Modules

16 results

A1.3 Stochastics16

Fundamentals of Mathematical StatisticsNo ratings for this module yet.A1.3.2 Modules in StatisticsYou 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 semesterMA5441Probabilistische Techniken und Algorithmen in der DatenanalyseNo ratings for this module yet.A1.3.2 Modules in StatisticsYou will learn probabilistic techniques and algorithms used in data analysis for dimensionality reduction and data recovery from incomplete information. In the end, you will understand the basics of random matrices, assess randomized algorithms, and apply and analyze methods such as JL embeddings, compressed sensing, and randomness-based matrix/tensor reconstruction.6 ECTSruns this semesterMA4803Statistical Foundations of LearningNo ratings for this module yet.A1.3.2 Modules in StatisticsYou 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 semesterCIT4230004Statistical LearningNo ratings for this module yet.A1.3.2 Modules in StatisticsYou learn the basics and advanced methods of supervised and unsupervised statistical learning. In the end you will be able to understand and apply models for regression and classification, use techniques for dimensionality reduction and cluster analysis, and follow probabilistic formulations of learning problems while designing new algorithms.6 ECTSruns this semesterMA4802CausalityNo ratings for this module yet.A1.3.2 Modules in StatisticsYou 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 semesterIN2410
11 more in A1.3 StochasticsComputational StatisticsNo ratings for this module yet.A1.3.2 Modules in StatisticsYou will learn methods of computational statistics for high-dimensional, hierarchical, and latent data structures and how to apply them. The focus is on simulation (univariate and multivariate), Bayesian inference with MCMC (Gibbs, Metropolis-Hastings, Hamiltonian MC), bootstrap procedures and the EM algorithm for missing or latent data. In the end you can theoretically understand the algorithms, implement them in R, and interpret results statistically.5 ECTSno date this semesterMA4402Copulas: Inference and ApplicationsNo ratings for this module yet.A1.3.2 Modules in StatisticsYou will learn modern Copula models to describe dependencies, both static and dynamic variants, with a focus on estimation and testing procedures. In the end you can assess parametric, semiparametric and nonparametric approaches and apply them in applications of the finance and insurance industry (e.g., portfolio risk, multi-name pricing, risk management).3 ECTSno date this semesterMA5728Foundations of Data AnalysisNo ratings for this module yet.A1.3.2 Modules in StatisticsIn this module you will learn mathematical methods of data analysis, in particular linear and nonlinear procedures for data dimensionality reduction as well as techniques for reconstructive restoration of structured signals. By the end you will be able to apply and assess singular value decomposition, random matrices, compressive methods and manifold-based procedures.8 ECTSno date this semesterMA4800Generalized Linear ModelsNo ratings for this module yet.A1.3.2 Modules in StatisticsYou 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.A1.3.2 Modules in StatisticsIn 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 semesterMA5439High-dimensional StatisticsNo ratings for this module yet.A1.3.2 Modules in StatisticsYou learn methods for the analysis of data where the number of variables is large. After the module you can apply procedures for controlling false discoveries in large-scale multiple testing, use sparse regression methods (e.g., Lasso) and methods for group-specific or low-dimensional structured signals, as well as use regularization approaches for matrix parameters and graph models.5 ECTSno date this semesterMA5442Mathematical Foundations of Machine LearningNo ratings for this module yet.A1.3.2 Modules in StatisticsYou 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.A1.3.2 Modules in StatisticsYou 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 semesterCIT413048Statistical Analysis of CopulasNo ratings for this module yet.A1.3.2 Modules in StatisticsYou learn to model multivariate dependency structures using Copulas and to understand, estimate, and apply Vine-Copula models (C-, D- and R-Vines). In the end you can select suitable vine models, implement them in R with VineCopula/CDVine, simulate, interpret and assess results.5 ECTSno date this semesterMA5408Statistical Inference for Dynamical SystemsNo ratings for this module yet.A1.3.2 Modules in StatisticsIn this module you will learn how to model biological reaction networks with ordinary differential equations and how parameter values of these models can be reliably estimated from experimental data. You will acquire methods for parameter estimation (frequentist and Bayesian) as well as techniques for analyzing uncertainty and practicality of parameters and implement these in MATLAB.6 ECTSno date this semesterMA5612Statistical Inverse ProblemsNo ratings for this module yet.A1.3.2 Modules in StatisticsYou learn fundamental methods for the statistical treatment of inverse problems. The course covers linear inverse problems with random noise, regularization, convergence rates, adaptive procedures and model selection; at the end you can compare the results and apply them to concrete examples.5 ECTSno date this semesterMA5428