Adapting Skew-Probabilistic Neural Networks for Credit-Risk Probability Estimation

Skew-probabilistic neural networks (SkewPNN) blend Parzen classification with a skewed kernel and metaheuristic tuning. We adapt them to credit-risk probabilities as CRASK (Credit-Risk Adaptive Skew-normal Kernel): a skew-normal kernel with class- and feature-specific bandwidths, categorical smoothing and an adaptive multiplier, fitted by a self-excluded conditional log-loss. The lender’s question is whether these probabilities change acceptance decisions and losses. In an exploratory, fold-local benchmark on seven public credit data sets, CRASK with exact kernel sums improves AUC-ROC over the grid-tuned published-kernel SkewPNN baseline on average and on five of seven; with sums truncated to 150 neighbours, it improves log-loss on all seven after the same isotonic recalibration, and mean realised profit on the four outcome-labelled data sets. Logistic regression is ahead on average discrimination; tuned boosting, an explainable boosting machine and a tabular foundation model are ahead on discrimination, probability quality and profit. The raw posterior is over-dispersed (mean calibration slope 0.38); the recalibrated pipeline is the proposed probability model. In the rules tested, the fitted density adds nothing beyond a nearest-neighbour distance. In a retrospective comparison across one lender’s origination cohorts, not a real-time test, ranking transfers and the calibration loss lies at the clipped extreme blocks of the isotonic map.