Fair Localization of Function via the Shapley Value: Theory and Applications

Identifying the functional roles of elements in a neural network is one of the first challenges in understanding neural information processing. Aiming at this goal, lesion studies have been used in neuroscience, most of them employing single lesions and hence limited in their ability to reveal the significance of interacting elements. This paper presents the Multi-lesion Shapley value Analysis (MSA), an axiomatic, scalable and rigorous method addressing the challenge of calculating the contributions of network elements from a multi-lesion data set. The successful workings of the MSA are demonstrated in artificial systems as well as for biological data on deactivation studies of spatial attention in cats. The MSA successfully identifies the functional interactions characterizing the “paradoxical” effects previously reported in the literature, and points to new candidate cortical regions that may play a part in spatial attentional processing. MSA is a novel method for causal function localization, with a wide range of potential applications for the analysis of reversible deactivation experiments and TMS-induced “virtual lesions”. Multi-lesioning studies are to become a bare necessity; the MSA, being a harbinger of this new kind of studies, offers a novel and rigorous way for making sense of them.