The course introduces the relevant mathematical concepts and methods in the field of artificial intelligence (AI) and conveys the practical skills to apply these methods in guided practical projects dealing with real life data and issues.The recurrent theme is in establishing a joint stochastic/statistic perspective based on optimization paradigm and complexity estimates - for various mathematical methods and algorithms deployed in machine learning (ML) and AI.

The topics covered include:

• Introduction, biological, neurophysiological and mathematical foundations of living neural networks, mathematical implications of differences between living and common synthetic classes of artificial neural networks;
• Euclidean, non-Euclidean and information-theoretical measures in ML/AI;
• transformation of measures, embedding theorems (Whitney and Takens);
• deterministic vs. stochastic approximation of functions and integrals;
• deterministic vs. stochastic unconstrained optimization methods in AI;
• constrained optimization methods in AI, soft vs. hard constraints, necessary concepts from linear and quadratic programming;
• mathematical foundations of Markovian and Bayesian learning;
• dimension reduction and feature selection in ML/AI as an optimization problem for various measures;
• ill-posedness and “small data learning challenge”, information-theoretic vs. more common (L1/L2) regularizations in learning problems;
• mathematical concepts in eXplainable AI (XAI), Scalable Probabilistic Approximation family of learning methods and its extensions.