Estimations of integrated information based on algorithmic complexity and dynamic querying

​Information has emerged as a language in its own right, bridging sev-eral disciplines that analyze natural phenomena and man-made systems.Integrated information has been introduced as a metric to quantify theamount of information generated by a system beyond the informationgenerated by its elements. Yet, this intriguing notion comes with theprice of being prohibitively expensive to calculate, since the calculationsrequire an exponential number of sub-divisions of a system. Here weintroduce a novel framework to connect algorithmic randomness and in-tegrated information, and a numerical method for estimating integratedinformation using a perturbation test rooted in algorithmic informationdynamics. This method quantifies the change in program size of a sys-tem, when subjected to a perturbation. The intuition behind is that ifan object is random then random perturbations have little to no effectto what happens when a shorter program but when an objects has theability to move in both directions (towards or away from randomness) itwill be shown to be better integrated as a measure of sophistication tellingapart randomness and simplicity from structure. We show that an objectwith a high integrated information value is also more compressible, andis therefore more sensitive to perturbations. We find that such a pertur-bation test quantifying compression sensitivity, provides a system with ameans to extract explanations–causal accounts–of its own behaviour. Ourtechnique can reduce the number of calculations to arrive to some boundsor estimations, as the algorithmic perturbation test guides an efficientsearch for estimating integrated information. Our work sets the stage fora systematic exploration of connections between algorithmic complexityand integrated information at the level of both theory and practice.

Estimations of integrated information based on algorithmic complexity and dynamic querying.pdf