Peeking Inside the Black Box: Visualizing Statistical Learning With Plots of Individual Conditional Expectation

Abstract

This article presents individual conditional expectation (ICE) plots, a tool for visualizing the model estimated by any supervised learning algorithm. Classical partial dependence plots (PDPs) help visualize the average partial relationship between the predicted response and one or more features. In the presence of substantial interaction effects, the partial response relationship can be heterogeneous. Thus, an average curve, such as the PDP, can obfuscate the complexity of the modeled relationship. Accordingly, ICE plots refine the PDP by graphing the functional relationship between the predicted response and the feature for individual observations. Specifically, ICE plots highlight the variation in the fitted values across the range of a covariate, suggesting where and to what extent heterogeneities might exist. In addition to providing a plotting suite for exploratory analysis, we include a visual test for additive structure in the data-generating model. Through simulated examples and real datasets, we demonstrate how ICE plots can shed light on estimated models in ways PDPs cannot. Procedures outlined are available in the R package ICEbox.

Key Words:

• Exploratory data analysis
• Graphical method
• Model visualization

Notes

If we were to eliminate f₃ from the GAM then we would know a priori that $\widehat{f}$ would not display interaction effects.

Note that NN models are highly sensitive to the number of hidden units and weight decay parameter. We therefore offer the following results as merely representative of the type of plots which NN models can generate.

The curves at the top of the figure mainly correspond to younger people. Their estimated effect of high thickness is seen to be an extrapolation.