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a/joss.07334/10.21105.joss.07334.crossref.xml b/joss.07334/10.21105.joss.07334.crossref.xml new file mode 100644 index 0000000000..d7ca2eac15 --- /dev/null +++ b/joss.07334/10.21105.joss.07334.crossref.xml @@ -0,0 +1,306 @@ + + + + 20241112151341-b7717bd99852c6c0126a409df3efe730da6fec85 + 20241112151341 + + JOSS Admin + admin@theoj.org + + The Open Journal + + + + + Journal of Open Source Software + JOSS + 2475-9066 + + 10.21105/joss + https://joss.theoj.org + + + + + 11 + 2024 + + + 9 + + 103 + + + + DiscreteEntropy.jl: Entropy Estimation of Discrete +Random Variables with Julia + + + + David A. + Kelly + + King’s College London, UK + + https://orcid.org/0000-0002-5368-6769 + + + Ilaria Pia La + Torre + + University College London, UK + + https://orcid.org/0009-0006-2733-5283 + + + + 11 + 12 + 2024 + + + 7334 + + + 10.21105/joss.07334 + + + http://creativecommons.org/licenses/by/4.0/ + http://creativecommons.org/licenses/by/4.0/ + http://creativecommons.org/licenses/by/4.0/ + + + + Software archive + 10.5281/zenodo.14067392 + + + GitHub review issue + https://github.com/openjournals/joss-reviews/issues/7334 + + + + 10.21105/joss.07334 + https://joss.theoj.org/papers/10.21105/joss.07334 + + + https://joss.theoj.org/papers/10.21105/joss.07334.pdf + + + + + + On a statistical estimate for the entropy of +a sequence of independent random variables + Basharin + Theory of Probability & Its +Applications + 3 + 4 + 10.1137/1104033 + 1959 + Basharin, G. P. (1959). On a +statistical estimate for the entropy of a sequence of independent random +variables. Theory of Probability & Its Applications, 4(3), 333–336. +https://doi.org/10.1137/1104033 + + + Boosting fuzzer efficiency: An information +theoretic perspective + Böhme + Proceedings of the 14th joint meeting of the +european software engineering conference and the ACM SIGSOFT symposium +on the foundations of software engineering + 10.1145/3368089.3409748 + 2020 + Böhme, M., Manès, V., & Cha, S. +K. (2020). Boosting fuzzer efficiency: An information theoretic +perspective. Proceedings of the 14th Joint Meeting of the European +Software Engineering Conference and the ACM SIGSOFT Symposium on the +Foundations of Software Engineering, 970–981. +https://doi.org/10.1145/3368089.3409748 + + + Hyperfuzzing: Black-box security hypertesting +with a grey-box fuzzer + Blackwell + Empirical Software +Engineering + 1 + 30 + 10.1007/s10664-024-10556-3 + 2025 + Blackwell, D., Becker, I., & +Clark, D. (2025). Hyperfuzzing: Black-box security hypertesting with a +grey-box fuzzer. Empirical Software Engineering, 30(1), 1–28. +https://doi.org/10.1007/s10664-024-10556-3 + + + Information theory, inference, and learning +algorithms + MacKay + 10.1109/tit.2004.834752 + 2003 + MacKay, D. J. C. (2003). Information +theory, inference, and learning algorithms. Cambridge University Press. +https://doi.org/10.1109/tit.2004.834752 + + + Selecting an effective entropy estimator for +short sequences of bits and bytes with maximum entropy + Contreras Rodrı́guez + Entropy + 5 + 23 + 10.3390/e23050561 + 2021 + Contreras Rodrı́guez, L., +Madarro-Capó, E. J., Legón-Pérez, C. M., Rojas, O., & Sosa-Gómez, G. +(2021). Selecting an effective entropy estimator for short sequences of +bits and bytes with maximum entropy. Entropy, 23(5), 561. +https://doi.org/10.3390/e23050561 + + + Entropy estimates from insufficient +samplings + Grassberger + 2008 + Grassberger, P. (2008). Entropy +estimates from insufficient samplings. +https://arxiv.org/abs/physics/0307138 + + + Nonparametric estimation of Shannon’s +diversity index when there are unseen species in sample. Environ ecol +stat 10: 429-443 + Chao + Environmental and Ecological +Statistics + 10 + 10.1023/A:1026096204727 + 2003 + Chao, A., & Shen, T.