An Invitation to Statistics in Wasserstein Space
Springer International Publishing (Verlag)
978-3-030-38437-1 (ISBN)
This open access book presents the key aspects of statistics in Wasserstein spaces, i.e. statistics in the space of probability measures when endowed with the geometry of optimal transportation. Further to reviewing state-of-the-art aspects, it also provides an accessible introduction to the fundamentals of this current topic, as well as an overview that will serve as an invitation and catalyst for further research.
Statistics in Wasserstein spaces represents an emerging topic in mathematical statistics, situated at the interface between functional data analysis (where the data are functions, thus lying in infinite dimensional Hilbert space) and non-Euclidean statistics (where the data satisfy nonlinear constraints, thus lying on non-Euclidean manifolds). The Wasserstein space provides the natural mathematical formalism to describe data collections that are best modeled as random measures on Euclidean space (e.g. images and point processes). Such random measures carry the infinite dimensional traits of functional data, but are intrinsically nonlinear due to positivity and integrability restrictions. Indeed, their dominating statistical variation arises through random deformations of an underlying template, a theme that is pursued in depth in this monograph.
Professor Victor M. Panaretos holds the Chair of Mathematical Statistics at the EPFL. He completed his undergraduate studies in mathematics and statistics in Athens and Dublin. He then received his PhD in 2007 from the University of California at Berkeley, for which he was awarded the Erich Lehmann Award. He is an elected member of the International Statistical Institute, the recipient of an ERC Starting Grant Award, and a member of the editorial board of Biometrika, Annals of Applied Statistics, and the Electronic Journal of Statistics. Dr. Yoav Zemel recently graduated with a PhD Mathematics at the EPFL, and is currently a Postdoctoral researcher in the Chair of Mathematical Statistics. He completed his undergraduate studies in mathematics and economics at the Hebrew University of Jerusalem, and earned an MSc in Applied Mathematics at the EPFL. He is the recipient of the EPFL excellence scholarship, as well as the Hebrew University Amirim scholarship, Rector's Prize and Dean's Prize.
Optimal transportation.- The Wasserstein space.- Fréchet means in the Wasserstein space.- Phase variation and Fréchet means.- Construction of Fréchet means and multicouplings.
| Erscheinungsdatum | 14.03.2020 |
|---|---|
| Reihe/Serie | SpringerBriefs in Probability and Mathematical Statistics |
| Zusatzinfo | XIII, 147 p. 30 illus., 24 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 261 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Statistik |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| Schlagworte | Barycenter • Fréchet mean • functional data analysis • Geometrical statistics • Gradient descent • Manifold Statistics • Monge-Kantorovich problem • Multimarginal Transport • open access • Optimal Transportation • Phase variation • point processes • Procrustes analysis • Random Measures • Wasserstein metric |
| ISBN-10 | 3-030-38437-3 / 3030384373 |
| ISBN-13 | 978-3-030-38437-1 / 9783030384371 |
| Zustand | Neuware |
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