---
_id: '2851'
abstract:
- lang: eng
  text: The number of possible activity patterns in a population of neurons grows
    exponentially with the size of the population. Typical experiments explore only
    a tiny fraction of the large space of possible activity patterns in the case of
    populations with more than 10 or 20 neurons. It is thus impossible, in this undersampled
    regime, to estimate the probabilities with which most of the activity patterns
    occur. As a result, the corresponding entropy - which is a measure of the computational
    power of the neural population - cannot be estimated directly. We propose a simple
    scheme for estimating the entropy in the undersampled regime, which bounds its
    value from both below and above. The lower bound is the usual 'naive' entropy
    of the experimental frequencies. The upper bound results from a hybrid approximation
    of the entropy which makes use of the naive estimate, a maximum entropy fit, and
    a coverage adjustment. We apply our simple scheme to artificial data, in order
    to check their accuracy; we also compare its performance to those of several previously
    defined entropy estimators. We then apply it to actual measurements of neural
    activity in populations with up to 100 cells. Finally, we discuss the similarities
    and differences between the proposed simple estimation scheme and various earlier
    methods. © 2013 IOP Publishing Ltd and SISSA Medialab srl.
article_number: P03015
article_processing_charge: No
author:
- first_name: Michael
  full_name: Berry, Michael
  last_name: Berry
- first_name: Gasper
  full_name: Tkacik, Gasper
  id: 3D494DCA-F248-11E8-B48F-1D18A9856A87
  last_name: Tkacik
  orcid: 0000-0002-6699-1455
- first_name: Julien
  full_name: Dubuis, Julien
  last_name: Dubuis
- first_name: Olivier
  full_name: Marre, Olivier
  last_name: Marre
- first_name: Ravá
  full_name: Da Silveira, Ravá
  last_name: Da Silveira
citation:
  ama: Berry M, Tkačik G, Dubuis J, Marre O, Da Silveira R. A simple method for estimating
    the entropy of neural activity. <i>Journal of Statistical Mechanics Theory and
    Experiment</i>. 2013;2013(3). doi:<a href="https://doi.org/10.1088/1742-5468/2013/03/P03015">10.1088/1742-5468/2013/03/P03015</a>
  apa: Berry, M., Tkačik, G., Dubuis, J., Marre, O., &#38; Da Silveira, R. (2013).
    A simple method for estimating the entropy of neural activity. <i>Journal of Statistical
    Mechanics Theory and Experiment</i>. IOP Publishing. <a href="https://doi.org/10.1088/1742-5468/2013/03/P03015">https://doi.org/10.1088/1742-5468/2013/03/P03015</a>
  chicago: Berry, Michael, Gašper Tkačik, Julien Dubuis, Olivier Marre, and Ravá Da
    Silveira. “A Simple Method for Estimating the Entropy of Neural Activity.” <i>Journal
    of Statistical Mechanics Theory and Experiment</i>. IOP Publishing, 2013. <a href="https://doi.org/10.1088/1742-5468/2013/03/P03015">https://doi.org/10.1088/1742-5468/2013/03/P03015</a>.
  ieee: M. Berry, G. Tkačik, J. Dubuis, O. Marre, and R. Da Silveira, “A simple method
    for estimating the entropy of neural activity,” <i>Journal of Statistical Mechanics
    Theory and Experiment</i>, vol. 2013, no. 3. IOP Publishing, 2013.
  ista: Berry M, Tkačik G, Dubuis J, Marre O, Da Silveira R. 2013. A simple method
    for estimating the entropy of neural activity. Journal of Statistical Mechanics
    Theory and Experiment. 2013(3), P03015.
  mla: Berry, Michael, et al. “A Simple Method for Estimating the Entropy of Neural
    Activity.” <i>Journal of Statistical Mechanics Theory and Experiment</i>, vol.
    2013, no. 3, P03015, IOP Publishing, 2013, doi:<a href="https://doi.org/10.1088/1742-5468/2013/03/P03015">10.1088/1742-5468/2013/03/P03015</a>.
  short: M. Berry, G. Tkačik, J. Dubuis, O. Marre, R. Da Silveira, Journal of Statistical
    Mechanics Theory and Experiment 2013 (2013).
date_created: 2018-12-11T11:59:56Z
date_published: 2013-03-12T00:00:00Z
date_updated: 2025-09-29T13:41:46Z
day: '12'
department:
- _id: GaTk
doi: 10.1088/1742-5468/2013/03/P03015
external_id:
  isi:
  - '000316056900015'
intvolume: '      2013'
isi: 1
issue: '3'
language:
- iso: eng
month: '03'
oa_version: None
publication: Journal of Statistical Mechanics Theory and Experiment
publication_status: published
publisher: IOP Publishing
publist_id: '3941'
quality_controlled: '1'
scopus_import: '1'
status: public
title: A simple method for estimating the entropy of neural activity
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 2013
year: '2013'
...