Santa Fe Institute

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

Seminar

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.

References:
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

A Mayan, a Roman, and a New Yorker walk into a bar… June 12, 2015 -

A diverse collection of social and natural scientists, archeologists, and historians are at SFI to share data and techniques for quantitatively comparing ancient and pre-modern cities.

Audio: Why goals, objectives, and metrics inhibit innovation June 11, 2015 -

In podcast interview on the Santa Fe Radio Café, SFI Sabbatical Visitor Ken Stanley discusses the role of serendipity in making great discoveries and the dangers of constraint by objective.

Watch Alan Lightman's SFI lecture on 'The World You Thought You Knew' May 28, 2015 -

In an SFI Community Lecture on May 6, novelist and physicist Alan Lightman offered his perspective on timeless topics such as God, science, the universe, and religious experiences. Watch his ...

Congrats to teacher Dave Brooks and ten high school seniors selected for SFI's High School Prize May 14, 2015 -

In a ceremony Wednesday evening in Santa Fe, SFI awarded science teacher Dave Brooks and ten high school seniors the Institute's 2015 High School Prize for Scientific Excellence.

Video: Watch Susan Murphy's SFI lecture on healing with data April 20, 2015 -

During an April 8 SFI Community Lecture in Santa Fe, statistician Susan Murphy showed how a healthcare decision approach that adapts treatment to each patient over time can improve patient ...

More News