Explainable empirical risk minimization

The successful application of machine learning (ML) methods increasingly depends on their interpretability or explainability. Designing explainable ML (XML) systems is instrumental for ensuring transparency of automated decision-making that targets humans. The explainability of ML methods is also an essential ingredient for trustworthy artificial intelligence. A key challenge in ensuring explainability is its dependence on the specific human end user of an ML system. The users of ML methods might have vastly different background knowledge about ML principles, with some having formal training in the specific field and others having none. We use information-theoretic concepts to develop a novel measure for the subjective explainability of predictions delivered by a ML method. We construct this measure via the conditional entropy of predictions, given the user signal. Our approach allows for a wide range of user signals, ranging from responses to surveys to biophysical measurements. We use this measure of subjective explainability as a regularizer for model training. The resulting explainable empirical risk minimization (EERM) principle strives to balance subjective explainability and risk. The EERM principle is flexible and can be combined with arbitrary ML models. We present several practical implementations of EERM for linear models and decision trees. Numerical experiments demonstrate the application of EERM to weather prediction and detecting inappropriate language in social media.