The overarching goal of Explainable AI is to develop systems that not only exhibit intelligent behaviours, but also are able to explain their rationale and reveal insights. In explainable machine learning, methods that produce a high level of prediction accuracy as well as transparent explanations are valuable. In this work, we present an explainable classification method. Our method works by first constructing a symbolic Knowledge Base from the training data, and then performing probabilistic inferences on such Knowledge Base with linear programming. Our approach achieves a level of learning performance comparable to that of traditional classifiers such as random forests, support vector machines and neural networks. It identifies decisive features that are responsible for a classification as explanations and produces results similar to the ones found by SHAP, a state of the art Shapley Value based method. Our algorithms perform well on a range of synthetic and non-synthetic data sets.
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