Comprehensible credit scoring models using rule extraction from support vector machines.

In recent years, Support Vector Machines (SVMs) were successfully applied to a wide range of applications. Their good performance is achieved by an implicit non-linear transformation of the original problem to a high-dimensional (possibly infinite) feature space in which a linear decision hyperplane is constructed that yields a nonlinear classifier in the input space. However, since the classifier is described as a complex mathematical function, it is rather incomprehensible for humans. This opacity property prevents them from being used in many real- life applications where both accuracy and comprehensibility are required, such as medical diagnosis and credit risk evaluation. To overcome this limitation, rules can be extracted from the trained SVM that are interpretable by humans and keep as much of the accuracy of the SVM as possible. In this paper, we will provide an overview of the recently proposed rule extraction techniques for SVMs and introduce two others taken from the artificial neural networks domain, being Trepan and G-REX. The described techniques are compared using publicly avail- able datasets, such as Ripley's synthetic dataset and the multi-class iris dataset. We will also look at medical diagnosis and credit scoring where comprehensibility is a key requirement and even a regulatory recommendation. Our experiments show that the SVM rule extraction techniques lose only a small percentage in performance compared to SVMs and therefore rank at the top of comprehensible classification techniques.Credit; Credit scoring; Models; Model; Applications; Performance; Space; Decision; Yield; Real life; Risk; Evaluation; Rules; Neural networks; Networks; Classification; Research;

Country corruption analysis with self organizing maps and support vector machines.

During recent years, the empirical research on corruption has grown considerably. Possible links between government corruption and terrorism have attracted an increasing interest in this research field. Most of the existing literature discusses the topic from a socio-economical perspective and only few studies tackle this research field from a data mining point of view. In this paper, we apply data mining techniques onto a cross-country database linking macro-economical variables to perceived levels of corruption. In the first part, self organizing maps are applied to study the interconnections between these variables. Afterwards, support vector machines are trained on part of the data and used to forecast corruption for other countries. Large deviations for specific countries between these models' predictions and the actual values can prove useful for further research. Finally, projection of the forecasts onto a self organizing map allows a detailed comparison between the different models' behavior.cross-country;

Benchmarking least squares support vector machine classifiers.

In Support Vector Machines (SVMs), the solution of the classification problem is characterized by a ( convex) quadratic programming (QP) problem. In a modified version of SVMs, called Least Squares SVM classifiers (LS-SVMs), a least squares cost function is proposed so as to obtain a linear set of equations in the dual space. While the SVM classifier has a large margin interpretation, the LS-SVM formulation is related in this paper to a ridge regression approach for classification with binary targets and to Fisher's linear discriminant analysis in the feature space. Multiclass categorization problems are represented by a set of binary classifiers using different output coding schemes. While regularization is used to control the effective number of parameters of the LS-SVM classifier, the sparseness property of SVMs is lost due to the choice of the 2-norm. Sparseness can be imposed in a second stage by gradually pruning the support value spectrum and optimizing the hyperparameters during the sparse approximation procedure. In this paper, twenty public domain benchmark datasets are used to evaluate the test set performance of LS-SVM classifiers with linear, polynomial and radial basis function (RBF) kernels. Both the SVM and LS-SVM classifier with RBF kernel in combination with standard cross-validation procedures for hyperparameter selection achieve comparable test set performances. These SVM and LS-SVM performances are consistently very good when compared to a variety of methods described in the literature including decision tree based algorithms, statistical algorithms and instance based learning methods. We show on ten UCI datasets that the LS-SVM sparse approximation procedure can be successfully applied.least squares support vector machines; multiclass support vector machines; sparse approximation; discriminant-analysis; sparse approximation; learning algorithms; classification; framework; kernels; time; SISTA;

Support Vector Machines for Credit Scoring and discovery of significant features

The assessment of risk of default on credit is important for financial institutions. Logistic regression and discriminant analysis are techniques traditionally used in credit scoring for determining likelihood to default based on consumer application and credit reference agency data. We test support vector machines against these traditional methods on a large credit card database. We find that they are competitive and can be used as the basis of a feature selection method to discover those features that are most significant in determining risk of default. 1

Addressing preference heterogeneity in public health policy by combining Cluster Analysis and Multi-Criteria Decision Analysis: Proof of Method.

