Angelo & Font-Pomarol, Lluc & Sales-Pardo, Marta & Guimerà, Roger, 2024. "Bayesian estimation of information-theoretic metrics for sparsely sampled distributions," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
  • Handle: RePEc:eee:chsofr:v:180:y:2024:i:c:s0960077924001152
    DOI: 10.1016/j.chaos.2024.114564
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    References listed on IDEAS

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    2. De Gregorio, Juan & Sánchez, David & Toral, Raúl, 2022. "An improved estimator of Shannon entropy with applications to systems with memory," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    3. Schäfer Juliane & Strimmer Korbinian, 2005. "A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-32, November.
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