Sufficient, Necessary and Complete Causal Explanations in Image Classification

Existing algorithms for explaining the outputs of image classifiers are based on a variety of approaches and produce explanations that frequently lack formal rigour. On the other hand, logic-based explanations are formally and rigorously defined but their computability relies on strict assumptions about the model that do not hold on image classifiers. In this paper, we show that causal explanations, in addition to being formally and rigorously defined, enjoy the same formal properties as logic-based ones, while still lending themselves to black-box algorithms and being a natural fit for image classifiers. We prove formal properties of causal explanations and their equivalence to logic-based explanations. We demonstrate how to subdivide an image into its sufficient and necessary components. We introduce δ-complete explanations, which have a minimum confidence threshold and 1-complete causal explanations, explanations that are classified with the same confidence as the original image. We implement our definitions, and our experimental results demonstrate that different models have different patterns of sufficiency, necessity, and completeness. Our algorithms are efficiently computable, taking on average 6s per image on a ResNet model to compute all types of explanations, and are totally black-box, needing no knowledge of the model, no access to model internals, no access to gradient, nor requiring any properties, such as monotonicity, of the model.