The Shapley value is the prevalent solution for fair division problems in which a payout is to be divided among multiple agents. By adopting a game-theoretic view, the idea of fair division and the Shapley value can also be used in machine learning to quantify the individual contribution of features or data points to the performance of a predictive model.Despite its popularity and axiomatic justification, the Shapley value suffers from a computational complexity that scales exponentially with the number of entities involved, and hence requires approximation methods for its reliable estimation. We propose SVAkADD, a novel approximation method that fits a k-additive surrogate game. By taking advantage of k-additivity, we are able to elicit the exact Shapley values of the surrogate game and then use these values as estimates for the original fair division problem. The efficacy of our method is evaluated empirically and compared to competing methods.

The use of the Choquet integral in multicriteria decision making problems has gained attention in the last two decades. Despite of its usefulness, there is the issue of how to define the Choquet integral parameters, called capacity coefficients, specially the ones associated with coalitions of criteria. A possible approach to address this issue is based on unsupervised learning, which aims to define such parameters with the goal of mitigating undesirable effects provided by intercriteria relations. However, current unsupervised approaches present some drawbacks, as there is no guarantee that the parameters are equally prioritized in the learning procedure. In this article, we propose a novel unsupervised capacity identification approach which ensures a fair learning for all parameters. Moreover, in comparison with the existing methods, our proposal is less complex in terms of optimization, as it is based on a linear formulation. Experimental results in both synthetic and real datasets attest the applicability of our proposal.

Several practical applications can be formulated as a problem of estimating a source of interest from a set of mixed data collected by different sensors. Although a lot of effort has been done to address the optimization task in signal extraction, there is a lack in the literature on how to evaluate the contribution of each sensor in the extraction process. In this letter, we propose a model-agnostic approach that can be used to interpret both the contribution of each sensor in the estimated source and the interaction effects between them. Our proposal is based on a solution concept from game theory, called Shapley value. Numerical experiments on synthetic and real data attest the use of our proposal in blind source extraction problems.

In dimensionality reduction problems, the adopted technique may produce disparities between the representation errors of different groups. For instance, in the projected space, a specific class can be better represented in comparison with another one. In some situations, this unfair result may introduce ethical concerns. Aiming at overcoming this inconvenience, a fairness measure can be considered when performing dimensionality reduction through Principal Component Analysis. However, a solution that increases fairness tends to increase the overall re-construction error. In this context, this paper proposes to address this trade-off by means of a multi-objective-based approach. For this purpose, we adopt a fairness measure associated with the disparity between the representation errors of different groups. Moreover, we investigate if the solution of a classical Principal Component Analysis can be used to find a fair projection. Numerical experiments attest that a fairer result can be achieved with a very small loss in the overall reconstruction error.