Probabilistic Models of Artificial Intelligence

Course guarantor:

Jiřina Vejnarová

Lecturer:

Tutor:

Jiřina Vejnarová

Supervisor:

Department of Mathematics

Synopsis:

The course is devoted to the survey of methods used for uncertainty processing in the field of artificial inteligence. The main attention is paid to so-called graphical Markov models, particularly to Bayesian networks.

Requirements:

Basic course of probabilitz and mathematical statistics

Syllabus of lectures:

1. Introduction to artificial intelligence: problem solving, state spaces, search for solution, algorithm A star, optimality of solution. 2. Uncertainty in artificial intelligence: uncertainty in expert systems, pseudobayesian uncertainty processing in Prospector. 3. Imprecise probabilities: capacities, lower an upper probabilities, coherence, belief functions, possibility measures, credal sets. 4. Conditional independence and its properties: factorization lemma, block independence lemma. 5.Graphical Markov properties: pairwise, local and global Markov properties. 6. Triangulated graphs: graph decomposition, maximum cardinality search, perfect ordering of nodes and cliques, triangularization of graphs, running intersection property, junction trees. 7. Bayesian networks: consistency of distribution represented by a Bayesian network, dependence structure. 8. Computation in Bayesain networks: Shachter algorithm, transformation of Bayesian networks to decomposable models, message passing in junction trees.

Syllabus of tutorials:

Study Objective:

Uncertainty models in artificial inteligence and methods of its processing. Skills: Application of given methods to particular problems.

Study materials:

key references:

[1] P. Hájek, T. Havránek, R. Jiroušek, Uncertain Information Processing in Expert Systems, CRC Press 1992.

key references:

[1] P. Hájek, T. Havránek, R. Jiroušek, Uncertain Information Processing in Expert Systems, CRC Press 1992.

Note:

Time-table for winter semester 2024/2025:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon	room Vejnarová J. 13:00–14:50 (lecture parallel1)
Tue
Wed
Thu
Fri

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Aplikovaná algebra a analýza (elective course)
• Aplikované matematicko-stochastické metody (elective course)