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Conditional Independence Structures - NSTP160

Title:	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 [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	cancelled
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	RNDr. Milan Studený, DrSc.
Classification:	Mathematics > Probability and Statistics
Interchangeability :	NMTP576

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: G_M (20.05.2011)

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: T_KPMS (22.05.2008)

To explain basic mathematical methods for dealing with probabilistic

conditional independence structures

Literature - Czech

Last update: G_M (28.05.2008)

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

M. Studený: O strukturách podmíněné nezávislosti. Rukopis série

přednášek. ÚTIA 2008.

Teaching methods -

Last update: G_M (28.05.2008)

Lecture.

Syllabus -

Last update: T_KPMS (15.02.2007)

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.