Browsing Fakultät für Mathematik und Informatik (inkl. GAUSS) by Referee "Munk, Axel Prof. Dr."
Now showing items 1-20 of 41
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Domain decomposition for optimal transport and localized optimality conditions
(2024-12-19)Optimal transport (OT) is a fundamental tool in the study of the space of probability measures. Several algorithmic breakthroughs, such as the Sinkhorn algorithm, have allowed practicioners to solve the OT problem ... -
Statistical Limit Laws for Graph Cuts and Efficient Surrogate Algorithms
(2024-12-05)Graph cuts are a powerful tool that has been used in many applications, from image segmentation and machine learning to network analysis and cluster identification, often in the form of a convex relaxation such as spectral ... -
Statistical Optimal Transport and its Entropic Regularization: Compared and Contrasted
(2024-04-26)In recent years, statistical methodology based on optimal transport witnessed a considerable increase in practical and theoretical interest. A central reason for this trend is the ability of optimal transport to compare ... -
A Wasserstein-like Distance on Vector Fields
(2023-10-06)We introduce a new distance on the space of vector fields over a Riemannian manifold that is motivated by the construction and properties of the Wasserstein distance. The construction relies on a particular metric on the ... -
Statistical and Structural Aspects of Unbalanced Optimal Transport Barycenters
(2022-10-20)Optimal transport (OT) has seen a stellar rise in interest and relevance in the past two decades. More recently, severe limitation of OT have started to surface. Two key factors prevent it from becoming a standard tool in ... -
Computational methods for random tomography with applications to cryo-EM data
(2022-08-01)Over the last decade, Cryo Electron Microscopy (cryo-EM) has emerged as a powerful and reliable technique to determine the three-dimensional (3D) structure of large macro-molecular assemblies at near atomic resolution. ... -
Contributions to the Theory of Statistical Optimal Transport
(2022-07-01)The application of optimal transport based methodologies for statistical purposes has experienced a surge of interest and activity in recent years. This doctoral thesis collects the work of four research articles on the ... -
On minimax detection of localized signals from indirect or correlated data
(2022-05-05)This is a cumulative thesis consisting of two papers, in which we treat two problems related to the detectability of local anomalies within certain types of data. In the first paper, we suppose that a segment of a Gaussian ... -
Limit Laws for Empirical Optimal Transport
(2022-02-17)Optimal Transport (OT) has recently gained increasing attention in various fields ranging from biology to machine learning and mathematics. Especially OT based dissimilarity measures can be designed to respect the underlying ... -
Geometric convergence of slice sampling
(2021-10-19)In Bayesian statistics sampling w.r.t. a posterior distribution, which is given through a prior and a likelihood function, is a challenging task. The generation of exact samples is in general quite difficult, since the ... -
Convergence rates for variational regularization of inverse problems in exponential families
(2020-07-16)We consider statistical inverse problems with statistical noise. By using regularization methods one can approximate the true solution of the inverse problem by a regularized solution. The previous investigation of convergence ... -
A Statistical Model of Microscope Resolution
(2020-07-10)A general rule of thumb in imaging is that the resolution of a light microscope depends linearly on the full width at half maximum (FWHM) of its point spread function (psf). In the present work we carefully define a ... -
Multiscale Total Variation Estimators for Regression and Inverse Problems
(2019-06-28)In the context of nonparametric regression and inverse problems, variational multiscale methods combine multiscale dictionaries with regularization functionals in a variational framework. In recent years, these methods ... -
Semiparametric Estimation of Drift, Rotation and Scaling in Sparse Sequential Dynamic Imaging: Asymptotic theory and an application in nanoscale fluorescence microscopy
(2019-02-28)Light microscopy is an important instrument in life sciences. Over the last two decades, superresolution fluorescence microscopy techniques have been established, breaking the Abbé diffraction barrier, which before had ... -
Empirical Optimal Transport on Discrete Spaces: Limit Theorems, Distributional Bounds and Applications
(2019-01-09)Optimal Transport and especially distances based on optimal transport are a widely applied tool in different mathematical disciplines. Among others it is used in probability theory to study for example limit laws or derive ... -
Multiscale Scanning in Higher Dimensions: Limit theory, statistical consequences and an application in STED microscopy
(2018-07-17)Scan statistics have a broad area of applications ranging from astrophysics over genetic screening to fluorescence microscopy. Here, we consider a calibrated scan statistic based on local likelihood ratio tests of homogeneity ... -
Heterogeneous Multiscale Change-Point Inference and its Application to Ion Channel Recordings
(2018-02-09)Ion channel recordings by the patch clamp technique are a major tool to quantify the electrophysiological dynamics of ion channels in the cell membrane, which is for instance important in medicine for the development of ... -
Finite Alphabet Blind Separation
(2018-01-04)This thesis considers a particular blind source separation problem, where the sources are assumed to only take values in a known finite set, denoted as the alphabet. More precisely, one observes M linear mixtures of m ... -
Inference in inhomogeneous hidden Markov models with application to ion channel data
(2017-12-18)Ion channel recordings under a changing environment are hardly analyzed and are the main cause for the new model class we introduce. This thesis mainly concerns hidden Markov models with a homogeneous hidden Markov chain ... -
Wasserstein Distance on Finite Spaces: Statistical Inference and Algorithms
(2017-12-07)Wasserstein distances or, more generally, distances that quantify the optimal transport between probability measures on metric spaces have long been established as an important tool in probability theory. More recently, ...