Inferring directional interactions in collective dynamics: a critique to intrinsic mutual information

Pietro De Lellis, Manuel Ruiz Marín, Maurizio Porfiri

Research output: Contribution to journalArticlepeer-review


Pairwise interactions are critical to collective dynamics of natural and technological systems. Information theory is the gold standard to study these interactions, but recent work has identified pitfalls in the way information flow is appraised through classical metrics—time-delayed mutual information and transfer entropy. These pitfalls have prompted the introduction of intrinsic mutual information to precisely measure information flow. However, little is known regarding the potential use of intrinsic mutual information in the inference of directional influences to diagnose interactions from time-series of individual units. We explore this possibility within a minimalistic, mathematically tractable leader-follower model, for which we document an excess of false inferences of intrinsic mutual information compared to transfer entropy. This unexpected finding is linked to a fundamental limitation of intrinsic mutual information, which suffers from the same sins of time-delayed mutual information: a thin tail of the null distribution that favors the rejection of the null-hypothesis of independence.

Original languageEnglish (US)
Article number015001
JournalJournal of Physics: Complexity
Issue number1
StatePublished - Mar 1 2023


  • collective behavior
  • information flow
  • intrinsic mutual information
  • leader-follower interaction
  • statistical inference
  • time-series analysis
  • transfer entropy

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Computer Networks and Communications
  • Artificial Intelligence


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