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Dissimilarites de type spherique et positionnement multidimensionnel normé

Farid Beninel (2010)

RAIRO - Operations Research

Our concern here, is the characterization of dissimilarity indexes defined over finite sets, whose spatial representation is spherical. Consequently, we propose a methodology (Normed MultiDimensional Scaling) to determine the spherical euclidean representation of a set of items best accounting for the initial dissimilarity between items. This methodology has the advantage of being graphically readable on individual qualities of projection like the normed PCA, of which it constitutes a generalization....

Equivalence of compositional expressions and independence relations in compositional models

Francesco M. Malvestuto (2014)

Kybernetika

We generalize Jiroušek’s (right) composition operator in such a way that it can be applied to distribution functions with values in a “semifield“, and introduce (parenthesized) compositional expressions, which in some sense generalize Jiroušek’s “generating sequences” of compositional models. We say that two compositional expressions are equivalent if their evaluations always produce the same results whenever they are defined. Our first result is that a set system ℋ is star-like with centre X if...

High level quantile approximations of sums of risks

A. Cuberos, E. Masiello, V. Maume-Deschamps (2015)

Dependence Modeling

The approximation of a high level quantile or of the expectation over a high quantile (Value at Risk (VaR) or Tail Value at Risk (TVaR) in risk management) is crucial for the insurance industry.We propose a new method to estimate high level quantiles of sums of risks. It is based on the estimation of the ratio between the VaR (or TVaR) of the sum and the VaR (or TVaR) of the maximum of the risks. We show that using the distribution of the maximum to approximate the VaR is much better than using...

Interpretation of pattern classification results, obtained from a test set

Edgard Nyssen (1998)

Kybernetika

The present paper presents and discusses a methodology for interpreting the results, obtained from the application of a pattern classifier to an independent test set. It addresses the problem of testing the random classification null hypothesis in the multiclass case, by introducing an exact probability technique. The discussion of this technique includes the presentation of an interval estimation technique for the probability of correct classification, which is slightly more accurate than the ones...

Linear conform transformation: Errors in both coordinate systems

Lubomír Kubáček, Ludmila Kubáčková, Jan Ševčík (2002)

Applications of Mathematics

Linear conform transformation in the case of non-negligible errors in both coordinate systems is investigated. Estimation of transformation parameters and their statistical properties are described. Confidence ellipses of transformed nonidentical points and cross covariance matrices among them and identical points are determined. Some simulation for a verification of theoretical results are presented.

Notion of information and independent component analysis

Una Radojičić, Klaus Nordhausen, Hannu Oja (2020)

Applications of Mathematics

Partial orderings and measures of information for continuous univariate random variables with special roles of Gaussian and uniform distributions are discussed. The information measures and measures of non-Gaussianity including the third and fourth cumulants are generally used as projection indices in the projection pursuit approach for the independent component analysis. The connections between information, non-Gaussianity and statistical independence in the context of independent component analysis...

On computations with causal compositional models

Vladislav Bína, Radim Jiroušek (2015)

Kybernetika

The knowledge of causal relations provides a possibility to perform predictions and helps to decide about the most reasonable actions aiming at the desired objectives. Although the causal reasoning appears to be natural for the human thinking, most of the traditional statistical methods fail to address this issue. One of the well-known methodologies correctly representing the relations of cause and effect is Pearl's causality approach. The paper brings an alternative, purely algebraic methodology...

On factorization of probability distributions over directed graphs

František Matúš, Bernhard Strohmeier (1998)

Kybernetika

Four notions of factorizability over arbitrary directed graphs are examined. For acyclic graphs they coincide and are identical with the usual factorization of probability distributions in Markov models. Relations between the factorizations over circuits are described in detail including nontrivial counterexamples. Restrictions on the cardinality of state spaces cause that a factorizability with respect to some special cyclic graphs implies the factorizability with respect to their, more simple,...

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