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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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On Linear Probabilistic Opinion Pooling Based on Kullback-Leibler Divergence
Sečkárová, Vladimíra
In this contribution we focus on the finite collection of sources, providing their opinions about a hidden (stochastic) phenomenon, that is not directly observable. The assumption on obtaining opinions yields a decision making process commonly referred to as opinion pooling. Due to the complexity of the space of possible decisions we consider the probability distributions over this set rather than single values, exploited before, e.g., in [2]. The final decision (result of pooling) is then a combination of probability distributions provided by sources.
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On Approximate Fully Probabilistic Design of Decision-Making Units
Kárný, Miroslav
An efficient support of a single decision maker is vital in constructing scalable systems addressing complex decision-making (DM) tasks. Fully probabilistic design (FPD) of DM strategies, an extension of dynamic Bayesian DM, provides a firm basis for such a support. The limited cognitive and evaluation resources of the supported decision maker cause that theoretically optimal solutions are realised only approximately. Thus, the truly efficient support has to include reliable means for constructing approximate solutions of DM subtasks. The current paper deals with the design of the approximately optimal DM strategy for a known environment model and adequately described DM preferences. The design relies on: a) the explicit minimiser found within FPD; b) randomised nature of the strategy provided by FPD.
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