Zipf’s Law Arises Naturally When There Are Underlying, Unobserved Variables.

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  • Additional Information
    • Author-Supplied Keywords:
      Animal cells
      Bioinformatics
      Biology and life sciences
      Cell biology
      Cellular neuroscience
      Cellular types
      Computational linguistics
      Covariance
      Database and informatics methods
      Entropy
      Linguistics
      Mathematics
      Neurons
      Neuroscience
      Physical sciences
      Physics
      Probability distribution
      Probability theory
      Random variables
      Research and analysis methods
      Research Article
      Sequence analysis
      Social sciences
      Speech
      Statistical mechanics
      Thermodynamics
    • Abstract:
      Zipf’s law, which states that the probability of an observation is inversely proportional to its rank, has been observed in many domains. While there are models that explain Zipf’s law in each of them, those explanations are typically domain specific. Recently, methods from statistical physics were used to show that a fairly broad class of models does provide a general explanation of Zipf’s law. This explanation rests on the observation that real world data is often generated from underlying causes, known as latent variables. Those latent variables mix together multiple models that do not obey Zipf’s law, giving a model that does. Here we extend that work both theoretically and empirically. Theoretically, we provide a far simpler and more intuitive explanation of Zipf’s law, which at the same time considerably extends the class of models to which this explanation can apply. Furthermore, we also give methods for verifying whether this explanation applies to a particular dataset. Empirically, these advances allowed us extend this explanation to important classes of data, including word frequencies (the first domain in which Zipf’s law was discovered), data with variable sequence length, and multi-neuron spiking activity. [ABSTRACT FROM AUTHOR]
    • Abstract:
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    • Author Affiliations:
      1Gatsby Computational Neuroscience Unit, University College London, London, United Kingdom
      2Weill Medical College, Cornell University, New York, New York, United States of America
    • ISSN:
      1553-734X
    • Accession Number:
      10.1371/journal.pcbi.1005110
    • Accession Number:
      120314278
  • Citations
    • ABNT:
      AITCHISON, L.; CORRADI, N.; LATHAM, P. E. Zipf’s Law Arises Naturally When There Are Underlying, Unobserved Variables. PLoS Computational Biology, [s. l.], v. 12, n. 12, p. 1–32, 2016. DOI 10.1371/journal.pcbi.1005110. Disponível em: http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=asn&AN=120314278&custid=s8280428. Acesso em: 8 dez. 2019.
    • AMA:
      Aitchison L, Corradi N, Latham PE. Zipf’s Law Arises Naturally When There Are Underlying, Unobserved Variables. PLoS Computational Biology. 2016;12(12):1-32. doi:10.1371/journal.pcbi.1005110.
    • APA:
      Aitchison, L., Corradi, N., & Latham, P. E. (2016). Zipf’s Law Arises Naturally When There Are Underlying, Unobserved Variables. PLoS Computational Biology, 12(12), 1–32. https://doi.org/10.1371/journal.pcbi.1005110
    • Chicago/Turabian: Author-Date:
      Aitchison, Laurence, Nicola Corradi, and Peter E. Latham. 2016. “Zipf’s Law Arises Naturally When There Are Underlying, Unobserved Variables.” PLoS Computational Biology 12 (12): 1–32. doi:10.1371/journal.pcbi.1005110.
    • Harvard:
      Aitchison, L., Corradi, N. and Latham, P. E. (2016) ‘Zipf’s Law Arises Naturally When There Are Underlying, Unobserved Variables’, PLoS Computational Biology, 12(12), pp. 1–32. doi: 10.1371/journal.pcbi.1005110.
    • Harvard: Australian:
      Aitchison, L, Corradi, N & Latham, PE 2016, ‘Zipf’s Law Arises Naturally When There Are Underlying, Unobserved Variables’, PLoS Computational Biology, vol. 12, no. 12, pp. 1–32, viewed 8 December 2019, .
    • MLA:
      Aitchison, Laurence, et al. “Zipf’s Law Arises Naturally When There Are Underlying, Unobserved Variables.” PLoS Computational Biology, vol. 12, no. 12, Dec. 2016, pp. 1–32. EBSCOhost, doi:10.1371/journal.pcbi.1005110.
    • Chicago/Turabian: Humanities:
      Aitchison, Laurence, Nicola Corradi, and Peter E. Latham. “Zipf’s Law Arises Naturally When There Are Underlying, Unobserved Variables.” PLoS Computational Biology 12, no. 12 (December 20, 2016): 1–32. doi:10.1371/journal.pcbi.1005110.
    • Vancouver/ICMJE:
      Aitchison L, Corradi N, Latham PE. Zipf’s Law Arises Naturally When There Are Underlying, Unobserved Variables. PLoS Computational Biology [Internet]. 2016 Dec 20 [cited 2019 Dec 8];12(12):1–32. Available from: http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=asn&AN=120314278&custid=s8280428