Technical Report: Partial Dependence through Stratification

Abstract

Partial dependence curves (FPD) introduced by Friedman, are an important model interpretation tool, but are often not accessible to business analysts and scientists who typically lack the skills to choose, tune, and assess machine learning models. It is also common for the same partial dependence algorithm on the same data to give meaningfully different curves for different models, which calls into question their precision. Expertise is required to distinguish between model artifacts and true relationships in the data. In this paper, we contribute methods for computing partial dependence curves, for both numerical (StratPD) and categorical explanatory variables (CatStratPD), that work directly from training data rather than predictions of a model. Our methods provide a direct estimate of partial dependence, and rely on approximating the partial derivative of an unknown regression function without first fitting a model and then approximating its partial derivative. We investigate settings where contemporary partial dependence methods---including FPD, ALE, and SHAP methods---give biased results. Furthermore, we demonstrate that our approach works correctly on synthetic and plausibly on real data sets. Our goal is not to argue that model-based techniques are not useful. Rather, we hope to open a new line of inquiry into nonparametric partial dependence.