  Prediction and explanation are key objects in supervised machine learning,
where predictive models are known as black boxes and explanatory models are
known as glass boxes. Explanation provides the necessary and sufficient
information to interpret the model output in terms of the model input. It
includes assessments of model output dependence on important input variables
and measures of input variable importance to model output. High dimensional
model representation (HDMR), also known as the generalized functional ANOVA
expansion, provides useful insight into the input-output behavior of supervised
machine learning models. This article gives applications of HDMR in supervised
machine learning. The first application is characterizing information leakage
in ``big-data'' settings. The second application is reduced-order
representation of elementary symmetric polynomials. The third application is
analysis of variance with correlated variables. The last application is
estimation of HDMR from kernel machine and decision tree black box
representations. These results suggest HDMR to have broad utility within
machine learning as a glass box representation.
