UCL logo

UCL Discovery

UCL home » Library Services » Electronic resources » UCL Discovery

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

Aitchison, L; Corradi, N; Latham, PE; (2016) Zipf's Law Arises Naturally When There Are Underlying, Unobserved Variables. PLoS Comput Biol , 12 (12) , Article e1005110. 10.1371/journal.pcbi.1005110. Green open access

[img]
Preview
Text
journal.pcbi.1005110.pdf - ["content_typename_Published version" not defined]

Download (2MB) | Preview

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.

Type: Article
Title: Zipf's Law Arises Naturally When There Are Underlying, Unobserved Variables
Location: United States
Open access status: An open access version is available from UCL Discovery
DOI: 10.1371/journal.pcbi.1005110
Publisher version: http://dx.doi.org/10.1371/journal.pcbi.1005110
Language: English
Additional information: © 2016 Aitchison et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences > Gatsby Computational Neurosci Unit
URI: http://discovery.ucl.ac.uk/id/eprint/1535025
Downloads since deposit
72Downloads
Download activity - last month
Download activity - last 12 months
Downloads by country - last 12 months

Archive Staff Only

View Item View Item