Displaying similar documents to “From elementary martingale calculus to rigorous properties of mixtures of experts.”

Real-valued GCS classifier system

Łukasz Cielecki, Olgierd Unold (2007)

International Journal of Applied Mathematics and Computer Science

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Learning Classifier Systems (LCSs) have gained increasing interest in the genetic and evolutionary computation literature. Many real-world problems are not conveniently expressed using the ternary representation typically used by LCSs and for such problems an interval-based representation is preferable. A new model of LCSs is introduced to classify real-valued data. The approach applies the continous-valued context-free grammar-based system GCS. In order to handle data effectively, the...

Selection of variables in Discrete Discriminant Analysis

Anabela Marques, Ana Sousa Ferreira, Margarida G.M.S. Cardoso (2013)

Biometrical Letters

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In Discrete Discriminant Analysis one often has to deal with dimensionality problems. In fact, even a moderate number of explanatory variables leads to an enormous number of possible states (outcomes) when compared to the number of objects under study, as occurs particularly in the social sciences, humanities and health-related elds. As a consequence, classi cation or discriminant models may exhibit poor performance due to the large number of parameters to be estimated. In the present...

On the amount of information resulting from empirical and theoretical knowledge.

Igor Vajda, Arnost Vesely, Jana Zvarova (2005)

Revista Matemática Complutense

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We present a mathematical model allowing formally define the concepts of empirical and theoretical knowledge. The model consists of a finite set P of predicates and a probability space (Ω, S, P) over a finite set Ω called ontology which consists of objects ω for which the predicates π ∈ P are either valid (π(ω) = 1) or not valid (π(ω) = 0). Since this is a first step in this area, our approach is as simple as possible, but still nontrivial, as it is demonstrated by examples. More realistic...

Estimation of nuisance parameters for inference based on least absolute deviations

Wojciech Niemiro (1995)

Applicationes Mathematicae

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Statistical inference procedures based on least absolute deviations involve estimates of a matrix which plays the role of a multivariate nuisance parameter. To estimate this matrix, we use kernel smoothing. We show consistency and obtain bounds on the rate of convergence.

Least empirical risk procedures in statistical inference

Wojciech Niemiro (1993)

Applicationes Mathematicae

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We consider the empirical risk function Q n ( α ) = 1 n ∑ i = 1 n · f ( α , Z i ) (for iid Z i ’s) under the assumption that f(α,z) is convex with respect to α. Asymptotics of the minimum of Q n ( α ) is investigated. Tests for linear hypotheses are derived. Our results generalize some of those concerning LAD estimators and related tests.