SubjectsSubjects(version: 849)
Course, academic year 2019/2020
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Conditional Independence Structures - NMTP576
Title in English: Struktury podmíněné nezávislosti
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: RNDr. Milan Studený, DrSc.
Class: M Mgr. PMSE
M Mgr. PMSE > Volitelné
Classification: Mathematics > Probability and Statistics
Annotation -
Last update: T_KPMS (16.05.2013)
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.
Aim of the course -
Last update: RNDr. Milan Studený, DrSc. (24.05.2016)

To explain basic mathematical methods for dealing with probabilistic conditional independence structures.

Course completion requirements - Czech
Last update: RNDr. Jitka Zichová, Dr. (19.04.2018)

Složení ústní zkoušky.

Literature - Czech
Last update: RNDr. Milan Studený, DrSc. (24.05.2016)

S.L. Lauritzen: Graphical Models. Clarendon Press 1996.

M. Studený: Struktury podmíněné nezávislosti. MatfyzPress 2014. (skripta v češtině)

Teaching methods -
Last update: RNDr. Milan Studený, DrSc. (24.05.2016)

Lecture, possibly combined with consulted reading of the literature.

Requirements to the exam - Czech
Last update: RNDr. Jitka Zichová, Dr. (02.03.2018)

Zkouška je ústní.

Zkouší se pojmy a výsledky z cyklu přednášek, konkrétněji:

  • pravděpodobnostní podmíněná nezávislost a její základní formální vlastnosti (semigrafoidy),
  • metody konstrukce měr indukujících struktury PN, informačně-teoretické nástroje,
  • grafické metody popisu struktur PN, neorientované grafy, acyklické orientované grafy,
  • rozložitelné grafy a metoda lokálních výpočtů.

V rámci zkoušky se studentům zadají některá z cvičení k dané látce, jejich zadání bude dostupné na internetu.

Syllabus -
Last update: RNDr. Milan Studený, DrSc. (24.05.2016)

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.

Entry requirements -
Last update: RNDr. Milan Studený, DrSc. (20.05.2019)

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.

 
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