Extractable shared information and left monotonicity

  • Johannes Rauh (MPI MiS, Leipzig)
A3 02 (Seminar room)


The talk summarizes results of (joint work with P. Banerjee, E. Olbrich, J. Jost, N. Bertschinger).

We consider the problem of quantifying the information shared by a pair of random variables X1, X2 about another variable S. We propose a new measure of shared information, called extractable shared information, that is left monotonic; that is, the information shared about S is bounded from below by the information shared about f(S) for any function f. We show that our measure leads to a new nonnegative decomposition of the mutual information I(S;X1X2) into shared, complementary and unique components. We study properties of this decomposition and show that a left monotonic shared information is not compatible with a Blackwell interpretation of unique information. We also discuss whether it is possible to have a decomposition in which both shared and unique information are left monotonic.

Katharina Matschke

MPI for Mathematics in the Sciences Contact via Mail