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Interpretable deep learning is a fundamental building block towards safer AI,especially when the deployment possibilities of deep learning-basedcomputer-aided medical diagnostic systems are so eminent. However, without acomputational formulation of black-box interpretation, general interpretabilityresearch rely heavily on subjective bias. Clear decision structure of themedical diagnostics lets us approximate the decision process of a radiologistas a model - removed from subjective bias. We define the process ofinterpretation as a finite communication between a known model and a black-boxmodel to optimally map the black box's decision process in the known model.Consequently, we define interpretability as maximal information gain over theinitial uncertainty about the black-box's decision within finite communication.We relax this definition based on the observation that diagnosticinterpretation is typically achieved by a process of minimal querying. Wederive an algorithm to calculate diagnostic interpretability. The usualquestion of accuracy-interpretability tradeoff, i.e. whether a black-boxmodel's prediction accuracy is dependent on its ability to be interpreted by aknown source model, does not arise in this theory. With multiple examplesimulation experiments of various complexity levels, we demonstrate the workingof such a theoretical model in synthetic supervised classification scenarios.

A Theory of Diagnostic Interpretation in Supervised Classification