Modules

14 results

Elective Modules14

Applied Statistics and Data Analysis (TUM School of Computation, Information and Technology [CIT] and TUM School of Life Sciences [SoLS])No ratings for this module yet.Data AnalysisYou learn to analyze data from the life sciences statistically and to process it with R. The module covers data visualization, association methods for categorical data, analysis of variance, experimental design, and various regression methods up to linear mixed-effects models for longitudinal data. In the end you can select appropriate statistical methods, apply them in R, and interpret results.5 ECTSruns this semesterCIT5130001Fundamentals of Mathematical StatisticsNo ratings for this module yet.Data AnalysisYou will learn the fundamental principles and methods of statistical inference, including likelihood approaches, Bayesian methods and minimax estimation. You will deal with asymptotic theory for large samples and apply it in particular to the study and application of maximum-likelihood techniques.9 ECTSruns this semesterMA5441FunktionalanalysisNo ratings for this module yet.Data AnalysisYou will learn the basics of functional analysis in Banach and Hilbert spaces. In the end you will be able to analyze linear functionals and bounded as well as compact self-adjoint operators, understand duality, and apply concepts such as weak and weak* convergence.9 ECTSruns this semesterMA3001Nichtlineare OptimierungNo ratings for this module yet.Data AnalysisYou engage with theory and numerical methods of nonlinear optimization. You will learn advanced methods for unconstrained and, in particular, constrained optimization problems (e.g., SQP, barrier and interior-point methods) and you will be able to assess and apply convergence properties of such methods in the end.5 ECTSruns this semesterMA3503Probability TheoryNo ratings for this module yet.Data AnalysisYou will learn the measure-theoretic probability theory for sequences of random variables and martingales. By the end you will be able to understand and apply central results such as the law of large numbers, central limit theorems, and fundamental martingale results.9 ECTSruns this semesterMA2409
9 more in Elective ModulesStatistical Foundations of LearningNo ratings for this module yet.Data AnalysisYou learn statistical foundations of machine learning theory and mathematical tools for the analysis of learning algorithms. In the end you will be able to evaluate generalization and consistency questions, theoretically analyze algorithms such as k‑NN, SVM and simple neural networks, and contextualize newer developments such as overparameterization and training dynamics.8 ECTSruns this semesterCIT4230004Approximation AlgorithmsNo ratings for this module yet.Data AnalysisYou learn how to design and analyze efficient approximation algorithms for combinatorial optimization problems. In the end you can assess the running time and approximation guarantees of algorithms, apply known techniques (e.g. Greedy, LP-Rounding, Primal-Dual), and prove limits of approximability.9 ECTSno date this semesterCIT4100003CausalityNo ratings for this module yet.Data AnalysisYou engage with concepts and methods of causal inference: from probabilistic and graph-theoretic foundations through structural models to modern algorithms for causal discovery and estimation of causal effects. In the end you can judge whether and how causal conclusions are possible from given data and assumptions, select appropriate methods and apply them in practice.8 ECTSno date this semesterIN2410Generalized Linear ModelsNo ratings for this module yet.Data AnalysisYou learn methods of regression for non-normally distributed target variables (e.g., binary, count data, nominal, positive values). In addition to classical GLMs such as logistic, Probit-, Poisson-, Gamma-, and log-linear models, extensions (e.g., overdispersion, random effects) are covered. By the end you will be able to estimate models, validate them, and analyze and interpret the results with R.9 ECTSno date this semesterMA3403Graphical Models in StatisticsNo ratings for this module yet.Data AnalysisIn this module you will learn statistical models whose conditional independencies are described by graphs. The focus is on continuous distributions (in particular the multivariate normal distribution), undirected graphical models (Gaussian models) and directed acyclic graphs (Bayesian networks). By the end you will be able to represent dependency structures in data with graphical models and select appropriate model classes.9 ECTSno date this semesterMA5439Mathematical Foundations of Machine LearningNo ratings for this module yet.Data AnalysisYou will learn the mathematical foundations of modern machine learning methods: structure, learning algorithms and approximation properties of neural networks, theory and application of kernel methods in reproducing kernel Hilbert spaces as well as qualitative aspects such as loss functions, risk and complexity questions. By the end you will be able to construct networks, discuss their approximation properties, apply kernel methods and assess the statistical efficiency of procedures.6 ECTSno date this semesterMA4801Mathematical Foundations of Machine LearningNo ratings for this module yet.Data AnalysisYou will learn the mathematical foundations of modern methods of machine learning. By the end you can design neural networks and discuss their approximation properties, apply kernel methods in Reproducing Kernel Hilbert Spaces, and assess the statistical efficiency of learning procedures.9 ECTSno date this semesterCIT413048Modern Methods in Nonlinear OptimizationNo ratings for this module yet.Data AnalysisYou will learn selected modern methods of nonlinear optimization, e.g. convex and non-smooth optimization, interior-point methods, semidefinite programming, robustness concepts and duality. In the end you will be able to understand current research articles on the treated topics and you will be prepared to pursue your own research questions in nonlinear optimization.5 ECTSno date this semesterMA4503Polyhedral CombinatoricsNo ratings for this module yet.Data AnalysisYou learn how to approach combinatorial optimization problems through the geometry of polyhedra: representation of polytopes, the connection between geometry and optimization of linear functions, as well as modern algorithms such as branch-and-cut and separation/optimization. In the end you will be able to apply the methods to typical problems (e.g., matching, TSP polytopes) and assess their limits in the context of NP-hardness.6 ECTSno date this semesterMA5225
2 more modules match, but they are taught in German. Show themAnerkennung aus dem Ausland aus dem Bereich Data AnalysisNo ratings for this module yet.Data Analysisno date this semesterIN99650Anerkennung aus dem Ausland aus dem Bereich Data AnalysisNo ratings for this module yet.Data Analysisno date this semesterIN99651