GraphSVX: Shapley Value Explanations for Graph Neural Networks

The Shapley value for directed graph games

The Shapley value for directed graph (digraph) games, TU games with limited cooperation introduced by an arbitrary digraph prescribing the dominance relation among the players, is introduced. It is defined as the average of marginal contribution vectors corresponding to all permutations that do not violate the subordination of players. We assume that in order to cooperate players may join only ...

Extracting Explanations from Neural Networks

The use of neural networks is still difficult in many application areas due to the lack of explanation facilities (the « black box » problem). An example of such applications is multiple criteria decision making (MCDM), applied to location problems having environmental impact. However, the concepts and methods presented are also applicable to other problem domains. These concepts show how to ex...

Efficient Computation of the Shapley Value for Centrality in Networks

The Shapley Value is arguably the most important normative solution concept in coalitional games. One of its applications is in the domain of networks, where the Shapley Value is used to measure the relative importance of individual nodes. This measure, which is called node centrality, is of paramount significance in many real-world application domains including social and organisational networ...

Shapley value for assignment games ∗

We consider the problem of the axiomatization of the Shapley value on the class of assignment games. We show that Shapley’s original [21], Young’s [24], Chun’s [7], van den Brink’s [2], (5-6) Hart and Mas-Colell’s [12] potential function and consistency approaches and Roth’s [19] characterization do not work on the class of assignment games. We also consider Myerson’s [15] axiomatization of the...

Causal Lo alization of Neural Fun tion : The Shapley Value