445 research outputs found
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
Infinitary Combinatory Reduction Systems: Confluence
We study confluence in the setting of higher-order infinitary rewriting, in
particular for infinitary Combinatory Reduction Systems (iCRSs). We prove that
fully-extended, orthogonal iCRSs are confluent modulo identification of
hypercollapsing subterms. As a corollary, we obtain that fully-extended,
orthogonal iCRSs have the normal form property and the unique normal form
property (with respect to reduction). We also show that, unlike the case in
first-order infinitary rewriting, almost non-collapsing iCRSs are not
necessarily confluent
Modularity of Convergence and Strong Convergence in Infinitary Rewriting
Properties of Term Rewriting Systems are called modular iff they are
preserved under (and reflected by) disjoint union, i.e. when combining two Term
Rewriting Systems with disjoint signatures. Convergence is the property of
Infinitary Term Rewriting Systems that all reduction sequences converge to a
limit. Strong Convergence requires in addition that redex positions in a
reduction sequence move arbitrarily deep. In this paper it is shown that both
Convergence and Strong Convergence are modular properties of non-collapsing
Infinitary Term Rewriting Systems, provided (for convergence) that the term
metrics are granular. This generalises known modularity results beyond metric
\infty
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
Canonized Rewriting and Ground AC Completion Modulo Shostak Theories : Design and Implementation
AC-completion efficiently handles equality modulo associative and commutative
function symbols. When the input is ground, the procedure terminates and
provides a decision algorithm for the word problem. In this paper, we present a
modular extension of ground AC-completion for deciding formulas in the
combination of the theory of equality with user-defined AC symbols,
uninterpreted symbols and an arbitrary signature disjoint Shostak theory X. Our
algorithm, called AC(X), is obtained by augmenting in a modular way ground
AC-completion with the canonizer and solver present for the theory X. This
integration rests on canonized rewriting, a new relation reminiscent to
normalized rewriting, which integrates canonizers in rewriting steps. AC(X) is
proved sound, complete and terminating, and is implemented to extend the core
of the Alt-Ergo theorem prover.Comment: 30 pages, full version of the paper TACAS'11 paper "Canonized
Rewriting and Ground AC-Completion Modulo Shostak Theories" accepted for
publication by LMCS (Logical Methods in Computer Science
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