-J. (2003). +Nonparametric estimation of Shannon’s diversity index when there are +unseen species in sample. Environ ecol stat 10: 429-443. Environmental +and Ecological Statistics, 10, 429–443. +https://doi.org/10.1023/A:1026096204727 + + + Entropy and inference, +revisited + Nemenman + Proceedings of the 14th international +conference on neural information processing systems: Natural and +synthetic + 10.7551/mitpress/1120.003.0065 + 2001 + Nemenman, I., Shafee, F., & +Bialek, W. (2001). Entropy and inference, revisited. Proceedings of the +14th International Conference on Neural Information Processing Systems: +Natural and Synthetic, 471–478. +https://doi.org/10.7551/mitpress/1120.003.0065 + + + Entropy estimation in Turing’s +perspective + Zhang + Neural Computation + 5 + 24 + 10.1162/NECO_a_00266 + 0899-7667 + 2012 + Zhang, Z. (2012). Entropy estimation +in Turing’s perspective. Neural Computation, 24(5), 1368–1389. +https://doi.org/10.1162/NECO_a_00266 + + + Elements of information theory 2nd edition +(Wiley series in telecommunications and signal +processing) + Cover + 0471241954 + 2006 + Cover, T. M., & Thomas, J. A. +(2006). Elements of information theory 2nd edition (Wiley series in +telecommunications and signal processing). Hardcover; +Wiley-Interscience. ISBN: 0471241954 + + + Entropy inference and the James-Stein +estimator, with application to nonlinear gene association +networks + Hausser + 2009 + Hausser, J., & Strimmer, K. +(2009). Entropy inference and the James-Stein estimator, with +application to nonlinear gene association networks. +https://arxiv.org/abs/0811.3579 + + + PYM entropy estimator MATLAB reference +implementation + Pillowlab + GitHub repository + 2020 + Pillowlab. (2020). PYM entropy +estimator MATLAB reference implementation. In GitHub repository. GitHub. +https://github.com/pillowlab/PYMentropy/ + + + BUB + Paninski + Paninski, L. BUB. +http://www.stat.columbia.edu/~liam/research/code/BUBfunc.m [Accessed +2024-10-22]. + + + NSB entropy estimation + Nemenman + Nemenman, I. NSB entropy estimation. +https://sourceforge.net/projects/nsb-entropy/ [Accessed +2024-10-24]. + + + Unseen + Valiant + Valiant, P., & Valiant, G. +Unseen. https://theory.stanford.edu/~valiant/code.html [Accessed +2024-10-24]. + + + ndd - Bayesian entropy estimation from +discrete data + Marsili + GitHub repository + 2021 + Marsili, S. (2021). ndd - Bayesian +entropy estimation from discrete data. In GitHub repository. GitHub. +https://github.com/simomarsili/ndd + + + entropart: An R package to measure and +partition diversity + Marcon + Journal of Statistical +Software + 8 + 67 + 10.18637/jss.v067.i08 + 2015 + Marcon, E., & Hérault, B. (2015). +entropart: An R package to measure and partition diversity. Journal of +Statistical Software, 67(8), 1–26. +https://doi.org/10.18637/jss.v067.i08 + + + + + + From ab51187db2df5505ce3828b5b267631933f94817 Mon Sep 17 00:00:00 2001 From: The Open Journals editorial robot <89919391+editorialbot@users.noreply.github.com> Date: Tue, 12 Nov 2024 15:14:06 +0000 Subject: [PATCH 3/3] Creating 10.21105.joss.07334.jats --- .../paper.jats/10.21105.joss.07334.jats | 462 ++++++++++++++++++ 1 file changed, 462 insertions(+) create mode 100644 joss.07334/paper.jats/10.21105.joss.07334.jats diff --git a/joss.07334/paper.jats/10.21105.joss.07334.jats b/joss.07334/paper.jats/10.21105.joss.07334.jats new file mode 100644 index 0000000000..6b50735b3e --- /dev/null +++ b/joss.07334/paper.jats/10.21105.joss.07334.jats @@ -0,0 +1,462 @@ + + +

