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Cross-entropy based combination of discrete probability distributions for distributed decision making
Sečkárová, Vladimíra ; Kárný, Miroslav (advisor)
Dissertation abstract Title: Cross-entropy based combination of discrete probability distributions for distributed de- cision making Author: Vladimíra Sečkárová Author's email: seckarov@karlin.mff.cuni.cz Department: Department of Probability and Mathematical Statistics Faculty of Mathematics and Physics, Charles University in Prague Supervisor: Ing. Miroslav Kárný, DrSc., The Institute of Information Theory and Automation of the Czech Academy of Sciences Supervisor's email: school@utia.cas.cz Abstract: In this work we propose a systematic way to combine discrete probability distributions based on decision making theory and theory of information, namely the cross-entropy (also known as the Kullback-Leibler (KL) divergence). The optimal combination is a probability mass function minimizing the conditional expected KL-divergence. The ex- pectation is taken with respect to a probability density function also minimizing the KL divergence under problem-reflecting constraints. Although the combination is derived for the case when sources provided probabilistic type of information on the common support, it can applied to other types of given information by proposed transformation and/or extension. The discussion regarding proposed combining and sequential processing of available data, duplicate data, influence...
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Cross-entropy based combination of discrete probability distributions for distributed decision making
Sečkárová, Vladimíra ; Kárný, Miroslav (advisor) ; Jurečková, Jana (referee) ; Janžura, Martin (referee)
Dissertation abstract Title: Cross-entropy based combination of discrete probability distributions for distributed de- cision making Author: Vladimíra Sečkárová Author's email: seckarov@karlin.mff.cuni.cz Department: Department of Probability and Mathematical Statistics Faculty of Mathematics and Physics, Charles University in Prague Supervisor: Ing. Miroslav Kárný, DrSc., The Institute of Information Theory and Automation of the Czech Academy of Sciences Supervisor's email: school@utia.cas.cz Abstract: In this work we propose a systematic way to combine discrete probability distributions based on decision making theory and theory of information, namely the cross-entropy (also known as the Kullback-Leibler (KL) divergence). The optimal combination is a probability mass function minimizing the conditional expected KL-divergence. The ex- pectation is taken with respect to a probability density function also minimizing the KL divergence under problem-reflecting constraints. Although the combination is derived for the case when sources provided probabilistic type of information on the common support, it can applied to other types of given information by proposed transformation and/or extension. The discussion regarding proposed combining and sequential processing of available data, duplicate data, influence...
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Cross-entropy based combination of discrete probability distributions for distributed decision making
Sečkárová, Vladimíra ; Kárný, Miroslav (advisor)
Dissertation abstract Title: Cross-entropy based combination of discrete probability distributions for distributed de- cision making Author: Vladimíra Sečkárová Author's email: seckarov@karlin.mff.cuni.cz Department: Department of Probability and Mathematical Statistics Faculty of Mathematics and Physics, Charles University in Prague Supervisor: Ing. Miroslav Kárný, DrSc., The Institute of Information Theory and Automation of the Czech Academy of Sciences Supervisor's email: school@utia.cas.cz Abstract: In this work we propose a systematic way to combine discrete probability distributions based on decision making theory and theory of information, namely the cross-entropy (also known as the Kullback-Leibler (KL) divergence). The optimal combination is a probability mass function minimizing the conditional expected KL-divergence. The ex- pectation is taken with respect to a probability density function also minimizing the KL divergence under problem-reflecting constraints. Although the combination is derived for the case when sources provided probabilistic type of information on the common support, it can applied to other types of given information by proposed transformation and/or extension. The discussion regarding proposed combining and sequential processing of available data, duplicate data, influence...
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První experimenty s distribuovaným Bayesovským rozhodováním
Šmídl, Václav ; Andrýsek, Josef
Decision-making under uncertainty is a natural part of everyday life of every human being. In societal science, various aspects of decision-making were studied, mostly in the area of psychology. In technical science, the process was formalized using probability theory yielding so called Bayesian theory of decision making. However, one of the key assumptions of this theory is that the decision-maker is the only entity that intentionally influences the system. This assumption is certainly violated in more complicated systems, such as human society or distributed control. Recently, a series of papers attempts to offer an extension of the Bayesian theory for many decision-makers, i.e. decentralized stochastic control. Since there are no proofs of optimality of the proposed Bayesian distributed decision making available in the literature, we study this approach via experimental simulation studies.
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