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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: T_KPMS (16.05.2013)
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To explain basic mathematical methods for dealing with probabilistic conditional independence structures. Last update: Studený Milan, RNDr., DrSc. (24.05.2016)
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Oral exam. Last update: Zichová Jitka, RNDr., Dr. (17.05.2022)
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S.L. Lauritzen: Graphical Models. Clarendon Press 1996.
M. Studený: Struktury podmíněné nezávislosti. MatfyzPress 2014. (skripta v češtině) Last update: Studený Milan, RNDr., DrSc. (24.05.2016)
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Lecture, possibly combined with consulted reading of the literature. Last update: Studený Milan, RNDr., DrSc. (24.05.2016)
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Oral exam according to syllabus. Last update: Zichová Jitka, RNDr., Dr. (19.05.2024)
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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: Studený Milan, RNDr., DrSc. (24.05.2016)
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The students should be familiar with elementary concepts from measure theory and lattice theory, basic facts about matrices and with basic concepts from graph theory and convex geometry. The knowledge of basic statistical distributions is useful, although not necessary. All above mentioned concepts can be found in the appendix of the lecture notes. Last update: Studený Milan, RNDr., DrSc. (20.05.2019)
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