The module is designed to teach students the theoretical and practical aspects of probabilistic machine learning. A broad selection of tools from estimation theory is presented in such a way that both a formal, academic as well as a clear, intuitive understanding of the basic principle is attained. Furthermore, the functionality of state-of-art implementations in the relevant libraries will be reviewed. The focus is on the ability to solve a wide range of problems by linking individual numerical and theoretical tools in a modular fashion to form a formally correct and numerically computable processing pipeline. In each case, we examine the reliability of the results. All this is supported by a purely digital exercise with calculation and programming tasks.  

Presented numerical tools are interpolation, regression (linear and spline, Gaussian process), Deep Learning (Feed Forward Neural Network, Bayesian Neural Network), non-linear optimization (steepest descent, Newton), sampling (independent random, deterministic), cubature (Monte Carlo, quasi-Monte Carlo). 

Theoretical tools presented are factorization of the joint density with acyclic graphs, density representation (Gaussian, Exponential Family), least squares, maximum likelihood, risk minimization, error-tolerant estimation, Bayesian Model Selection, meta-priors, active inference.

Exam: Oral, appointments via Mail to pruefung-isas@kit.edu. Don't forget the additional registration in CAS. 

Enthält eine digitale Übung mit Programmieraufgaben.