Shapley Value in Partition Function Form Games: New Research Perspectives for Features Selection

The Shapley value assigns each game in Characteristic form a result (contribution) for each player. In games with externalities, there is a Partition Function assigned to the characteristic representation. Various generalisations or extensions of the Shapley value have been developed in the literature. The Shapley value for games in Partition Function Form can be interpreted as the ex ante value of a process of successive bilateral mergers. Game-theoretic formulations of feature importance are a way of explaining machine learning models. These methods define a cooperative game between features in a model and using Shapley’s value study the influence of input features. The externality modelled in the game is read as a further measure of the contribution of features and seeks to interpret causal structures in the data. Our aim is to construct a weighted elementary marginal contribution for each feauture, in order to select attributes that have explanatory value.