Advances in credit scoring: combining performance and interpretation in kernel discriminant analysis. (English) Zbl 1414.62421

Summary: Due to the recent financial turmoil, a discussion in the banking sector about how to accomplish long term success, and how to follow an exhaustive and powerful strategy in credit scoring is being raised up. Recently, the significant theoretical advances in machine learning algorithms have pushed the application of kernel-based classifiers, producing very effective results. Unfortunately, such tools have an inability to provide an explanation, or comprehensible justification, for the solutions they supply. In this paper, we propose a new strategy to model credit scoring data, which exploits, indirectly, the classification power of the kernel machines into an operative field. A reconstruction process of the kernel classifier is performed via linear regression, if all predictors are numerical, or via a general linear model, if some or all predictors are categorical. The loss of performance, due to such approximation, is balanced by better interpretability for the end user, which is able to order, understand and to rank the influence of each category of the variables set in the prediction. An Italian bank case study has been illustrated and discussed; empirical results reveal a promising performance of the introduced strategy.


62P05 Applications of statistics to actuarial sciences and financial mathematics
62H30 Classification and discrimination; cluster analysis (statistical aspects)
Full Text: DOI


[1] Abdou, H.; Pointon, J.; Masry, A., Neural nets versus conventional techniques in credit scoring in Egyptian banking, Expert Syst Appl, 35, 1275-1292, (2008)
[2] Akkoç, S., An empirical comparison of conventional techniques, neural networks and the three stage hybrid adaptive neuro fuzzy inference system (anfis) model for credit scoring analysis: The case of Turkish credit card data, Eur J Oper Res, 222, 168-178, (2012)
[3] Altman, E.; Sabato, G., Modeling credit risk for SMES: evidence from U.S. market, ABACUS, 43, 332-357, (2007)
[4] Altman, E.; Sabato, G.; Wilson, N., The value of non-financial information in small and medium-sized enterprise risk management, J Credit Risk, 6, 95-127, (2010)
[5] Angelini, E.; Tollo, G.; Roli, A., A neural network approach for credit risk evaluation, Q Rev Econ Finance, 48, 733-755, (2008)
[6] Back B, Laitinen T, Sere K, van Wezel M (1996) Choosing bankruptcy predictors using discriminant analysis, logit analysis, and genetic algorithms. In: Proceedings of the 1st international meeting on artificial intelligence in accounting, finance and tax, pp 337-356
[7] Baesens, B.; Gestel, T.; Viaene, S.; Stepanova, M.; Suykens, J.; Vanthienen, J., Benchmarking state-of-the-art classification algorithms for credit scoring, J Oper Res Soc, 54, 627-635, (2003) · Zbl 1097.91516
[8] Barakat, N.; Bradley, AP, Evaluating consumer loans using neural networks, Neurocomputing, 74, 178-190, (2010)
[9] Basel I (2011) A global regulatory framework for more resilient banks and banking systems
[10] Baudat, G.; Anouar, F., Generalized discriminant analysis using a kernel approach, Neural Comput, 12, 2385-2404, (2000)
[11] Benzécri J (1973) L’analyse des données, No. v. 2. L’analyse des données, Dunod
[12] Benzécri JP (1979) Sur le calcul des taux d’inertie dans l’analyse d’un questionnaire, addendum et erratum à (bin. mult.). Cah Anal Données 4(3):377-378
[13] Bozdogan, H.; Camillo, F.; Liberati, C.; Zani, S. (ed.); Cerioli, A. (ed.); Riani, M. (ed.); Vichi, M. (ed.), On the choice of the kernel function in kernel discriminant analysis using information complexity, 11-21, (2006), Berlin
[14] Cawley, GC; Talbot, NLC, Efficient leave-one-out cross-validation of kernel Fisher discriminant classifiers, Pattern Recognit, 36, 2585-2592, (2003) · Zbl 1059.68101
[15] Chapelle, O.; Vapnik, V.; Bousquet, O.; Mukherjee, S., Choosing multiple parameters for support vector machines, Mach Learn, 46, 131-159, (2002) · Zbl 0998.68101
