Balancing Performance and Reject Inclusion: A Novel Confident Inlier Extrapolation Framework for Credit Scoring

TL;DR

This work tackles sample bias in credit scoring caused by training on accepted applicants only. It proposes CI-EX, a semi-supervised, iterative framework that combines outlier detection with confidence-based labeling to selectively infer rejected data, aiming to reduce extrapolation bias. To assess RI performance, the paper introduces Area Under the Kickout ($AUK$) alongside traditional $AUC$ and Kickout metrics, and demonstrates that CI-EX delivers strong RI-specific gains while remaining competitive on $AUC$ across HomeCredit and Lending Club datasets. The findings underscore the potential of distribution-aware, confidence-guided extrapolation for fairer, more inclusive credit scoring, while highlighting trade-offs and directions for efficiency and broader validation.

Abstract

Reject Inference (RI) methods aim to address sample bias by inferring missing repayment data for rejected credit applicants. Traditional approaches often assume that the behavior of rejected clients can be extrapolated from accepted clients, despite potential distributional differences between the two populations. To mitigate this blind extrapolation, we propose a novel Confident Inlier Extrapolation framework (CI-EX). CI-EX iteratively identifies the distribution of rejected client samples using an outlier detection model and assigns labels to rejected individuals closest to the distribution of the accepted population based on probabilities derived from a supervised classification model. The effectiveness of our proposed framework is validated through experiments on two large real-world credit datasets. Performance is evaluated using the Area Under the Curve (AUC) as well as RI-specific metrics such as Kickout and a novel metric introduced in this work, denoted as Area under the Kickout. Our findings reveal that RI methods, including the proposed framework, generally involve a trade-off between AUC and RI-specific metrics. However, the proposed CI-EX framework consistently outperforms existing RI models from the credit literature in terms of RI-specific metrics while maintaining competitive performance in AUC across most experiments.

Figures (19)

• Figure 1: (A) Pipeline that discards rejected clients data, versus (B) pipeline that applies Reject Inference.
• Figure 2: Representation of CI-EX framework to perform Reject Inference.
• Figure 3: (A) Outside view of the pipeline. (B) Inside view of the Pipeline. The pipeline is fitted with the training set and used for pre-processing and classification on all datasets.
• Figure 4: Illustration of how the Kickout metric is calculated. TP stands for True Positives, FP for False Positives, TN for True Negatives, and FN for False Negatives.
• Figure 5: Correlation of $\pi$ value and the metrics studied.