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Bias in O-Information Estimation.

Johanna Gehlen1, Jie Li1, Cillian Hourican1

  • 1Computational Science Lab, Informatics Institute, University of Amsterdam, 1098 Amsterdam, The Netherlands.

Entropy (Basel, Switzerland)
|October 25, 2024
PubMed
Summary
This summary is machine-generated.

Estimating system synergy and redundancy using O-information can be biased. For independent systems, small sample sizes severely bias O-information towards synergy, potentially misidentifying independent systems.

Keywords:
O-informationbiascomplex systemshigher-order relationshipsinformation synergy

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Area of Science:

  • Complex systems science
  • Information theory
  • Statistical analysis

Background:

  • Higher-order relationships are crucial in complex systems.
  • O-information quantifies synergy and redundancy using Shannon entropy.
  • Bias in O-information estimation for discrete variables is not well understood.

Purpose of the Study:

  • To explain the source of bias in O-information estimation.
  • To explore bias in synergistic, redundant, and independent systems (n=3).
  • To investigate the impact of sample size and bin number on O-information bias.

Main Methods:

  • Simulated systems with varying degrees of synergy/redundancy.
  • Analysis of O-information estimation bias.
  • Derivation of a bias approximation using the Miller-Maddow method.

Main Results:

  • O-information is significantly biased towards synergy for independent systems when sample size is insufficient.
  • Bias is influenced by sample size and the number of bins used.
  • The Miller-Maddow bias approximation partially corrects O-information bias for n=3 systems.

Conclusions:

  • Small sample sizes can lead to misinterpretation of independent systems as synergistic.
  • Bias approximation offers partial correction, but simulations of independent systems remain essential as null models.
  • Accurate estimation of higher-order relationships requires careful consideration of O-information bias.