Partial dependence through stratification

Abstract

Partial dependence curves (FPD) are commonly used to explain feature importance once a supervised learning model has been fitted to data. However, it is common for the same partial dependence algorithm to give meaningfully different curves for different supervised models, even when the algorithm is applied to the same data. As a result, it is difficult to distinguish between model artifacts and true relationships in the data. In this paper, we contribute metods for computing partial dependence curves, for both numerical (StratPD) and categorical explanatory variables (CatStratPD), that work directly from training data rather than the predictions of a fitted model. Our methods provide a direct estimate of partial dependence, and rely on approximating the partial derivative of an unknown regression function. We investigate settings where contemporary partial dependence methods – including FPD, Accumulated Local Effects (ALE), and SHapley Additive exPlanations (SHAP) methods – give biased results. We demonstrate that our approach works correctly on synthetic data and plausibly on real data sets. This work motivates a new line of inquiry into nonparametric partial dependence that provides robust information about the variables considered in a supervised learning task.

Keywords

• Decision trees
• Feature importance
• Random forests
• Variable importance