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Wasserstein Distance on Finite Spaces: Statistical Inference and Algorithms

dc.contributor.advisorMunk, Axel Prof. Dr.
dc.contributor.authorSommerfeld, Max
dc.date.accessioned2017-12-07T09:28:53Z
dc.date.available2017-12-07T09:28:53Z
dc.date.issued2017-12-07
dc.identifier.urihttp://hdl.handle.net/11858/00-1735-0000-0023-3FA1-C
dc.identifier.urihttp://dx.doi.org/10.53846/goediss-6631
dc.language.isoengde
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subject.ddc510de
dc.titleWasserstein Distance on Finite Spaces: Statistical Inference and Algorithmsde
dc.typedoctoralThesisde
dc.contributor.refereeMunk, Axel Prof. Dr.
dc.date.examination2017-10-18
dc.description.abstractengWasserstein 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, it has found its way into statistical theory, applications and machine learning - not only as a theoretical tool but also as a quantity of interest in its own right. Examples include goodness-of-fit, two-sample and equivalence testing, classification and clustering, exploratory data analysis using Fr ́echet means and geodesics in the Wasserstein metric. This advent of the Wasserstein distance as a statistical tool manifests two major challenges. First, knowledge on the theoretical properties of empirical, i.e. sample-based, Wasserstein distances remains incomplete, in particular as far as distributional limits on spaces other than the real line are concerned. Second, any application of the Wasserstein distance invokes massive computational challenges, leaving many practically interesting problems outside of the scope of available algorithms. The main thesis of this work is that restricting ourselves to the Wasserstein distance on finite spaces offers a perspective that is able to solve or at least avoid these problems and is still general enough to include many practical problems. Indeed, this work will present comprehensive distributional limits for empirical Wasserstein distances on finite spaces, strategies to apply these limits with controllable computational burden in large-scale in- ference and a fast probabilistic approximation scheme for optimal transport distances.de
dc.contributor.coRefereeHuckemann, Stephan Prof. Dr.
dc.subject.engWasserstein distancede
dc.subject.engOptimal transportde
dc.subject.engDistributional limitsde
dc.subject.engFast approximationde
dc.identifier.urnurn:nbn:de:gbv:7-11858/00-1735-0000-0023-3FA1-C-6
dc.affiliation.instituteFakultät für Mathematik und Informatikde
dc.subject.gokfullMathematics (PPN61756535X)de
dc.identifier.ppn1008120855


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