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Fast Dependency-Aware Feature Selection in Very-High-Dimensional Pattern Recognition Problems
Somol, Petr ; Grim, Jiří
The paper addresses the problem of making dependency-aware feature selection feasible in pattern recognition problems of very high dimensionality. The idea of individually best ranking is generalized to evaluate the contextual quality of each feature in a series of randomly generated feature subsets. Each random subset is evaluated by a criterion function of arbitrary choice (permitting functions of high complexity). Eventually, the novel dependency-aware feature rank is computed, expressing the average benefit of including a feature into feature subsets. The method is efficient and generalizes well especially in very-high-dimensional problems, where traditional context-aware feature selection methods fail due to prohibitive computational complexity or to over-fitting. The method is shown well capable of over-performing the commonly applied individual ranking which ignores important contextual information contained in data.
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Ramsey Stochastic Model via Multistage Stochastic Programming
Kaňková, Vlasta
Ramsey model belongs to ``classical" economic dynamic models. It has been (1928)originally constructed (with a farmer interpretation)in a deterministic setting. Later this model has been generalized to a stochastic version. Time horizont in the original deterministic model as well as in modified stochastic one can be considered finite or infinite. The contribution deals with the stochastic model and finite horizont. However, in spite of the classical approach to analyze it we employ a stochastic programming technique. This approach gives a possibility to employ well known results on stability and empirical estimates also in the case of Ramsey model. However, first, we introduce some confidence intervals. To obtain the new assertions we restrict our consideration mostly to the case when the ``underlying" random element follows autoregressive (or at least Markov) sequence.
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Dva způsoby stanovení meze stability
Půst, Ladislav ; Kozánek, Jan
V příspěvku jsou analyzovány dvě metody pro stanovení meze stability dynamického systému na experimentálně určeném matematickém modelu aerodynamického ložiska. Ukázalo se, že metoda komplexních vlastních čísel dává prakticky stejné výsledky jako řešení pohybové rovnice integrálními metodami Runge-Kutta.
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Problém dvou manažérů a problematika úloh stochastického programování s lineární kompenzací
Kaňková, Vlasta
Úlohy stochastického programování s lineární kompenzací odpovídají mnoha ekonomickým problémům. Tyto úlohy jsou kompozicí dvou úloh (vnitřní a vnější). Řešení vnější úlohy závisí na pravděpodobnostní míře, řešení vnitřní úlohy závisí na řešení vnější úlohy a na realizaci náhodného elementu. Evidentně, optimální chování dvou manažérů může být (v mnoha případech) modelováno pomocí shora popsaného modelu, ve kterém chování hlavního manažéra je popsáno vnější úlohou a chování vedlejšího manažéra odpovídá vnitřní úloze. Práce je zaměřena na zkoumání vntřní úlohy.
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Empirické odhady a stabilita ve stochastickém programování
Kaňková, Vlasta
It is known that optimization problems depending on a probability measure correspond to many applications. It is also known that these problems belong mostly to a class of nonlinear optimization problems and, moreover, that very often an ``underlying" probability measure is not completely known. The aim of the research report is to deal with the case when an empirical measure substitutes the theoretical one. In particular, the aim is to generalize reults dealing with convergence rate in the case of empirical esrimates. The introduced results are based on the stability results corresponding to the Wasserstein metric. A relationship berween tails of one-dimensional marginal distribution functions and exponentional rate of convergence are introduced. The corresponding results are focus mainly on ``classical" type of problems corresponding to the cases with penalty and recourse. However, an integer simple recourse case and some special risk funkcionals are discussed also.
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