Drake Caraker

2papers

2 Papers

4.1LGMar 22Code
First-Mover Bias in Gradient Boosting Explanations: Mechanism, Detection, and Resolution

Drake Caraker, Bryan Arnold, David Rhoads

We isolate and empirically characterize first-mover bias -- a path-dependent concentration of feature importance caused by sequential residual fitting in gradient boosting -- as a specific mechanistic cause of the well-known instability of SHAP-based feature rankings under multicollinearity. When correlated features compete for early splits, gradient boosting creates a self-reinforcing advantage for whichever feature is selected first: subsequent trees inherit modified residuals that favor the incumbent, concentrating SHAP importance on an arbitrary feature rather than distributing it across the correlated group. Scaling up a single model amplifies this effect -- a Large Single Model with the same total tree count as our method produces the worst explanations of any approach tested. We demonstrate that model independence is sufficient to resolve first-mover bias in the linear regime, and remains the most effective mitigation under nonlinear data-generating processes. Both our proposed method, DASH (Diversified Aggregation of SHAP), and simple seed-averaging (Stochastic Retrain) restore stability by breaking the sequential dependency chain, confirming that the operative mechanism is independence between explained models. At rho=0.9, both achieve stability=0.977, while the single-best workflow degrades to 0.958 and the Large Single Model to 0.938. On the Breast Cancer dataset, DASH improves stability from 0.32 to 0.93 (+0.61) against a tree-count-matched baseline. DASH additionally provides two diagnostic tools -- the Feature Stability Index (FSI) and Importance-Stability (IS) Plot -- that detect first-mover bias without ground truth, enabling practitioners to audit explanation reliability before acting on feature rankings. Software and reproducible benchmarks are available at https://github.com/DrakeCaraker/dash-shap.

10.7LGApr 8
The Attribution Impossibility: No Feature Ranking Is Faithful, Stable, and Complete Under Collinearity

Drake Caraker, Bryan Arnold, David Rhoads

No feature ranking can be simultaneously faithful, stable, and complete when features are collinear. For collinear pairs, ranking reduces to a coin flip. We prove this impossibility, quantify it for four model classes, resolve it via ensemble averaging (DASH), and machine-verify it with 305 Lean 4 theorems. We characterize the complete attribution design space: exactly two families of methods exist -- faithful-complete methods (unstable, with rankings that flip up to 50% of the time) and ensemble methods like DASH (stable, reporting ties for symmetric features) -- and no method lies outside this dichotomy. The impossibility is quantitative: the attribution ratio diverges as 1/(1-rho^2) for gradient boosting, is infinite for Lasso, and converges for random forests. DASH (Diversified Aggregation of SHAP) is provably Pareto-optimal among unbiased aggregations, achieving the Cramer-Rao variance bound with a tight ensemble size formula. In a survey of 77 public datasets, 68% exhibit attribution instability. Switching to conditional SHAP does not escape the impossibility when features have equal causal effects. The framework includes practical diagnostics -- a Z-test workflow and single-model screening tool -- and has direct consequences for fairness auditing: SHAP-based proxy discrimination audits are provably unreliable under collinearity. The design space theorem, diagnostics, and impossibility are mechanically verified in Lean 4 (305 theorems from 16 axioms, 0 sorry) -- to our knowledge, the first formally verified impossibility in explainable AI.