+ + + + +Journal of Open Source Software +JOSS + +2475-9066 + +Open Journals + + + +7334 +10.21105/joss.07334 + +DiscreteEntropy.jl: Entropy Estimation of Discrete Random +Variables with Julia + + + +https://orcid.org/0000-0002-5368-6769 + +Kelly +David A. + + +* + + +https://orcid.org/0009-0006-2733-5283 + +Torre +Ilaria Pia La + + + + + +King’s College London, UK + + + + +University College London, UK + + + + +* E-mail: + +9 +103 +7334 + +Authors of papers retain copyright and release the +work under a Creative Commons Attribution 4.0 International License (CC +BY 4.0) +2024 +The article authors + +Authors of papers retain copyright and release the work under +a Creative Commons Attribution 4.0 International License (CC BY +4.0) + + + +julia +discrete entropy estimation +information theory +mutual information + + + + + + Summary +

DiscreteEntropy.jl is a Julia package to + facilitate entropy estimation of discrete random variables. The + entropy of a random variable, X, is the average + amount of surprise associated with the different outcomes of that + variable. When X is known completely, + calculating the entropy is easy. It is given by

+

+ + H(X)=xXp(x)log(p(x))

+

However, it is a very hard problem when knowledge of the + distribution is incomplete. It is well known that the + MaximumLikelihood (or Plugin) estimator + underestimates the true entropy on average + (Basharin, + 1959). This difficulty has led to a large number of improved + estimators. Contreras Rodrı́guez et al. + (2021), + for example, evaluate 18 different estimators, among which are + Grassberger + (Grassberger, + 2008), Chao Shen + (Chao + & Shen, 2003), NSB + (Nemenman + et al., 2001), Zhang + (Zhang, + 2012), and James-Stein + (Hausser + & Strimmer, 2009). These estimators were scattered across 3 + different programming languages and 7 different libraries. Some of + these estimators are hard to find or poorly maintained. Each + implementation calculates and reports entropy to a different number of + significant digits, which can lead to difficulties in comparison.

+

If one can estimate entropy more accurately, then one can also + estimate mutual information more accurately. There are numerous, + cross-domain, applications for entropy and mutual information, such as + in telecommunications, machine learning + (MacKay, + 2003), and software engineering + (Blackwell + et al., 2025; + Böhme + et al., 2020). DiscreteEntropy.jl makes + it easy to apply different estimators to the problem of mutual + information, cross entropy and Kullback–Leibler divergence + (Cover + & Thomas, 2006), amongst other measures.

+

DiscreteEntropy.jl provides a comprehensive + collection of popular entropy estimators and utilities for working + with other Shannon measures. DiscreteEntropy.jl + implements a variety of different entropy estimators, which were + previously scattered over different languages and libraries. Some of + these scattered implementations are slow, hard to find, or difficult + to compile. DiscreteEntropy.jl removes all of + these problems. DiscreteEntropy.jl also + provides functions for estimating cross entropy, KL divergence, mutual + information and many other Shannon measures. + DiscreteEntropy.jl is intended to be easy to + use, with a flexible but type safe interface.

+
+ + Statement of need +

The DiscreteEntropy.jl package has native + Julia implementations of all of the estimators explored in Contreras + Rodrı́guez et al. + (2021) + and a number of estimators which were not considered. + DiscreteEntropy.jl provides a unified and + consistent interface for those who wish to estimate entropy and other + Shannon measures for their research, or those who want to research + entropy estimation directly.

+

There is no other open-source software package known to us, in any + language, with similar features or similar breadth of estimators. The + R entropy + (Hausser + & Strimmer, 2009) package covers many basic estimators, + such as the maximum likelihood, Miller-Madow, Chao Shen, and many + Bayesian estimators. Code for PYM + (Pillowlab, + 2020), BUB + (Paninski), + and Unseen + (Valiant + & Valiant) estimators are found only in the Matlab + implementations by the authors of the original papers. Other + estimators, such as Zhang and Grassberger, can be found in the R + Entropart + (Marcon + & Hérault, 2015) library. Code for the NSB estimator exists + in multiple different versions, in C++ + (Nemenman), + Matlab + (Nemenman), + and Python + (Marsili, + 2021). The estimators in + DiscreteEntropy.jl were mostly implemented from + the original papers, though some (such as BUB and Unseen) are + idiomatic ports of original Matlab code.

+

DiscreteEntropy.jl is a fast, simple to use + library that fills a gap between the scattered implementations + available online. It ensures type safety throughout, even preventing + confusion between vectors of samples or vectors which represent + histograms of samples.

+
+ + Example +

DiscreteEntropy.jl allows the user to call + each estimator directly, or to use a helper function + estimate_h. The + estimate_h function is the easiest entry to the + library. This function takes a CountData + object, which can be constructed from a vector using either + from_data, from_counts + or from_samples. Both + from_data and estimate_h + are parameterised by types, making them both typesafe and allowing for + simple autocompletion. All results are in nats, + but DiscreteEntropy.jl provides helper + functions to convert between units.