[16] Cunningham P, Doyle D, Loughrey J (2003) An evaluation of the usefulness of case-based explanation. In: Langley P (ed) Proceedings of the fifth international conference on case-based reasoning (ICCBR 2003). Morgan Kaufmann, New York, pp 122-130 · Zbl 1045.68682
[17] Derelioğlu, G.; Gürgen, F., Knowledge discovery using neural approach for SME+S credit risk analysis problem in Turkey, Expert Syst Appl, 38, 9313-9318, (2011)
[18] Duda RO, Hart P, Stork D (2000) Pattern classification. Wiley, New York · Zbl 0968.68140
[19] Friedman, JH, Regularized discriminant analysis, J Am Stat Assoc, 84, 165-175, (1989)
[20] Gönen GB, Gönen M, Gürgen F (2012) Credit rating analysis with support vector machines and neural networks: a market comparative study. Expert Syst Appl 39:11709-11717
[21] Greenacre MJ (1984) Theory and applications of correspondence analysis. Academic Press, London · Zbl 0555.62005
[22] Grunet J, Norden L, Weber M (2008) The role of non-financial factors in internal credit ratings. J Bank Finance 2:509-531
[23] Hill P, Wilson N (2007) Predicting the insolvency of unlisted companies. In: Working paper, CMRC, Leeds University
[24] Hosmer D, Lemeshow S (1989) Applied logistic regression. Wiley, New York · Zbl 0967.62045
[25] Huang, CL; Wang, CJ, A GA-based feature selection and parameters optimization for support vector machines, Expert Syst Appl, 31, 231-240, (2006)
[26] Huang, Z.; Chen, H.; Hsu, CJ; Chen, WH; Wu, S., Credit rating analysis with support vector machines and neural networks: a market comparative study, Decis Support Syst, 37, 543-558, (2004)
[27] Huang, YM; Hung, C.; Jiau, HC, Evaluation of neural networks and data mining methods on a credit assessment task for class imbalance problem, Nonlinear Anal Real World Appl, 7, 720-747, (2006) · Zbl 1160.91368
[28] Huang, CL; Chen, MC; Wang, CJ, Credit scoring with a data mining approach based on support vector machines, Expert Syst Appl, 33, 847-856, (2007)
[29] Karush W (1939) Minima of functions of several variables with inequalities as side constraints. M.sc. thesis, University of Chicago
[30] Khandani, AE; Kim, AJ; Lo, AW, Consumer credit-risk models via machine-learning algorithms, J Bank Finance, 34, 2767-2787, (2010)
[31] Khashman, A., Neural networks for credit risk evaluation: investigation of different neural models and learning schemes, Expert Syst Appl, 37, 6233-6239, (2010)
[32] Kim, HS; Sohn, SY, Support vector machines for default prediction of SMES based on technology credit, Eur J Oper Res, 201, 838-846, (2010) · Zbl 1173.90458
[33] Kuhn, HW; Tucker, AW, Nonlinear programming, 481-492, (1951), Berkeley
[34] Lebart L, Morineau A, Warwick K (1984) Multivariate descriptive statistical analysis. Wiley, New York · Zbl 0658.62069
[35] Liberati, C.; Howe, A.; Bozdogan, H., Data adaptive simultaneous parameter and kernel selection in kernel discriminant analysis (KDA) using information complexity, J Pattern Recognit Res, 4, 119-132, (2009)
[36] Malhotra, R.; Malhotra, DK, Evaluating consumer loans using neural networks, Omega, 31, 83-96, (2003)
[37] Mavri, M.; Angelis, V.; Loannou, G., A two-stage dynamic credit scoring model based on customers profiles and time horizon, J Financ Serv Market, 13, 17-27, (2008)
[38] Mays E (2004) Credit scoring for risk managers. The handbook for lenders, Thomson Learning
[39] Mercer J (1909) Functions of positive and negative type and their connection with the theory of integral equations. Philos Trans R Soc Lond · JFM 40.0408.02
[40] Mika S, Rätsch G, Weston J, Schölkopf B, Müller KR (1999) Fisher discriminant analysis with kernels. In: Neural networks for signal processing, vol IX. Proceedings of the 1999 IEEE signal processing society workshop, pp 41-48
[41] Müller, KR; Mika, S.; Rätsch, G.; Tsuda, K.; Schölkopf, B., An introduction to kernel-based learning algorithms, IEEE Trans Neural Netw, 2, 181-201, (2001)
