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.
Support vector machines are used in @cite_19 to extend the self-training (SL) algorithm, by adding the hypothesis that the rejected applications are riskier The self-training algorithm is an iterative approach where highly confident predictions about the unlabeled data are added to retrain the model. This procedure is repeated as many times as the user specify it. The main criticism of this method is that it can strengthen poor predictions @cite_13 . . Specifically, their approach iteratively adds rejected applications with higher confidence, i.e. vectors far from the decision-hyperplane, to retrain a SVM (just as in the SL algorithm). However, vectors close to the hyperplane are penalized since the uncertainty about their true label is higher. Their proposed iterative approach shows superior performance compared to other reject inference configurations using SVMs, including semi-supervised support vector machines (S3VM). In addition to higher performance, the iterative procedure in @cite_19 is faster than the S3VM.
@cite_19 @cite_13
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This paper presents a novel semi-supervised approach that determines a linear predictor using Support Vector Machines (SVMs) and incorporates information on rejected loans, assuming that the labeled data (accepted applicants) and unlabeled data (rejected applicants) are not drawn from the same distribution. We use a self-training algorithm in order to predict how likely a rejected applicant would have repaid had the applicant received credit. A modification to the self-training algorithm based on Platt's probabilistic output for SVMs is introduced. Experiments with two toy data sets; one well-known benchmark Credit Scoring data set, and one project performed for a Chilean financial institution demonstrate that our approach accomplishes the best classification performance compared to well-known reject inference alternatives and another state-of-the-art semi-supervised method for SVMs (Transductive SVM). The ever-increasing size of modern data sets combined with the difficulty of obtaining label information has made semi-supervised learning one of the problems of significant practical importance in modern data analysis. We revisit the approach to semi-supervised learning with generative models and develop new models that allow for effective generalisation from small labelled data sets to large unlabelled ones. Generative approaches have thus far been either inflexible, inefficient or non-scalable. We show that deep generative models and approximate Bayesian inference exploiting recent advances in variational methods can be used to provide significant improvements, making generative approaches highly competitive for semi-supervised learning.