Causality-Driven Inference in Complex Systems

Random field model of a causal network (drawing by A. Carmi)

Causality-driven inference algorithm identifies leader in a group

A Complex system is characterized by a collective behavior that is qualitatively different from the superposition of its separate constituents. Most often, such systems, consisting of multiple locally-interacting entities, are characterized by complex processes of pattern formations generated through similarity and hierarchy. While the literature is abundant with tools and methods for simulating complex systems, less theory is devoted to the inverse problem, that of identifying individuals and inferring patterns within a given complex systems. This work aims to fill this gap by introducing a new approach for inference in complex systems. The new approach relies on the notion of causality and the application thereof to a new complex-systems inference mechanism called a causal network. In this formalism, each individual constituent of a complex system is evaluated based on a string of causal coefficients. Hierarchies and patterns in the system are identified using the total causal intensity, which is based on a the l1 norm of a causality matrix and is strongly related to the Fisher information matrix. A probabilistic interpretation of the new formalism is provided in terms of parametric random fields. A Kalman-filter based inference scheme is then implemented, showing how leaders and followers can be distinguished in a multi-agent swarm, and how human leaders can be identified in a group of people by using only video images of the group.