A $k$-additive Choquet integral-based approach to approximate the SHAP values for local interpretability in machine learning

Besides accuracy, recent studies on machine learning models have been addressing the question on how the obtained results can be interpreted. Indeed, while complex machine learning models are able to provide very good results in terms of accuracy even in challenging applications, it is difficult to interpret them. Aiming at providing some interpretability for such models, one of the most famous methods, called SHAP, borrows the Shapley value concept from game theory in order to locally explain the predicted outcome of an instance of interest. As the SHAP values calculation needs previous computations on all possible coalitions of attributes, its computational cost can be very high. Therefore, a SHAP-based method called Kernel SHAP adopts an efficient strategy that approximate such values with less computational effort. In this paper, we also address local interpretability in machine learning based on Shapley values. Firstly, we provide a straightforward formulation of a SHAP-based method for local interpretability by using the Choquet integral, which leads to both Shapley values and Shapley interaction indices. Moreover, we also adopt the concept of $k$-additive games from game theory, which contributes to reduce the computational effort when estimating the SHAP values. The obtained results attest that our proposal needs less computations on coalitions of attributes to approximate the SHAP values.

Assessing the value of a candidate. Comparing belief function and possibility theories

The problem of assessing the value of a candidate is viewed here as a multiple combination problem. On the one hand a candidate can be evaluated according to different criteria, and on the other hand several experts are supposed to assess the value of candidates according to each criterion. Criteria are not equally important, experts are not equally competent or reliable. Moreover levels of satisfaction of criteria, or levels of confidence are only assumed to take their values in qualitative scales which are just linearly ordered. The problem is discussed within two frameworks, the transferable belief model and the qualitative possibility theory. They respectively offer a quantitative and a qualitative setting for handling the problem, providing thus a way to compare the nature of the underlying assumptions.

The Choquet integral for the aggregation of interval scales in multicriteria decision making

This paper addresses the question of which models fit with information concerning the preferences of the decision maker over each attribute, and his preferences about aggregation of criteria (interacting criteria). We show that the conditions induced by these information plus some intuitive conditions lead to a unique possible aggregation operator: the Choquet integral.