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This paper reviews and advocates against the use of permute-and-predict (PaP)methods for interpreting black box functions. Methods such as the variableimportance measures proposed for random forests, partial dependence plots, andindividual conditional expectation plots remain popular because they are bothmodel-agnostic and depend only on the pre-trained model output, making themcomputationally efficient and widely available in software. However, numerousstudies have found that these tools can produce diagnostics that are highlymisleading, particularly when there is strong dependence among features. Thepurpose of our work here is to (i) review this growing body of literature, (ii)provide further demonstrations of these drawbacks along with a detailedexplanation as to why they occur, and (iii) advocate for alternative measuresthat involve additional modeling. In particular, we describe how breakingdependencies between features in hold-out data places undue emphasis on sparseregions of the feature space by forcing the original model to extrapolate toregions where there is little to no data. We explore these effects acrossvarious model setups and find support for previous claims in the literaturethat PaP metrics can vastly over-emphasize correlated features in both variableimportance measures and partial dependence plots. As an alternative, we discussand recommend more direct approaches that involve measuring the change in modelperformance after muting the effects of the features under investigation.

Unrestricted Permutation forces Extrapolation: Variable Importance Requires at least One More Model, or There Is No Free Variable Importance