Directly test whether off-manifold behavior explains model-dependent PDP distortion

Determine whether the differing refitting gains of tree ensembles and smooth models under strong feature dependence are caused by the models' distinct on-manifold and off-manifold behavior in partial dependence estimation, specifically by comparing partial dependence estimates evaluated on marginally generated feature combinations with the models' behavior on combinations supported by the joint data distribution.

Background

Under strong feature correlation, the paper observes that multilayer perceptrons and radial-basis-function support vector machines gain substantially more from refitting partial-dependence curves than random forests and gradient-boosting models. The authors hypothesize that marginal partial dependence evaluates models at feature combinations that are rare or absent under the joint distribution.

The proposed explanation is that tree ensembles remain bounded by learned leaf values away from the data manifold, whereas smooth global models may extrapolate and produce systematically mis-scaled partial dependence curves. A coefficient-refitting step could then correct this distortion. The paper explicitly identifies direct comparison of on-manifold and off-manifold partial dependence estimates as the required test, but does not perform it.

References

We offer the following explanation, and flag that we have not tested it directly. A partial dependence function averages $f$ over the marginal distribution of the remaining features, so at $\rho = 0.85$ it evaluates the model at feature combinations that the joint distribution almost never produces. How badly the resulting curve is distorted therefore depends on how the model behaves away from the data. A tree ensemble is piecewise constant on axis-aligned cells and its predictions off the data manifold are bounded by the leaf values it learned on it, so its partial dependence curves stay close to the right scale. An RBF support vector machine and a multilayer perceptron are smooth global functions that extrapolate, and off-manifold they can return systematically inflated or deflated values, which distorts the amplitude of their curves. A single coefficient per feature is exactly the correction such a distortion needs, which is why refitting buys them so much. Testing this would require comparing on-manifold and off-manifold partial dependence estimates directly, which we did not do.

— Evaluating Explanation Methods by the Predictors They Induce  (2609.20058 - Selbæk et al., 17 Sep 2026) in Section 'Why the tree ensembles gain so much less' in the Results