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.
In @cite_42 Gaussian mixture models (GMM) are used for density estimation of the default probability. The idea is that each component in the mixture density models a class-conditional distribution. Then, the model parameters are estimated using the expectation-maximization (EM) algorithm, which can estimate the parameters even when the class labels for the rejected applications are missing. The EM algorithm is also used for reject inference in @cite_8 . Both papers report high model performance. However, the results in @cite_42 are based on artificial data and @cite_8 only judge performance based on the Confusion matrix. Finally, the major limitation of the EM algorithm is that we need to be able to estimate the expectation over the latent variables. We show in Section that deep generative models circumvent this restriction by approximation.
@cite_42 @cite_8
2005213340 2055625998
Reject inference is the process of estimating the risk of defaulting for loan applicants that are rejected under the current acceptance policy. We propose a new reject inference method based on mixture modeling, that allows the meaningful inclusion of the rejects in the estimation process. We describe how such a model can be estimated using the EM algorithm. An experimental study shows that inclusion of the rejects can lead to a substantial improvement of the resulting classification rule. Copyright © 1999 John Wiley & Sons, Ltd. Reject inference is one of the key processes required to build relevant credit scorecard models. Reject inference is used to infer the good or bad loan status to credit applicants that were rejected by the financial institution. If rejected applicants data is not used in the updating of the credit scoring model, the model is biased because it will not be representative of the entire applicant population. Many reject inference techniques perform an extrapolation method to infer the good or bad loan status of the rejected applicants. The issues with extrapolation are discussed, and this study provides a novel reject inference technique in which the rejected applicants are included in the model estimation process. The extrapolation problem is avoided using the methodology in this paper. The newly proposed reject inference technique is shown to outperform the standard extrapolation technique using a simulation study.