An Information-Theoretic Approach to Explainable Machine Learning

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Abstract
A key obstacle to the successful deployment of machine learning (ML) methods to important application domains is the (lack of) explainability of predictions. Explainable ML is challenging since explanations must be tailored (personalized) to individual users with varying backgrounds. On one extreme, users can have received graduate level education in machine learning while on the other extreme, users might have no formal education in linear algebra. Linear regression with few features might be perfectly interpretable for the first group but must be considered a black-box for the latter. Using a simple probabilistic model for the predictions and user knowledge, we formalize explainable ML using information theory. Providing an explanation is then considered as the task of reducing the "surprise" incurred by a prediction. Moreover, the effect of an explanation is measured by the conditional mutual information between the explanation and prediction, given the user background.

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