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 this research we propose a novel Bayesian inference approach for reject inference in credit scoring, which uses Gaussian mixture models and differs from @cite_45 @cite_42 in that our models are based on variational inference, neural networks, and stochastic gradient optimization. The main advantages of our proposed method are that (i) inference of the rejected applications is based on an approximation of the posterior distribution and on the exact enumeration of the two possible outcomes that the rejected applications could have taken, (ii) the models use a latent representation of the customers' data, which contain powerful information, and (iii) deep generative models scale to large data sets.
@cite_45 @cite_42
2298695453 2020821583 2101893470 1972671391
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. Many researchers see the need for reject inference in credit scoring models to come from a sample selection problem whereby a missing variable results in omitted variable bias. Alternatively, practitioners often see the problem as one of missing data where the relationship in the new model is biased because the behaviour of the omitted cases differs from that of those who make up the sample for a new model. To attempt to correct for this, differential weights are applied to the new cases. The aim of this paper is to see if the use of both a Heckman style sample selection model and the use of sampling weights, together, will improve predictive performance compared with either technique used alone. This paper will use a sample of applicants in which virtually every applicant was accepted. This allows us to compare the actual performance of each model with the performance of models which are based only on accepted cases. Despite having various attractive qualities such as high prediction accuracy and the ability to quantify uncertainty and avoid over-fitting, Bayesian Matrix Factorization has not been widely adopted because of the prohibitive cost of inference. In this paper, we propose a scalable distributed Bayesian matrix factorization algorithm using stochastic gradient MCMC. Our algorithm, based on Distributed Stochastic Gradient Langevin Dynamics, can not only match the prediction accuracy of standard MCMC methods like Gibbs sampling, but at the same time is as fast and simple as stochastic gradient descent. In our experiments, we show that our algorithm can achieve the same level of prediction accuracy as Gibbs sampling an order of magnitude faster. We also show that our method reduces the prediction error as fast as distributed stochastic gradient descent, achieving a 4.1 improvement in RMSE for the Netflix dataset and an 1.8 for the Yahoo music dataset. If a credit scoring model is built using only applicants who have been previously accepted for credit such a non-random sample selection may produce bias in the estimated model parameters and accordingly the model's predictions of repayment performance may not be optimal. Previous empirical research suggests that omission of rejected applicants has a detrimental impact on model estimation and prediction. This paper explores the extent to which, given the previous cutoff score applied to decide on accepted applicants, the number of included variables influences the efficacy of a commonly used reject inference technique, reweighting. The analysis benefits from the availability of a rare sample, where virtually no applicant was denied credit. The general indication is that the efficacy of reject inference is little influenced by either model leanness or interaction between model leanness and the rejection rate that determined the sample. However, there remains some hint that very lean models may benefit from reject inference where modelling is conducted on data characterized by a very high rate of applicant rejection.