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The lecture is conceived as an introduction to the above mentioned topic and it leads to the methods of
(mathematical)
description of probabilistic conditional independence (CI) structures by means of tools of discrete mathematics, in
particular
by means of graphs whose nodes correspond to random variables. Because CI structures occur both in modern
statistics
and in artificial inteligence (so-called probabilistic expert systems) the lecture is suitable both for students of
probability and
statistics and for the students of informatics.
Last update: G_M (20.05.2011)
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To explain basic mathematical methods for dealing with probabilistic conditional independence structures Last update: T_KPMS (22.05.2008)
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S.L. Lauritzen: Graphical Models. Clarendon Press 1996.
M. Studený: O strukturách podmíněné nezávislosti. Rukopis série přednášek. ÚTIA 2008. Last update: G_M (28.05.2008)
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Lecture. Last update: G_M (28.05.2008)
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The concept of conditional independence (CI). Basic formal properties of CI, the concept of a semi-graphoid and (formal) CI structure. Basic method of construction of measures inducing CI structures. Information-theoretical tools for CI structure study. Graphical methods for CI structure description: undirected graphs (= Markov networks), acyclic directed graphs (= Bayesian networks). The method of local computation. Possible additional topics: The (non-existence of a) finite axiomatic characterization of CI structures. Learning graphical models from data. Chain graphs. Last update: T_KPMS (15.02.2007)
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