The use of subgroups based on biological-clinical and socio-demographic variables to deal with population heterogeneity is well-established in public policy. The use of subgroups based on preferences is rare, except when religion based, and controversial. If it were decided to treat subgroup preferences as valid determinants of public policy, a transparent analytical procedure is needed. In this proof of method study we show how public preferences could be incorporated into policy decisions in a way that respects both the multi-criterial nature of those decisions, and the heterogeneity of the population in relation to the importance assigned to relevant criteria. It involves combining Cluster Analysis (CA), to generate the subgroup sets of preferences, with Multi-Criteria Decision Analysis (MCDA), to provide the policy framework into which the clustered preferences are entered. We employ three techniques of CA to demonstrate that not only do different techniques produce different clusters, but that choosing among techniques (as well as developing the MCDA structure) is an important task to be undertaken in implementing the approach outlined in any specific policy context. Data for the illustrative, not substantive, application are from a Randomized Controlled Trial of online decision aids for Australian men aged 40-69 years considering Prostate-specific Antigen testing for prostate cancer. We show that such analyses can provide policy-makers with insights into the criterion-specific needs of different subgroups. Implementing CA and MCDA in combination to assist in the development of policies on important health and community issues such as drug coverage, reimbursement, and screening programs, poses major challenges -conceptual, methodological, ethical-political, and practical - but most are exposed by the techniques, not created by them

Credit Risk Management: basic concepts: financial risk components, rating analysis, models, economic and regulatory capital

Credit Risk Management: Basic Concepts is the first book of a series of three with the objective of providing an overview of all aspects, steps, and issues that should be considered when undertaking credit risk management, including the Basel II Capital Accord, which all major banks must comply with in 2008. The introduction of the recently suggested Basel II Capital Accord has raised many issues and concerns about how to appropriately manage credit risk. Managing credit risk is one of the next big challenges facing financial institutions. The importance and relevance of efficiently managing credit risk is evident from the huge investments that many financial institutions are making in this area, the booming credit industry in emerging economies (e.g. Brazil, China, India, ...), the many events (courses, seminars, workshops, ...) that are being organised on this topic, and the emergence of new academic journals and magazines in the field (e.g. Journal of Credit Risk, Journal of Risk Model Validation, Journal of Risk Management in Financial Institutions, ...). Basic Concepts provides the introduction to the concepts, techniques, and practical examples to guide both young and experienced practitioners and academics in the fascinating, but complex world of risk modelling. Financial risk management, an area of increasing importance with the recent Basel II developments, is discussed in terms of practical business impact and the increasing profitability competition, laying the foundation for books II and III. <br/

Identification of the Circulant Modulated Poisson Process: a Time Domain Approach

In this paper we discuss a new time domain method for the traffic identification problem in ATM networks. Our identification approach for the circulant modulated Poisson process (CMPP) consists of two steps: the identification of the first order parameters and the determination of the circulant stochastic matrix which matches the second order statistics of the data

From linear to non-linear kernel based classifiers for bankruptcy prediction

Bankruptcy prediction has been a topic of research for decades, both within the financial and the academic world. The implementations of international financial and accounting standards, such as Basel II and IFRS, as well as the recent credit crisis, have accentuated this topic even further. This paper describes both regularized and non-linear kernel variants of traditional discriminant analysis techniques, such as logistic regression, Fisher discriminant analysis (FDA) and quadratic discriminant analysis (QDA). Next to a systematic description of these variants, we contribute to the literature by introducing kernel QDA and providing a comprehensive benchmarking study of these classification techniques and their regularized and kernel versions for bankruptcy prediction using 10 real-life data sets. Performance is compared in terms of binary classification accuracy, relevant for evaluating yes/no credit decisions and in terms of classification accuracy, relevant for pricing differentiated credit granting. The results clearly indicate the significant improvement for kernel variants in both percentage correctly classified (PCC) test instances and area under the ROC curve (AUC), and indicate that bankruptcy problems are weakly non-linear. On average, the best performance is achieved by LSSVM, closely followed by kernel quadratic discriminant analysis. Given the high impact of small improvements in performance, we show the relevance and importance of considering kernel techniques within this setting. Further experiments with backwards input selection improve our results even further. Finally, we experimentally investigate the relative ranking of the different categories of variables: liquidity, solvency, profitability and various, and as such provide new insights into the relative importance of these categories for predicting financial distress

Stochastic System Identification for ATM Network Traffic Models: a Time Domain Approach

In this paper we discuss a time domain approach for traffic identification problems in ATM networks, for which we propose to identify a Markov modulated Poisson process and a circulant Markov modulated Poisson process, based on unconstrained optimisation algorithms. By applying a nonnegative least squares algorithm we obtain in a very fast way a description of the first order statistics of the data. This first order characterisation also includes an estimate for the model order. Consequently, we manage to identify a Markov modulated Poisson process without a priori knowledge of the model order. Keywords: traffic identification, Markov modulated Poisson process, mixture distributions, ATM, subspace identification, parameter estimation. 1 Research Assistant with the I.W.T. (Flemish Institute for Scientific and Technological Research in Industry). 2 Research Assistant with the F.W.O. (Fund for Scientific Research-Flanders). 3 Senior Research Associate with the F.W.O. (Fund for Scient..