Visualizing the effects of predictor variables in black box supervised learning models

Daniel W. Apley*, Jingyu Zhu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

425 Scopus citations


In many supervised learning applications, understanding and visualizing the effects of the predictor variables on the predicted response is of paramount importance. A shortcoming of black box supervised learning models (e.g. complex trees, neural networks, boosted trees, random forests, nearest neighbours, local kernel-weighted methods and support vector regression) in this regard is their lack of interpretability or transparency. Partial dependence plots, which are the most popular approach for visualizing the effects of the predictors with black box supervised learning models, can produce erroneous results if the predictors are strongly correlated, because they require extrapolation of the response at predictor values that are far outside the multivariate envelope of the training data. As an alternative to partial dependence plots, we present a new visualization approach that we term accumulated local effects plots, which do not require this unreliable extrapolation with correlated predictors. Moreover, accumulated local effects plots are far less computationally expensive than partial dependence plots. We also provide an R package ALEPlot as supplementary material to implement our proposed method.

Original languageEnglish (US)
Pages (from-to)1059-1086
Number of pages28
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Issue number4
StatePublished - Sep 1 2020


  • Functional analysis of variance
  • Marginal plots
  • Partial dependence plots
  • Supervised learning
  • Visualization

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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