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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We introduce a semi-supervised support vector machine (S3VM) method. Given a training set of labeled data and a working set of unlabeled data, S3VM constructs a support vector machine using both the training and working sets. We use S3VM to solve the transduction problem using overall risk minimization (ORM) posed by Vapnik. The transduction problem is to estimate the value of a classification function at the given points in the working set. This contrasts with the standard inductive learning problem of estimating the classification function at all possible values and then using the fixed function to deduce the classes of the working set data. We propose a general S3VM model that minimizes both the misclassification error and the function capacity based on all the available data. We show how the S3VM model for 1-norm linear support vector machines can be converted to a mixed-integer program and then solved exactly using integer programming. Results of S3VM and the standard 1-norm support vector machine approach are compared on ten data sets. Our computational results support the statistical learning theory results showing that incorporating working data improves generalization when insufficient training information is available. In every case, S3VM either improved or showed no significant difference in generalization compared to the traditional approach. 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). Linear support vector machines (SVM) are useful for classifying large-scale sparse data. Problems with sparse features are common in applications such as document classification and natural language processing. In this paper, we propose a novel coordinate descent algorithm for training linear SVM with the L2-loss function. At each step, the proposed method minimizes a one-variable sub-problem while fixing other variables. The sub-problem is solved by Newton steps with the line search technique. The procedure globally converges at the linear rate. As each sub-problem involves only values of a corresponding feature, the proposed approach is suitable when accessing a feature is more convenient than accessing an instance. Experiments show that our method is more efficient and stable than state of the art methods such as Pegasos and TRON. The Support Vector Machine (SVM) is a new and very promising classification technique developed by Vapnik and his group at AT &T Bell Labs. This new learning algorithm can be seen as an alternative training technique for Polynomial, Radial Basis Function and Multi-Layer Perceptron classifiers. An interesting property of this approach is that it is an approximate implementation of the Structural Risk Minimization (SRM) induction principle. The derivation of Support Vector Machines, its relationship with SRM, and its geometrical insight, are discussed in this paper. Training a SVM is equivalent to solve a quadratic programming problem with linear and box constraints in a number of variables equal to the number of data points. When the number of data points exceeds few thousands the problem is very challenging, because the quadratic form is completely dense, so the memory needed to store the problem grows with the square of the number of data points. Therefore, training problems arising in some real applications with large data sets are impossible to load into memory, and cannot be solved using standard non-linear constrained optimization algorithms. We present a decomposition algorithm that can be used to train SVM''s over large data sets. The main idea behind the decomposition is the iterative solution of sub-problems and the evaluation of, and also establish the stopping criteria for the algorithm. We present previous approaches, as well as results and important details of our implementation of the algorithm using a second-order variant of the Reduced Gradient Method as the solver of the sub-problems. As an application of SVM''s, we present preliminary results we obtained applying SVM to the problem of detecting frontal human faces in real images.