Discovering additive structure in black box functions

Many automated learning procedures lack interpretability, operating effectively as a black box: providing a prediction tool but no explanation of the underlying dynamics that drive it. A common approach to interpretation is to plot the dependence of a learned function on one or two predictors. We present a method that seeks not to display the behavior of a function, but to evaluate the importance of nonadditive interactions within any set of variables. Should the function be close to a sum of low dimensional components, these components can be viewed and even modeled parametrically. Alternatively, the work here provides an indication of where intrinsically high-dimensional behavior takes place. The calculations used in this paper correspond closely with the functional ANOVA decomposition; a well-developed construction in Statistics. In particular, the proposed score of interaction importance measures the loss associated with the projection of the prediction function onto a space of additive models. The algorithm runs in linear time and we present displays of the output as a graphical model of the function for interpretation purposes.