Modules

30 results

A1.3 Stochastics30

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 semesterMA5441Large DeviationsNo ratings for this module yet.A1.3.1 Modules in Probability TheoryYou will learn the theory of large deviations, which describes how unlikely events occur in probability models and how quickly their probabilities decay. In the end you will be able to apply fundamental techniques of large-deviation theory and understand applications such as for sums of random variables and empirical distributions.5 ECTSruns this semesterMA5417Probabilistische 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 semesterMA4803Random Graphs and NetworksNo ratings for this module yet.A1.3.1 Modules in Probability TheoryYou will learn models of random graphs and how they describe real networks. The focuses are Erdős–Rényi models, generalized random graphs, the configuration model and preferential-attachment models as well as proof techniques for the number of components, degree distribution and distances.5 ECTSruns this semesterMA5436Statistical 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 semesterCIT4230004
25 more in A1.3 StochasticsStatistical 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 semesterMA4802Branching Random WalksNo ratings for this module yet.A1.3.1 Modules in Probability TheoryYou will learn the basics and advanced aspects of branching random walks. In the end you will know the classical theory of branching processes and Galton‑Watson trees as well as the connections to partial differential equations and relevant application areas.3 ECTSno date this semesterCIT413035CausalityNo 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 semesterIN2410Computational 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 semesterMA4402Concentration of MeasureNo ratings for this module yet.A1.3.1 Modules in Probability TheoryYou will learn fundamental inequalities and techniques of Concentration of Measure (e.g., Chernoff, Hoeffding, Bernstein inequalities, isoperimetry, Johnson–Lindenstrauss, Martingale methods, Poincaré and Gromov–Milman theorems). In the end you will be able to understand these inequalities and apply them to simple examples from applications.5 ECTSno date this semesterCIT4100004Conformal Mapping and ProbabilityNo ratings for this module yet.A1.3.1 Modules in Probability TheoryThe module covers conformal mappings and their connection with stochastic processes in the plane. You will learn how conformal methods can solve probabilistic problems, and gain insight into two-dimensional critical systems and their scaling limits (e.g., percolation, loop-erased random walks, Ising model) as well as SLE and loop ensembles.5 ECTSno date this semesterMA5432Copulas: 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 semesterMA5442Markov ProcessesNo ratings for this module yet.A1.3.1 Modules in Probability TheoryYou will learn theory and methods of continuous-time Markov processes: continuous-time Markov chains, the Markov property, Feller processes as well as properties of transition semigroups and their generators. In the end you can analyze the long-term behavior of processes, apply ergodic theorems and use them in examples (e.g. queueing theory, interacting particle systems, time series).9 ECTSno date this semesterMA4408Mathematical 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 semesterCIT413048Mathematics of Reinforcement LearningNo ratings for this module yet.A1.3.1 Modules in Probability TheoryYou will learn the mathematical foundations of reinforcement learning: Markov decision processes (MDPs), tabular RL methods such as Monte Carlo, Temporal Difference, SARSA and Q-Learning, as well as basics of stochastic approximation to analyze the convergence of these algorithms. In the end you can formulate dynamic decision problems under uncertainty as MDPs and solve them with tabular RL algorithms.6 ECTSno date this semesterCIT413036Perfect Simulation for Chains of Finite and Infinite OrderNo ratings for this module yet.A1.3.1 Modules in Probability TheoryYou will learn about models of stochastic processes beyond finite Markov chains, in particular chains of infinite order, their properties and how to simulate them exactly (perfect simulation). In the end you will be able to assess existence and uniqueness questions, classify examples and apply perfect-simulation algorithms for such processes.5 ECTSno date this semesterCIT413043Probability on GraphsNo ratings for this module yet.A1.3.1 Modules in Probability TheoryYou will learn stochastic models on graphs, e.g. Random Walks, percolation and random graphs. In the end you will be able to analyse Random Walks on networks, use the connection to electrical networks to show recurrence/transience, and understand phase transitions and random spanning trees.5 ECTSno date this semesterMA4406Random Matrices: Theory, Numerical Methods, and ApplicationNo ratings for this module yet.A1.3.1 Modules in Probability TheoryYou will receive an introduction to large random matrices, their eigenvalue distributions and eigenvalue spacings. At the end of the module you will know the fundamental methods (e.g. Stieltjes transform, orthogonal polynomials, Fredholm determinants, free probability) and you will be able to compute limit distributions and apply them to models in applications.3 ECTSno date this semesterMA5306Self-interacting Random Walks and Statistical PhysicsNo ratings for this module yet.A1.3.1 Modules in Probability TheoryYou will learn methods for the analysis of self-interacting random walks and their connections to statistical physics. In the end you will be able to understand and apply central models (e.g. edge-/vertex-reinforced processes), proofs of localization/delocalization, and connections to supersymmetric sigma models and random Schrödinger operators.3 ECTSno date this semesterMA5941Statistical 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 semesterMA5428Stochastic AnalysisNo ratings for this module yet.A1.3.1 Modules in Probability TheoryYou will learn the theory and fundamental applications of stochastic analysis. The focus is on Brownian motion (construction and properties), stochastic integrals and the Itô formula, as well as stochastic differential equations and methods such as Girsanov transformation and Donsker's invariance principle. In the end you will be able to formulate central statements and perform simple calculations with Itô integrals and SDEs.9 ECTSno date this semesterMA4405Theorie der ZufallsmatrizenNo ratings for this module yet.A1.3.1 Modules in Probability TheoryYou learn non-asymptotic deviation estimates for random variables and vectors (in particular subgaussian and subexponential as well as isotropic vectors) and apply these concepts to random matrices with independent rows or columns. In the end you can formulate statements about the extreme singular values of such matrices, compare them and apply them to concrete examples as well as applications such as dimensionality reduction and Compressed Sensing.5 ECTSno date this semesterMA5346Topics in the Theory of Markov ProcessesNo ratings for this module yet.A1.3.1 Modules in Probability TheoryYou engage with analytical aspects of Markov processes, in particular Itô diffusions (linear and nonlinear). By the end you will be able to understand Markov semigroups and generators, classify basic existence and uniqueness results for McKean-SDEs/McKean–Vlasov equations, and make statements about long-term behavior as well as phase transitions for nonlinear Fokker–Planck equations.3 ECTSno date this semesterMA5424