+ data = [1,2,3,4,5,4,3,2,1] +count_data = from_data(data, Histogram) + +estimate_h(count_data, MaximumLikelihood) +2.078803548653078 +

Unsurprisingly, different estimators give different results, + depending on their underlying assumptions:

+ estimate_h(count_data, ChaoShen) +2.2526294444274044 +

These assumptions can have a profound effect on estimations of more + complex measures, such as mutual information:

+ to_bits(mutual_information(Matrix([1 0; 0 1]), MaximumLikelihood)) +1.0 + +to_bits(mutual_information(Matrix([1 0; 0 1]), ChaoWangJost)) +1.7548875021634693 +
+ + Acknowledgements +

David Kelly was funded by UKRI Trustworthy Autonomous Systems Hub + (reference EP/V00784X/1) and Trustworthy Autonomous Systems Node in + Verifiability (reference EP/V026801/2). Ilaria La Torre was partially + supported by Meta’s Flaky project.

+
+ + + + + + + + BasharinG. P. + + On a statistical estimate for the entropy of a sequence of independent random variables + Theory of Probability & Its Applications + 1959 + 4 + 3 + https://doi.org/10.1137/1104033 + 10.1137/1104033 + 333 + 336 + + + + + + BöhmeMarcel + ManèsValentin + ChaSang Kil + + Boosting fuzzer efficiency: An information theoretic perspective + Proceedings of the 14th joint meeting of the european software engineering conference and the ACM SIGSOFT symposium on the foundations of software engineering + 2020 + 10.1145/3368089.3409748 + 970 + 981 + + + + + + BlackwellDaniel + BeckerIngolf + ClarkDavid + + Hyperfuzzing: Black-box security hypertesting with a grey-box fuzzer + Empirical Software Engineering + Springer + 2025 + 30 + 1 + 10.1007/s10664-024-10556-3 + 1 + 28 + + + + + + MacKayDavid J. C. + + Information theory, inference, and learning algorithms + Cambridge University Press + 2003 + 10.1109/tit.2004.834752 + + + + + + Contreras Rodrı́guezLianet + Madarro-CapóEvaristo José + Legón-PérezCarlos Miguel + RojasOmar + Sosa-GómezGuillermo + + Selecting an effective entropy estimator for short sequences of bits and bytes with maximum entropy + Entropy + MDPI + 2021 + 23 + 5 + 10.3390/e23050561 + 561 + + + + + + + GrassbergerP. + + Entropy estimates from insufficient samplings + 2008 + https://arxiv.org/abs/physics/0307138 + + + + + + ChaoAnne + ShenTsung-Jen + + Nonparametric estimation of Shannon’s diversity index when there are unseen species in sample. Environ ecol stat 10: 429-443 + Environmental and Ecological Statistics + 200312 + 10 + 10.1023/A:1026096204727 + 429 + 443 + + + + + + NemenmanIlya + ShafeeFariel + BialekWilliam + + Entropy and inference, revisited + Proceedings of the 14th international conference on neural information processing systems: Natural and synthetic + MIT Press + Cambridge, MA, USA + 2001 + 10.7551/mitpress/1120.003.0065 + 471 + 478 + + + + + + ZhangZhiyi + + Entropy estimation in Turing’s perspective + Neural Computation + 201205 + 24 + 5 + 0899-7667 + https://doi.org/10.1162/NECO\_a\_00266 + 10.1162/NECO_a_00266 + 1368 + 1389 + + + + + + CoverThomas M. + ThomasJoy A. + + Elements of information theory 2nd edition (Wiley series in telecommunications and signal processing) + Hardcover; Wiley-Interscience + 2006 + 0471241954 + + + + + + HausserJean + StrimmerKorbinian + + Entropy inference and the James-Stein estimator, with application to nonlinear gene association networks + 2009 + https://arxiv.org/abs/0811.3579 + + + + + + Pillowlab + + PYM entropy estimator MATLAB reference implementation + GitHub repository + GitHub + 2020 + https://github.com/pillowlab/PYMentropy/ + + + + + + PaninskiLiam + + BUB + http://www.stat.columbia.edu/~liam/research/code/BUBfunc.m [Accessed 2024-10-22] + + + + + + NemenmanIlya + + NSB entropy estimation + https://sourceforge.net/projects/nsb-entropy/ [Accessed 2024-10-24] + + + + + + ValiantPaul + ValiantGregory + + Unseen + https://theory.stanford.edu/~valiant/code.html [Accessed 2024-10-24] + + + + + + MarsiliSimone + + ndd - Bayesian entropy estimation from discrete data + GitHub repository + GitHub + 2021 + https://github.com/simomarsili/ndd + + + + + + MarconEric + HéraultBruno + + entropart: An R package to measure and partition diversity + Journal of Statistical Software + 2015 + 67 + 8 + 10.18637/jss.v067.i08 + 1 + 26 + + + + +