  When fitting black box supervised learning models (e.g., complex trees,
neural networks, boosted trees, random forests, nearest neighbors, local
kernel-weighted methods, etc.), visualizing the main effects of the individual
predictor variables and their low-order interaction effects is often important,
and partial dependence (PD) plots are the most popular approach for
accomplishing this. However, PD plots involve a serious pitfall if the
predictor variables are far from independent, which is quite common with large
observational data sets. Namely, PD plots require extrapolation of the response
at predictor values that are far outside the multivariate envelope of the
training data, which can render the PD plots unreliable. Although marginal
plots (M plots) do not require such extrapolation, they produce substantially
biased and misleading results when the predictors are dependent, analogous to
the omitted variable bias in regression. We present a new visualization
approach that we term accumulated local effects (ALE) plots, which inherits the
desirable characteristics of PD and M plots, without inheriting their preceding
shortcomings. Like M plots, ALE plots do not require extrapolation; and like PD
plots, they are not biased by the omitted variable phenomenon. Moreover, ALE
plots are far less computationally expensive than PD plots.
