Fair attribution of functional contribution in artificial and biological networks.

This letter presents the multi-perturbation Shapley value analysis (MSA), an axiomatic, scalable, and rigorous method for deducing causal function localization from multiple perturbations data. The MSA, based on fundamental concepts from game theory, accurately quantifies the contributions of network elements and their interactions, overcoming several shortcomings of previous function localization approaches. Its successful operation is demonstrated in both the analysis of a neurophysiological model and of reversible deactivation data. The MSA has a wide range of potential applications, including the analysis of reversible deactivation experiments, neuronal laser ablations, and transcranial magnetic stimulation "virtual lesions," as well as in providing insight into the inner workings of computational models of neurophysiological systems.