[42] Ong, C.; Huang, J.; Tzeng, GH, Building credit scoring models using genetic programming, Expert Syst Appl, 29, 41-47, (2005)
[43] Peel, M.; Peel, D., A multi-logit approach to predicting corporate failure—some evidence for the UK corporate sector, Omega Int J Manag Sci, 16, 309-318, (1989)
[44] Ping Y, Yongheng L (2011) Neighborhood rough set and SVM based hybrid credit scoring classifier. Expert Syst Appl 38:11300-11304
[45] Press S (1975) Estimation of a normal covariance matrix. Santa Monica Rand Corporation, Santa Monica
[46] Saporta G (1977) Une méthode et un programme d’analyse discriminante sur variables qualitatives. In: Diday E (ed) Analyse des Données et Informatique, INRIA, pp 201-210
[47] Schölkopf B, Burges C, Smola AJ (1999a) Advances in kernel methods. MIT Press, Cambrige · Zbl 0935.68084
[48] Schölkopf, B.; Mika, S.; Burges, C.; Knirsch, P.; Müller, KR; Rätsch, G.; Smola, AJ, Input space versus feature space in kernel-based methods, IEEE Trans Neural Netw, 5, 1000-1017, (1999)
[49] Shi, Y.; Wise, M.; Luo, M.; Lin, Y.; Koksalan, M. (ed.); Zionts, S. (ed.), Data mining in credit card portfolio management: a multiple criteria decision making approach, 427-436, (2001), Heidelberg · Zbl 1027.90523
[50] Shi, Y.; Peng, Y.; Xu, W.; Tang, X., Data mining via multiple criteria linear programming: applications in credit card portfolio management, Int J Inf Technol Decis Mak, 1, 131-151, (2002)
[51] Smalz, R.; Conrad, M., Combining evolution with credit apportionment: a new learning algorithm for neural nets, Neural Netw, 7, 341-351, (1994)
[52] Soares C, Brazdil PB (2006) Selecting parameters of SVM using meta-learning and kernel matrix-based meta-features. In: Proceedings of the 2006 ACM symposium on applied computing, ACM, New York, SAC ’06, pp 564-568. doi:10.1145/1141277.1141408
[53] Suykens, J.; Vandewalle, J., Least squares support vector machine classifiers, Neural Process Lett, 9, 293-300, (1999) · Zbl 0958.93042
[54] Suykens JAK, Van Gestel T, De Brabanter J, De Moor B, Vandewalle J (2002) Least squares support vector machines. World Scientific, Singapore · Zbl 1017.93004
[55] Thomaz, C.; Boardman, J.; Hill, D.; Hajnal, J.; Edwards, D.; Rutherford, M.; Gillies, D.; Rueckert, D., Using a maximum uncertainty LDA-based approach to classify and analyse MR brain images, 291-300, (2004), Berlin
[56] Gestel, T.; Baesens, B.; Suykens, JAK; Poel, D.; Baestaens, DE; Willekens, M., Bayesian kernel based classification for financial distress detection, Eur J Oper Res, 172, 979-1003, (2006) · Zbl 1111.90330
[57] Vapnik V (1995) The nature of statistical learning theory. Springer, New York · Zbl 0833.62008
[58] Vapnik V (1998) Statistical learning theory. Wiley, New York · Zbl 0935.62007
[59] Varetto, F., Genetic algorithms applications in the analysis of insolvency risk, J Bank Finance, 22, 1421-1439, (1998)
[60] Wiginton, JC, A note on the comparison of logit and discriminant models of consumer credit behavior, J Financ Quant Anal, 15, 757-770, (1980)
[61] Yao P, Wu C, Yang M (2009) Credit risk assessment model of commercial banks based on fuzzy neural network. In: Proceedings of the sixth international symposium on neural networks
[62] Yap BW, Ong SH, Husain N (2011) Using data mining to improve assessment of credit worthiness via credit scoring models. Expert Syst Appl 38:13274-13283
[63] Yoon, JS; Kwon, YS, A practical approach to bankruptcy prediction for small businesses: substituting the unavailable financial data for credit card sales information, Expert Syst Appl, 37, 3624-3629, (2010)
[64] Zhang K, Lan L, Wang Z, Moerchen F (2012) Scaling up kernel svm on limited resources: a low-rank linearization approach. J Mach Learn Res Proc Track 22:1425-1434
[65] Zhou, X.; Shi, W.; Tian, Y., Genetic algorithms applications in the analysis of insolvency risk, Expert Syst Appl, 38, 4272-4279, (2011)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.