Feature Selection via Minimal Covering Sets for Industrial Internet of Things Applications

High stakes decision making requires that any decision support systems must be able to come up with plausible explanations about the decisions they propose to the user. Several popular approaches to explaining black-box AI systems, such as neural networks, focus either on highlighting the features that matter the most in one particular decision as in the SHAP models, or on developing a local to the particular instance data model that is explainable by nature, such as a decision tree. ML systems that are by default explainable and/or interpretable, such as decision trees, or rule-based systems do not require such third-party approaches, as they are themselves explainable. Nevertheless, presenting a consistent (small) set of features to the users as explanations for any given proposed decision can increase the confidence of the users towards the reliability of the system. For this reason, we have developed a system that given a set of rules that hold on a training dataset, finds a minimal cardinality set of features that are used in a set of rules that together cover the entire training dataset. We develop a parallel heuristic algorithm for finding such a minimal variables set, and we show it outperforms all state-of-the-art optimization solvers for finding the solution to a MIP formulation of the problem. Experiments with data from use cases applying AI in public policy decision making as well as in medical use cases show that the proposed small set of features is sufficient to explain all the cases in the test dataset via rules containing only variables from the proposed set of features.