  The problem of counterfactual visual explanations is considered. A new family
of discriminant explanations is introduced. These produce heatmaps that
attribute high scores to image regions informative of a classifier prediction
but not of a counter class. They connect attributive explanations, which are
based on a single heat map, to counterfactual explanations, which account for
both predicted class and counter class. The latter are shown to be computable
by combination of two discriminant explanations, with reversed class pairs. It
is argued that self-awareness, namely the ability to produce classification
confidence scores, is important for the computation of discriminant
explanations, which seek to identify regions where it is easy to discriminate
between prediction and counter class. This suggests the computation of
discriminant explanations by the combination of three attribution maps. The
resulting counterfactual explanations are optimization free and thus much
faster than previous methods. To address the difficulty of their evaluation, a
proxy task and set of quantitative metrics are also proposed. Experiments under
this protocol show that the proposed counterfactual explanations outperform the
state of the art while achieving much higher speeds, for popular networks. In a
human-learning machine teaching experiment, they are also shown to improve mean
student accuracy from chance level to 95\%.
