Santa Fe Institute

Shared Information — New Insights and Problems in Decomposing Information in Complex System


February 07, 2013
12:30 PM
Collins Conference Room

Eckehard Olbrich (Max Planck Institute for Mathematics in the Sciences)

Abstract.  How can the information that a set of random variables contains about another random variable be decomposed?  To what extent do different subgroups provide the same, i.e. shared or redundant, information, carry unique information or interact for the emergence of synergistic information?

Recently Williams and Beer proposed such a decomposition based on natural properties for shared information. While these properties fix the structure of the decomposition, they do not uniquely specify the values of the different terms.  Therefore, we investigate additional properties such as strong symmetry and left monotonicity. We find that strong symmetry is incompatible with the properties proposed by Williams and Beer. Although left monotonicity is a very natural property for an information measure it is not fulfilled by any of the proposed measures.

We also study a geometric framework for information decompositions and ask whether it is possible to represent shared information by a family of posterior distributions.

Finally, we draw connections to the notions of shared knowledge and common knowledge in game theory.  While many people believe that independent variables cannot share information, we show that in game theory independent agents can have shared knowledge, but not common knowledge.

We conclude that intuition and heuristic arguments do not suffice when arguing about information. We expect that further progress requires a more precise, operational idea of what shared information should be.

Nils Bertschinger, Johannes Rauh, Eckehard Olbrich, and Jürgen Jost.  "Shared Information — New Insights and Problems in Decomposing Information in Complex Systems."  arXiv:1210.5902 (2012)

Williams, P., and R. Beer. "Nonnegative decomposition of multivariate information."  arXiv:1004.2515v1 (2010)

Purpose: Research Collaboration

SFI Host: David Wolpert

More Info

  • * SFI community lectures are free, open, & accessible to the public.
  • * Seminars & colloquia are geared for scientists but free & open to the interested public.
  • * All other SFI events are by invitation only.
  • * Note: We are unable to accommodate members of the public for SFI's limited lunch service; you're welcome to bring your own.

Events News

Video: Patricia Churchland on the self as brain Nov. 24, 2015 -

During an SFI Community Lecture November 18 in Santa Fe, neurophilosopher Patricia Churchland explained the neural workings that underlie identity. Watch it here.

Apply now for SFI's 2016 Complex Systems Summer School Nov. 10, 2015 -

SFI is accepting applications for its signature education program for graduate students and postdocs -- the 2016 Complex Systems Summer School, June 12-July 8, 2015, in Santa Fe. Apply by January ...

One reporter's account of SFI's 'Genius and Madness' event in August Nov. 9, 2015 -

Months before the release of Cormac McCarthy's forthcoming novel, an auditorium-capacity crowd – including a reporter from Sueddeutsche Zeitung, the largest-circulation daily newspaper in Germany – was treated to a reading ...

Getting our arms around obesity Oct. 29, 2015 -

A working group this week at SFI takes on the complex social problem of obesity, as collaborators test and refine an agent-based model for a pilot intervention.

Why some organisms adopt complex life strategies Oct. 28, 2015 -

Ecologists, evolutionary biologists, and other experts are gathered at SFI this week to ask why certain species, when faced with environmental stressors, invest in complex life strategies.

More News