Theoretical Fundamentals of Neural Networks

Garant předmětu:

Martin Holeňa

Lecturer:

Martin Holeňa

Tutor:

Martin Holeňa

Supervisor:

Department of Mathematics

Synopsis:

Keywords:

Functional approximation, supervised learning, Vapnik-Chervonenkis-dimension

Requirements:

Some selected topics in this lecture are closely related to the content of the lecture „Probabilistic learning models“ that presents these selected topics in a much broader and deeper form.

Syllabus of lectures:

1.Approach to artificial neural networks from the theory of function approximation.

2.Approach to artificial neural networks from the probability theory.

3.Analysis of the solvability of selected tasks neural network models.

4.Qualitative measure of neural networks (VC-dimension, pseudodimension, sensitivity dimension).

5.Theoretical background of neural networks learning.

6.Selected advanced classification applications of artificial neural networks.

Syllabus of tutorials:

Study Objective:

Acquired knowledge:

The theoretical foundation for the study of the properties and potential of artificial neural networks models.

Acquired skills:

Advanced ability to analyze the appropriateness and effectiveness of artificial neural networks models for practical applications. The fundamental basis for the expansion of theoretical knowledge enabling greater understanding and development of artificial intelligence.

Study materials:

Compulsory literature:

[1] J. Šíma, R. Neruda. Teoretické otázky neuronových sítí. Matfyzpress. 1996

Optional literature:

[2] M. Anthony, P. L. Bartlett. Neural Network Learning: Theoretical foundations. Cambridge university Press, 2009.

[3] M. Vidyasagar. A theory of Learning and Generalization. Springer 1997.

[4] V. Roychowdhury, K-Y. Siu, A. Orlitsky. Theoretical advances in neural computation and learning. Kluwer Academic Publishers. 1994.

[5] H. White. Artificial Neural Networks: Approximation and Learning Theory. Blackwell Publishers. Cambridge. 1992.

Note:

Time-table for winter semester 2023/2024:

Time-table is not available yet

Time-table for summer semester 2023/2024:

Time-table is not available yet

The course is a part of the following study plans:

• Matematické inženýrství (elective course)
• Aplikované matematicko-stochastické metody (elective course)
• Matematická informatika (compulsory course in the program)