  Counterfactual examples identify how inputs can be altered to change the
predicted class of a classifier, thus opening up the black-box nature of, e.g.,
deep neural networks. We propose a method, ECINN, that utilizes the generative
capacities of invertible neural networks for image classification to generate
counterfactual examples efficiently. In contrast to competing methods that
sometimes need a thousand evaluations or more of the classifier, ECINN has a
closed-form expression and generates a counterfactual in the time of only two
evaluations. Arguably, the main challenge of generating counterfactual examples
is to alter only input features that affect the predicted outcome, i.e.,
class-dependent features. Our experiments demonstrate how ECINN alters
class-dependent image regions to change the perceptual and predicted class of
the counterfactuals. Additionally, we extend ECINN to also produce heatmaps
(ECINNh) for easy inspection of, e.g., pairwise class-dependent changes in the
generated counterfactual examples. Experimentally, we find that ECINNh
outperforms established methods that generate heatmap-based explanations.
