The Curve Is an Average of Worlds: What Partial Dependence Actually Shows

Abstract

Partial dependence plots are often interpreted as direct response curves: set a feature to a value, average the predictions, and read the resulting line as an explanation. This paper evaluates a narrower object. A marginal partial-dependence curve averages a frozen predictive model over an empirical population after replacing one feature with values from a declared grid. Seven tree systems developed across Papers 09–15 are reconstructed without changing their official hyperparameters, representations, stages, or selected endpoints. The established temporal protocol is preserved: 307 vehicles from 1970–1979 form the development population, while 85 vehicles from 1980–1982 form the temporal population. Continuous features are evaluated over 21 development-defined quantiles from the 5th to the 95th percentiles. Cylinders, model year, and origin use their observed development values. The same development-defined grids are applied separately to the development and temporal populations. Partial dependence plots summarize mean predictions, while centered individual conditional expectation trajectories retain observation-level responses. Weight has the largest development partial-dependence range in all seven frozen systems. It also has the largest temporal range in six systems, while AdaBoost.R2 ranks horsepower first temporally. Mean within-model development-to-temporal rank correlation is 0.968. A development-derived nearest-neighbor support audit finds a mean temporal off-support fraction of 0.719 across all feature-grid cells, with a maximum cell value of 1.000. This aggregate is calculated across grid cells rather than as an unweighted mean of the seven feature-level summaries; features with more grid points consequently contribute more cells. Weight ICE heterogeneity reaches 0.245 of its partial-dependence range. The results show that stable response rankings do not guarantee supported counterfactual combinations and that an average curve can conceal material individual variation. Partial dependence is therefore a model-behavior summary under a declared grid-replacement and averaging operation. It is not a causal dose-response function and does not establish that every point on the curve represents a plausible observation. The paper introduces the Partial Dependence Validity Map and includes cross-model response curves, individual conditional expectation analysis, development-to-temporal transport, a nearest-neighbor support audit, heterogeneity measurements, comparisons with SHAP and permutation importance, causal claim boundaries, machine-readable outputs, source-generated figures, and a complete reproducibility package.