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 comparison of different reject inference methods, e.g. augmentation, parceling, fuzzy parceling and the Heckman's model, is presented in @cite_26 . The parceling and fuzzy parceling methods are very similar. They first fit a logistic regression model using the accepted applications. Then they use this model to estimate the default probability for all rejected applications. The difference is that the parceling method chooses a threshold on the default probability to assign the unknown outcome @math to the rejected applications. On the other hand, the fuzzy parceling method assumes that each reject application has both outcomes @math and @math , with weights given by the fitted model using only the accepted applications. Finally, the parcelling (fuzzy parceling) method fits a new (weighted) logistic regression using both accepted and rejected applications. The results in @cite_26 do not show higher model performance using the reject inference methods. However, the parameter estimates are different when applying the augmentation and parceling approaches. Hence, reject inference has a statistical and economic impact on the final model in this case.
@cite_26
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Credit scoring models are commonly developed using only accepted Known Good Bad (G B) applications, called KGB model, because we only know the performance of those accepted in the past. Obviously, the KGB model is not indicative of the entire through-the-door population, and reject inference precisely attempts to address the bias by assigning an inferred G B status to rejected applications. In this paper, we discuss the pros and cons of various reject inference techniques, and pitfalls to avoid when using them. We consider a real dataset of a major French consumer finance bank to assess the effectiveness of the practice of using reject inference. To do that, we rely on the logistic regression framework to model probabilities to become good bad, and then validate the model performance with and without sample selection bias correction. Our main results can be summarized as follows. First, we show that the best reject inference technique is not necessarily the most complicated one: reweighting and parceling provide more accurate and relevant results than fuzzy augmentation and Heckmans two-stage correction. Second, disregarding rejected applications significantly impacts the forecast accuracy of the scorecard. Third, as the sum of standard errors dramatically reduces when the sample size increases, reject inference turns out to produce an improved representation of the population. Finally, reject inference appears to be an effective way to reduce overfitting in model selection.