A novel measure of multivariate redundant information

  • Artemy Kolchinsky (Santa Fe Institute, USA)
A3 02 (Seminar room)


Consider a situation in which a set of n random variables X1...Xn carry information about some random variable of interest Y. For example, Y could represent an external stimulus while X1...Xn could represent the activity of n brain regions; alternatively, Y could be the output of a digital logic gate while X1...Xn could be the n inputs of the gate. Recent work in information theory has considered the problem of quantifying the amount of redundancy among X1...Xn about Y, i.e., the amount of information about Y that is found individually within all X1...Xn. Several approaches to quantifying redundancy have been proposed, but most lack a clear operational motivation, or only apply in the case of two X variables. Here we propose a novel measure of redundancy which applies to an arbitrary number of variables. We show that our measure has decision-theoretic, set-algebraic, geometric, and axiomatic interpretations. Our approach also sheds new light on the difficulties encountered by existing ways of quantifying redundant and synergistic information.

Katharina Matschke

MPI for Mathematics in the Sciences Contact via Mail