doi:10.1016/j.neucom.2004.01.046
Copyright © 2004 Elsevier B.V. All rights reserved.
Causal localization of neural function: the Shapley value method
a Schools of Computer Science, Tel-Aviv University, Ramat Aviv, Tel-Aviv 69978, Israel
b School of Mathematical Sciences, Tel-Aviv University, Ramat Aviv, Tel-Aviv 69978, Israel
c School of Engineering and Science, International University Bremen, Bremen, Germany
d School of Medicine, Tel-Aviv University, Ramat Aviv, Tel-Aviv 69978, Israel
Available online 2 March 2004.
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Abstract
Identifying the functional roles of elements of a neural network is one of the fundamental challenges in understanding neural information processing. Aiming at this goal, lesion studies have been used extensively in neuroscience. Most of these employ single lesions and hence, limited ability in revealing the significance of interacting elements. This paper presents the multi-perturbation Shapley value analysis (MSA), an axiomatic, scalable and rigorous method, addressing the challenge of determining the contributions of network elements from a data set of multi-lesions or other perturbations. The successful workings of the MSA are demonstrated on artificial and biological data. 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”.
Author Keywords: Localization of function; Multi-lesions; Shapley value; Contributions analysis; Interactions; Multi-perturbations
Fig. 1. (A) The MSA contributions (Shapley value) for a test case are compared with the contributions yielded by single lesion analysis and with the FCA contributions (mean and standard deviations across 10 FCA runs using the full set of all 24 multi-lesions). All three values are normalized such that the sum over all elements equals 1. (B) MSA contributions, FCA contributions and predicted MSA contributions of the EAA's neurons. All are based on the full set of 210 multi-lesions and are normalized such that the sum of the contributions of all the neurons equals 1.
Fig. 2. Agent performance as a function of pruning level, by MSA and by FCA. In both methods the synapses are incrementally lesioned by ascending order of their contribution. The figure focuses on the first 80 synapses pruned, where the agent has still viable performance.
Fig. 3. Two-dimensional MSA of reversible deactivation experiments. (A) Predicted MSA contributions of the eight regions. Regions 6 and 8 represent SCR-deep and SCL-deep, respectively. (B) The symmetric interaction between each pair of regions.