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Inference in Bayesian Networks
Šimeček, Josef ; Rozman, Jaroslav (referee) ; Zbořil, František (advisor)
This master's thesis deals with demonstration of various approaches to probabilistic inference in Bayesian networks. Basics of probability theory, introduction to Bayesian networks, methods for Bayesian inference and applications of Bayesian networks are described in theoretical part. Inference techniques are explained and complemented by their algorithm. Techniques are also illustrated on example. Practical part contains implementation description, experiments with demonstration applications and conclusion of the results.
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Gaussian Process Regression under Location Uncertainty using Monte Carlo Approximation
Ptáček, Martin
Gaussian Process Regression (GPR) is a commonstatistical framework for spatial function estimation. While itsflexibility and availability of closed-form estimation solutionafter training are its advantages, it suffers on applicabilityconstraints in scenarios with uncertain training positions. Thispaper presents the derivation of the exact GPR operating onuncertain training positions along with approximation of theresulting terms using Monte Carlo (MC) sampling. This methodis then implemented in a simulation environment and shown toimprove the estimation quality over the standard GPR approachwith uncertain training positions.
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Inference in Bayesian Networks
Šimeček, Josef ; Rozman, Jaroslav (referee) ; Zbořil, František (advisor)
This master's thesis deals with demonstration of various approaches to probabilistic inference in Bayesian networks. Basics of probability theory, introduction to Bayesian networks, methods for Bayesian inference and applications of Bayesian networks are described in theoretical part. Inference techniques are explained and complemented by their algorithm. Techniques are also illustrated on example. Practical part contains implementation description, experiments with demonstration applications and conclusion of the results.
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Aplikace bayesovských sítích ve hře Minesweepe
Vomlelová, M. ; Vomlel, Jiří
We use the computer game of Minesweeper to illustrate few modeling tricks utilized when applying Bayesian network (BN) models in real applications. Among others, we apply rank-one decomposition (ROD) toconditional probability tables (CPTs) representing addition. Typically, this transformation helps to reduce the computational complexity of probabilistic inference with the BN model. However, in this paper we will see that (except for the total sum node) when ROD is applied to the whole CPT it does not bring any savings for the BN model of Minesweeper. Actually, in order to gain from ROD we need minimal rank-one decompositions of CPTs when the state of the dependent variable is observed. But this is not known and it is a topic for our future research.
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