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In recent years, Artificial Intelligence (AI) algorithms have been proven tooutperform traditional statistical methods in terms of predictivity, especiallywhen a large amount of data was available. Nevertheless, the "black box" natureof AI models is often a limit for a reliable application in high-stakes fieldslike diagnostic techniques, autonomous guide, etc. Recent works have shown thatan adequate level of interpretability could enforce the more general concept ofmodel trustworthiness. The basic idea of this paper is to exploit the humanprior knowledge of the features' importance for a specific task, in order tocoherently aid the phase of the model's fitting. This sort of "weighted" AI isobtained by extending the empirical loss with a regularization term encouragingthe importance of the features to follow predetermined constraints. Thisprocedure relies on local methods for the feature importance computation, e.g.LRP, LIME, etc. that are the link between the model weights to be optimized andthe user-defined constraints on feature importance. In the fairness area,promising experimental results have been obtained for the Adult dataset. Manyother possible applications of this model agnostic theoretical framework aredescribed.

Logic Constraints to Feature Importances