Probabilistic and Statistical Fuzzy Set Foundations of Competitive Exception Learning

15 Pages Posted: 21 Feb 2003

See all articles by J. van den Berg

J. van den Berg

Delft University of Technology, Faculty of Technology, Policy and Management, Section of ICT

W. M. van den Bergh

Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE); Erasmus Research Institute of Management (ERIM)

U. Kaymak

Erasmus University Rotterdam (EUR) - Faculty of Economics - Department of Computer Science; Erasmus Research Institute of Management (ERIM)

Date Written: March 2001 7,

Abstract

Recently, a Competitive Exception Learning Algorithm (CELA) was introduced [1, 2]. This algorithm establishes an optimal mapping from a (continuous) M-dimensional input sample space to an N-dimensional (continuous) output sample space. CELA is aimed to discover regimes (i.e. local behavior in the input sample space) for which the conditional probability distribution in the output sample space systematically deviates from the average unconditional distribution. Previous papers on CELA dealt with the introduction of the algorithm by sketching its background and by describing the algorithmic sub-steps. The algorithm was tested successfully on both simulated and real world data, mainly in the field of financial markets. However, until now a precise and firm theoretical foundation of CELA is still lacking. The current paper resolves this imperfection. The contribution to be made here is twofold. First, we present, in section 2, a probability theory and statistics of fuzzy sets which in itself is interesting. Second, we re-formulate, in section 3, the CELA-algorithm within the probabilistic fuzzy framework introduced. We finalize with a discussion and outlook.

Keywords: probability theory, statistics, fuzzy set, exception learning

JEL Classification: M, M11, R4, C19

Suggested Citation

van den Berg, J. and van den Bergh, W. M. and Kaymak, Uzay, Probabilistic and Statistical Fuzzy Set Foundations of Competitive Exception Learning (March 2001 7,). Available at SSRN: https://ssrn.com/abstract=370896

J. Van den Berg (Contact Author)

Delft University of Technology, Faculty of Technology, Policy and Management, Section of ICT ( email )

P.O. Box 5015
2600 GB Delft
Netherlands

HOME PAGE: http://tbm.tudelft.nl/index.php?id=30084&L=1

W. M. Van den Bergh

Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE) ( email )

Burgemeester Oudlaan 50
3062 PA Rotterdam, NL 3062 PA
Netherlands

Erasmus Research Institute of Management (ERIM)

P.O. Box 1738
3000 DR Rotterdam
Netherlands

Uzay Kaymak

Erasmus University Rotterdam (EUR) - Faculty of Economics - Department of Computer Science ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands

Erasmus Research Institute of Management (ERIM)

P.O. Box 1738
3000 DR Rotterdam
Netherlands

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