Explainable Empirical Risk Minimization

The widespread use of modern machine learning methods in decision making crucially depends on their interpretability or explainability. The human users (decision makers) of machine learning methods are often not only interested in getting accurate predictions or projections. Rather, as a decision-maker, the user also needs a convincing answer (or explanation) to the question of why a particular prediction was delivered. Explainable machine learning might be a legal requirement when used for decision making with an immediate effect on the health of human beings. As an example consider the computer vision of a self-driving car whose predictions are used to decide if to stop the car. We have recently proposed an information-theoretic approach to construct personalized explanations for predictions obtained from ML. This method was model-agnostic and only required some training samples of the model to be explained along with a user feedback signal. This paper uses an information-theoretic measure for the quality of an explanation to learn predictors that are intrinsically explainable to a specific user. Our approach is not restricted to a particular hypothesis space, such as linear maps or shallow decision trees, whose predictor maps are considered as explainable by definition. Rather, we regularize an arbitrary hypothesis space using a personalized measure for the explainability of a particular predictor.