  We take a formal approach to the explainability problem of machine learning
systems. We argue against the practice of interpreting black-box models via
attributing scores to input components due to inherently conflicting goals of
attribution-based interpretation. We prove that no attribution algorithm
satisfies specificity, additivity, completeness, and baseline invariance. We
then formalize the concept, sound explanation, that has been informally adopted
in prior work. A sound explanation entails providing sufficient information to
causally explain the predictions made by a system. Finally, we present the
application of feature selection as a sound explanation for cancer prediction
models to cultivate trust among clinicians.
