MAC-Stack: Calibrated Multi-Model Ensemble Learning with Exact SHAP Attribution for Explainable Financial Distress Prediction

Multi-model ensembles of gradient-boosted trees are among the most accurate tools for financial distress prediction, but they are usually deployed as three loosely coupled steps: ad hoc fusion weights, post-hoc probability calibration and SHAP explanations of individual members. This paper proposes MAC-Stack (margin-additive calibrated stacking), which combines heterogeneous learners (regularized logistic regression, LightGBM, XGBoost, CatBoost and a liquidity-view expert) through one non-negative logistic stacker fitted on cross-fitted log-odds margins. Because fusion and calibration form a single affine map in log-odds space, calibration preserves the ensemble ranking, the ensemble Shapley attributions follow in closed form from the members' TreeSHAP values and sum exactly to the calibrated log-odds, and no attribution can contradict a unanimous sign of the members. On six tasks from two public benchmarks (five Polish forecasting horizons and a Taiwanese panel), evaluated on deduplicated data with nested stratified cross-validation, MAC-Stack achieved the best average rank in PR-AUC, ROC-AUC, Brier score and log-loss (mean PR-AUC 0.709, ROC-AUC 0.948). It exceeded a re-implementation of a recent log-odds/isotonic early-warning framework with its published settings by 0.111 PR-AUC on average (0.086–0.120 per task), whereas adding isotonic recalibration to MAC-Stack reduced PR-AUC by 0.025 without lowering the Brier score. The ensemble attributions were exact to within 5.0×10−6 in log-odds, showed no sign-consistency violations (versus up to 2.6% for unconstrained stacking) and recovered the leading distress drivers previously reported for the same horizon.