  Machine Learning has proved its ability to produce accurate models but the
deployment of these models outside the machine learning community has been
hindered by the difficulties of interpreting these models. This paper proposes
an algorithm that produces a continuous global interpretation of any given
continuous black-box function. Our algorithm employs a variation of projection
pursuit in which the ridge functions are chosen to be Meijer G-functions,
rather than the usual polynomial splines. Because Meijer G-functions are
differentiable in their parameters, we can tune the parameters of the
representation by gradient descent; as a consequence, our algorithm is
efficient. Using five familiar data sets from the UCI repository and two
familiar machine learning algorithms, we demonstrate that our algorithm
produces global interpretations that are both highly accurate and parsimonious
(involve a small number of terms). Our interpretations permit easy
understanding of the relative importance of features and feature interactions.
Our interpretation algorithm represents a leap forward from the previous state
of the art.
