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.
This paper develops a branch-and-bound algorithm to solve the 2-norm soft margin semi-supervised support vector machine. First, the original problem is reformulated as a non-convex quadratically constrained quadratic programming problem with a simple structure. Then, we propose a new lower bound estimator which is conceptually simple and easy to be implemented in the branch-and-bound scheme. Since this estimator preserves both a high efficiency and a relatively good quality in the convex relaxation, it leads to a high total efficiency in the whole computational process. The numerical tests on both artificial and real-world data sets demonstrate the better effectiveness and efficiency of this proposed approach, which is compared to other well-known methods on different semi-supervised support vector machine models. Semi-supervised Support Vector Machines for reject inference are proposed.The method uses information of both the accepted and rejected applicants.The method deals with labelled and unlabelled classes of the outcome.The model is tested on real consumer loans with a low acceptance rate.Predictive accuracy is improved by the new model compared to traditional methods.