Credit scoring models based on accepted applications may be biased and their consequences can have a statistical and economic impact. Reject inference is the process of attempting to infer the creditworthiness status of the rejected applications. Inspired by the promising results of semi-supervised deep generative models, this research develops two novel Bayesian models for reject inference in credit scoring combining Gaussian mixtures and auxiliary variables in a semi-supervised framework with generative models. To the best of our knowledge this is the first study coupling these concepts together. The goal is to improve the classification accuracy in credit scoring models by adding reject applications. Further, our proposed models infer the unknown creditworthiness of the rejected applications by exact enumeration of the two possible outcomes of the loan (default or non-default). The efficient stochastic gradient optimization technique used in deep generative models makes our models suitable for large data sets. Finally, the experiments in this research show that our proposed models perform better than classical and alternative machine learning models for reject inference in credit scoring, and that model performance increases with the amount of data used for model training.

基于接受的申请的信用评分模型可能会有偏差，其后果可能会产生统计和经济影响。拒绝推断是尝试推断被拒绝的应用程序的信誉状态的过程。受半监督深度生成模型令人鼓舞的结果的启发，本研究开发了两种新颖的贝叶斯模型，用于在信用评分中将高斯混合和辅助变量结合在生成模型的半监督框架中进行信用评分。据我们所知，这是将这些概念结合在一起的第一个研究。目的是通过添加拒绝申请来提高信用评分模型中的分类准确性。进一步，我们提出的模型通过精确枚举贷款的两种可能的结果（违约或非违约）来推断被拒绝申请的未知信用度。深度生成模型中使用的高效随机梯度优化技术使我们的模型适用于大型数据集。最后，本研究中的实验表明，对于信用评分中的拒绝推理，我们提出的模型的性能优于经典和替代机器学习模型，并且模型性能随着用于模型训练的数据量的增加而提高。