Students are able to represent expert knowledge expressed by rules as fuzzy systems.

• Recognizing, analyzing and formalising data or expert based modeling tasks (K1, K3, K4, K6)
• Evaluating the performance of a data based model (K3)
• Knowing, applying, evaluating and adopting techniques from statistical learning theory (K1, K3, K5, K6)
• Proofing and interpreting selected results from data and knowledge based modeling theory (K2, K3, K4)
• Knowing and designing selected types of fuzzy systems (K1, K2, K3)
• Knowing and applying necessary mathematical tools and techniques (K1, K2, K3)

Basic terminology: (un)supervised learning, regression vs. classification tasks, data generation model (iid samples), hypothesis class, risk/loss function, empirical risk minimization, regularized risk minimization, Bayes risk and optimal predictor, (agnostic) PAC learning, consistency, error decomposition, VC dimension, model validation, under/over-fitting, bias-variance trade off

Selected models may comprise: linear predictors/separators, regression models, support vector machines, kernel methods, neural networks, decision trees, random forests, clustering

Algorithmic aspects: least squares estimation, perceptron algorithm, (stochastic) gradient descent algorithm

Selected theoretical results: representer theorem, Mercer’s theorem, no free lunch theorems, convergence of perceptron algorithm, convex learning problems

expert based modeling:

Basic terminology: Fuzzy sets, fuzzy inference schemes, semantic models in fuzzy logic

Selected models: Mamdani, Tagaki-Sugeno-Kang fuzzy systems