Statistical regularization and promising machine learning methods

Lecture 1. Introductory lecture. Basic concepts and overview of artificial intelligence methods.

Lecture 2. Fundamentals of regularization theory. Modern regularization methods. Bayesian formalism and inverse problems.

Seminar 1. Practical exercises on solving inverse problems.

Lecture 3. Bayesian model selection methods. Maximum evidence methods.

Lecture 4. The concept of latent variables. Gaussian mixture models. A Bayesian approach to the support vector method.

Seminar 2. Applying the Bayesian approach to machine learning models.

Lecture 5. Variational inference and variational autoencoders.

Lecture 6. Markov Chain Monte Carlo method. Hamiltonian dynamics.

Seminar 3. Practical application of variational inference.

Lecture 7. Gaussian processes and Dirichlet processes.

Seminar 4. Practical application of Gaussian processes.

Lecture 8. Diffusion models.

Seminar 5. Practical application of diffusion models.

Lecture 9. Generative models.

Seminar 6. Practical application of generative models.

Lecture 10. Dimensionality reduction methods and manifold learning. Fundamentals of topological data analysis.

Student assessment. Listening to student presentations and reviewing calculation results on assigned topics.