Decomposing Multivariate Information in Complex Systems

The main focus of the conference was on partial information decomposition (PID), a recent extension of information
theory that seeks to partition the total information provided by a set of sources into its unique, redundant and
synergistic components, a task that is not addressed by Shannon’s information theory.
Due to the nascent state of PID theory, important theoretical work is ongoing and the conference proved very
important to bring the field forward in this regard.

The question addressed by PID, however, is ubiquitous in many branches of natural sciences, and the conference
thus covered also a range of early practical applications of PID theory, especially from the fields of machine learning
and neuroscience. Here, the workshop format proved valuable to the participants as recent advances in PID theory
helped to interpret these early empirical findings much more precisely.

In a field like PID that is still very much in flux, every participant is important, and often essential contributions
are made by outsiders and newcomers. Thus, it is somewhat difficult to name the most important participants.
Historically, however, the first insights into the PID problem were obtained roughly a decade ago by Randall Beer,
University of Indiana, Bloomington, whom we could win to give a keynote lecture on how the ideas leading to PID
were conceived. Certain other participants can be considered important due to their established status in fields
related to PID, such as applied mathematics, represented by Jürgen Jost, MPI Mathematics in the Sciences, artificial
intelligence, represented by Daniel Polani, University of Hartfordshire and Greg ver Steg, Caltech , complex systems
and information geometry, represented for example by Nihat Ay, Santa Fe Institute and Hamburg University), and
information theory in neuroscience, represented by Stefano Panzeri, Italian Institute of Technology and Hamburg
University.

However, in a young field often the newcomers make important contributions. The newcomers were fully integrated
into the workshop track, i.e. we made little to no difference between presentations slots for newcomers versus es-
tablished researchers. Several newcomers indeed made important contributions. Most of them may be a bit too
technical for the scope of this report, but to give an example Aaron Gutknecht presented a unifying framework which
formally explained why multiple approaches to the PID problem exist and that all of these approaches can be neatly
organized into just 4 families – immediately rendering the field of PID much less confusing and more accessible.

Aaron Gutknecht’s organization scheme encompassing and systematically relating the different PID approaches was
also one of the main scientific results. The other important result arose from a discussion around the presentation
of Artemy Kolchinsky, who showed that PIDs not respecting the set-theoretic inclusion-exclusion principle should be
considered. In the course of the ensuing discussion it turned out that approaches to PID may be sorted into: (A)
approaches that require the union information to be a random variable –enabling the use of information channels and
the Blackwell ordering on channels, but often conflicting with the inclusion exclusion principle–, and (B) approaches honoring the inclusion-exclusion principle, but potentially sacrificing the representation of the parts of a PID a
(auxiliary) random variables.

Overall, participants really enjoyed the workshop very much, not least because larger meetings on this topics have
been rare in the past – despite of the rapid gain in attention that the field of PID gets. Therefore, the organizers
and the participants would like to thank the Max Planck Institute for the Physics of Complex Systems
again for the amazing opportunity to hold this meeting in Dresden, and to stress the importance of this
support for them.