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On a result of K. P. Hart about non-existence of measurable solutions to the discrete expectation maximization problem

Vladimir G. Pestov (2023)

Commentationes Mathematicae Universitatis Carolinae

It was shown that there is a statistical learning problem – a version of the expectation maximization (EMX) problem – whose consistency in a domain of cardinality continuum under the family of purely atomic probability measures and with finite hypotheses is equivalent to a version of the continuum hypothesis, and thus independent of ZFC. K. P. Hart had subsequently proved that no solution to the EMX problem can be Borel measurable with regard to an uncountable standard Borel structure on X , and...

On the comparison of some fuzzy clustering methods for privacy preserving data mining: Towards the development of specific information loss measures

Vicenç Torra, Yasunori Endo, Sadaaki Miyamoto (2009)

Kybernetika

Policy makers and researchers require raw data collected from agencies and companies for their analysis. Nevertheless, any transmission of data to third parties should satisfy some privacy requirements in order to avoid the disclosure of sensitive information. The areas of privacy preserving data mining and statistical disclosure control develop mechanisms for ensuring data privacy. Masking methods are one of such mechanisms. With them, third parties can do computations with a limited risk of disclosure....

On the learning of weights in some aggregation operators: the weigthed mean and OWA operators.

Vicenç Torra (1999)

Mathware and Soft Computing

We study the determination of weights for two types of aggregation operators: the weighted mean and the OWA operator. We assume that there is at our disposal a set of examples for which the outcome of the aggregation operator is known. In the case of the OWA operator, we compare the results obtained by our method with another one in the literature. We show that the optimal weighting vector is reached with less cost.

Operating on formal concept abstraction.

Anio O. Arigoni, Andrea Rossi (1994)

Mathware and Soft Computing

The subject of this paper regards a procedure to obtain the abstract form of concepts, directly from their most natural form, thus these can be efficiently learned and the possibility of operating formally on them is reached. The achievement of said type of form results also useful to compute conceptual parameters symbolic and numerical in nature.

Optimal estimators in learning theory

V. N. Temlyakov (2006)

Banach Center Publications

This paper is a survey of recent results on some problems of supervised learning in the setting formulated by Cucker and Smale. Supervised learning, or learning-from-examples, refers to a process that builds on the base of available data of inputs x i and outputs y i , i = 1,...,m, a function that best represents the relation between the inputs x ∈ X and the corresponding outputs y ∈ Y. The goal is to find an estimator f z on the base of given data z : = ( ( x ₁ , y ₁ ) , . . . , ( x m , y m ) ) that approximates well the regression function f ρ of...

Optimization of the maximum likelihood estimator for determining the intrinsic dimensionality of high-dimensional data

Rasa Karbauskaitė, Gintautas Dzemyda (2015)

International Journal of Applied Mathematics and Computer Science

One of the problems in the analysis of the set of images of a moving object is to evaluate the degree of freedom of motion and the angle of rotation. Here the intrinsic dimensionality of multidimensional data, characterizing the set of images, can be used. Usually, the image may be represented by a high-dimensional point whose dimensionality depends on the number of pixels in the image. The knowledge of the intrinsic dimensionality of a data set is very useful information in exploratory data analysis,...

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