The probability of default in internal ratings based (IRB) models in Basel II: an application of the rough sets methodology

El nuevo Acuerdo de Capital de junio de 2004 (Basilea II) da cabida e incentiva la implantación de modelos propios para la medición de los riesgos financieros en las entidades de crédito. En el trabajo que presentamos nos centramos en los modelos internos para la valoración del riesgo de crédito (IRB) y concretamente en la aproximación a uno de sus componentes: la probabilidad de impago (PD). Los métodos tradicionales usados para la modelización del riesgo de crédito, como son el análisis discriminante y los modelos logit y probit, parten de una serie de restricciones estadísticas. La metodología rough sets se presenta como una alternativa a los métodos estadísticos clásicos, salvando las limitaciones de estos. En nuestro trabajo aplicamos la metodología rought sets a una base de datos, compuesta por 106 empresas, solicitantes de créditos, con el objeto de obtener aquellos ratios que mejor discriminan entre empresas sanas y fallidas, así como una serie de reglas de decisión que ayudarán a detectar las operaciones potencialmente fallidas, como primer paso en la modelización de la probabilidad de impago. Por último, enfrentamos los resultados obtenidos con los alcanzados con el análisis discriminante clásico, para concluir que la metodología de los rough sets presenta mejores resultados de clasificación, en nuestro caso.The new Capital Accord of June 2004 (Basel II) opens the way for and encourages credit entities to implement their own models for measuring financial risks. In the paper presented, we focus on the use of internal rating based (IRB) models for the assessment of credit risk and specifically on the approach to one of their components: probability of default (PD). In our study we apply the rough sets methodology to a database composed of 106 companies, applicants for credit, with the object of obtaining those ratios that discriminate best between healthy and bankrupt companies, together with a series of decision rules that will help to detect the operations potentially in default, as a first step in modelling the probability of default. Lastly, we compare the results obtained against those obtained using classic discriminant análisis. We conclude that the rough sets methodology presents better risk classification results.Junta de Andalucía P06-SEJ-0153

A Rough Set Approach to Dimensionality Reduction for Performance Enhancement in Machine Learning

Machine learning uses complex mathematical algorithms to turn data set into a model for a problem domain. Analysing high dimensional data in their raw form usually causes computational overhead because the higher the size of the data, the higher the time it takes to process it. Therefore, there is a need for a more robust dimensionality reduction approach, among other existing methods, for feature projection (extraction) and selection from data set, which can be passed to a machine learning algorithm for optimal performance. This paper presents a generic mathematical approach for transforming data from a high dimensional space to low dimensional space in such a manner that the intrinsic dimension of the original data is preserved using the concept of indiscernibility, reducts, and the core of the rough set theory. The flue detection dataset available on the Kaggle website was used in this research for demonstration purposes. The original and reduced datasets were tested using a logistic regression machine learning algorithm yielding the same accuracy of 97% with a training time of 25 min and 11 min respectively

Attribute Selection Methods in Rough Set Theory

Attribute selection for rough sets is an NP-hard problem, in which fast heuristic algorithms are needed to find reducts. In this project, two reduct methods for rough set were implemented: particle swarm optimization and Johnson’s method. Both algorithms were evaluated with five different benchmarks from the KEEL repository. The results obtained from both implementations were compared with results obtained by the ROSETTA software using the same benchmarks. The results show that the implementations achieve better correction rates than ROSETTA

A Scalable and Effective Rough Set Theory based Approach for Big Data Pre-processing

International audienceA big challenge in the knowledge discovery process is to perform data pre-processing, specifically feature selection, on a large amount of data and high dimensional attribute set. A variety of techniques have been proposed in the literature to deal with this challenge with different degrees of success as most of these techniques need further information about the given input data for thresholding, need to specify noise levels or use some feature ranking procedures. To overcome these limitations, rough set theory (RST) can be used to discover the dependency within the data and reduce the number of attributes enclosed in an input data set while using the data alone and requiring no supplementary information. However, when it comes to massive data sets, RST reaches its limits as it is highly computationally expensive. In this paper, we propose a scalable and effective rough set theory-based approach for large-scale data pre-processing, specifically for feature selection, under the Spark framework. In our detailed experiments, data sets with up to 10,000 attributes have been considered, revealing that our proposed solution achieves a good speedup and performs its feature selection task well without sacrificing performance. Thus, making it relevant to big data