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. In this research, we use deep generative models to develop two new semi-supervised Bayesian models for reject inference in credit scoring, in which we model the data generating process to be dependent on a Gaussian mixture. The goal is to improve the classification accuracy in credit scoring models by adding reject applications. 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.
A Bayesian approach for reject inference is presented in @cite_45 . In this method the default probability is inferred from the missing data mechanism. The authors use the bound-collapse approach This model is originally presented in Sebastiani and Ramoni (2000) "Bayesian inference with missing data using bound and collapse". to estimate the posterior distribution over the score and class label, which is assumed to have a Dirichlet distribution as well as the marginal distribution of the missing class label. The reason for using the bound-collapse method is to avoid exhaustive numerical procedures, like the Gibbs Sampling, to estimate the posterior distributions in this model. Their results show that the Bayesian bound-collapse method perform better than the augmentation and Heckman's model.
@cite_45
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Reject inference is a method for inferring how a rejected credit applicant would have behaved had credit been granted. Credit-quality data on rejected applicants are usually missing not at random (MNAR). In order to infer credit-quality data MNAR, we propose a flexible method to generate the probability of missingness within a model-based bound and collapse Bayesian technique. We tested the method's performance relative to traditional reject-inference methods using real data. Results show that our method improves the classification power of credit scoring models under MNAR conditions.