  Response curves exhibit the magnitude of the response of a sensitive system
to a varying stimulus. However, response of such systems may be sensitive to
multiple stimuli (i.e., input features) that are not necessarily independent.
As a consequence, the shape of response curves generated for a selected input
feature (referred to as "active feature") might depend on the values of the
other input features (referred to as "passive features"). In this work, we
consider the case of systems whose response is approximated using regression
neural networks. We propose to use counterfactual explanations (CFEs) for the
identification of the features with the highest relevance on the shape of
response curves generated by neural network black boxes. CFEs are generated by
a genetic algorithm-based approach that solves a multi-objective optimization
problem. In particular, given a response curve generated for an active feature,
a CFE finds the minimum combination of passive features that need to be
modified to alter the shape of the response curve. We tested our method on a
synthetic dataset with 1-D inputs and two crop yield prediction datasets with
2-D inputs. The relevance ranking of features and feature combinations obtained
on the synthetic dataset coincided with the analysis of the equation that was
used to generate the problem. Results obtained on the yield prediction datasets
revealed that the impact on fertilizer responsivity of passive features depends
on the terrain characteristics of each field.
