An Invitation To Statistics In Wasserstein Space
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An Invitation To Statistics In Wasserstein Space
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Author : Victor M. Panaretos
language : en
Publisher: Springer Nature
Release Date : 2020-03-10
An Invitation To Statistics In Wasserstein Space written by Victor M. Panaretos and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-10 with Mathematics categories.
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.
An Invitation To Statistics In Wasserstein Space
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Author : Victor M Panaretos
language : en
Publisher:
Release Date : 2020-10-09
An Invitation To Statistics In Wasserstein Space written by Victor M Panaretos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-09 with Mathematics categories.
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.; Gives a succinct introduction to necessary mathematical background, focusing on the results useful for statistics from an otherwise vast mathematical literature. Presents an up to date overview of the state of the art, including some original results, and discusses open problems. Suitable for self-study or to be used as a graduate level course text. Open access. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.
Object Oriented Data Analysis
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Author : J. S. Marron
language : en
Publisher: CRC Press
Release Date : 2021-11-18
Object Oriented Data Analysis written by J. S. Marron and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-18 with Computers categories.
Object Oriented Data Analysis is a framework that facilitates inter-disciplinary research through new terminology for discussing the often many possible approaches to the analysis of complex data. Such data are naturally arising in a wide variety of areas. This book aims to provide ways of thinking that enable the making of sensible choices. The main points are illustrated with many real data examples, based on the authors' personal experiences, which have motivated the invention of a wide array of analytic methods. While the mathematics go far beyond the usual in statistics (including differential geometry and even topology), the book is aimed at accessibility by graduate students. There is deliberate focus on ideas over mathematical formulas. J. S. Marron is the Amos Hawley Distinguished Professor of Statistics, Professor of Biostatistics, Adjunct Professor of Computer Science, Faculty Member of the Bioinformatics and Computational Biology Curriculum and Research Member of the Lineberger Cancer Center and the Computational Medicine Program, at the University of North Carolina, Chapel Hill. Ian L. Dryden is a Professor in the Department of Mathematics and Statistics at Florida International University in Miami, has served as Head of School of Mathematical Sciences at the University of Nottingham, and is joint author of the acclaimed book Statistical Shape Analysis.
Machine Learning For Econometrics And Related Topics
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Author : Vladik Kreinovich
language : en
Publisher: Springer Nature
Release Date :
Machine Learning For Econometrics And Related Topics written by Vladik Kreinovich and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Optimal Transport Statistics For Economics And Related Topics
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Author : Nguyen Ngoc Thach
language : en
Publisher: Springer Nature
Release Date : 2023-12-04
Optimal Transport Statistics For Economics And Related Topics written by Nguyen Ngoc Thach and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-04 with Technology & Engineering categories.
This volume emphasizes techniques of optimal transport statistics, but it also describes and uses other econometric techniques, ranging from more traditional statistical techniques to more innovative ones such as quantiles (in particular, multidimensional quantiles), maximum entropy approach, and machine learning. Applications range from general analysis of GDP growth, stock market, and consumer prices to analysis of specific sectors of economics (construction, credit and banking, energy, health, labor, textile, tourism, international trade) to specific issues affecting economy such as bankruptcy, effect of Covid-19 pandemic, effect of pollution, effect of gender, cryptocurrencies, and the existence of shadow economy. Papers presented in this volume also cover data processing techniques, with economic and financial application being the unifying theme. This volume shows what has been achieved, but even more important are remaining open problems. We hope that this volume will: ˆ inspire practitioners to learn how to apply state-of-the-art techniques, especially techniques of optimal transport statistics, to economic and financial problems, and ˆ inspire researchers to further improve the existing techniques and to come up with new techniques for studying economic and financial phenomena.
Research In Computational Topology 2
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Author : Ellen Gasparovic
language : en
Publisher: Springer Nature
Release Date : 2022-05-10
Research In Computational Topology 2 written by Ellen Gasparovic and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-10 with Mathematics categories.
This second volume of Research in Computational Topology is a celebration and promotion of research by women in applied and computational topology, containing the proceedings of the second workshop for Women in Computational Topology (WinCompTop) as well as papers solicited from the broader WinCompTop community. The multidisciplinary and international WinCompTop workshop provided an exciting and unique opportunity for women in diverse locations and research specializations to interact extensively and collectively contribute to new and active research directions in the field. The prestigious senior researchers that signed on to head projects at the workshop are global leaders in the discipline, and two of them were authors on some of the first papers in the field. Some of the featured topics include topological data analysis of power law structure in neural data; a nerve theorem for directional graph covers; topological or homotopical invariants for directed graphs encoding connections among a network of neurons; and the issue of approximation of objects by digital grids, including precise relations between the persistent homology of dual cubical complexes.
Distributional Reinforcement Learning
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Author : Marc G. Bellemare
language : en
Publisher: MIT Press
Release Date : 2023-05-30
Distributional Reinforcement Learning written by Marc G. Bellemare and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-30 with Computers categories.
The first comprehensive guide to distributional reinforcement learning, providing a new mathematical formalism for thinking about decisions from a probabilistic perspective. Distributional reinforcement learning is a new mathematical formalism for thinking about decisions. Going beyond the common approach to reinforcement learning and expected values, it focuses on the total reward or return obtained as a consequence of an agent's choices—specifically, how this return behaves from a probabilistic perspective. In this first comprehensive guide to distributional reinforcement learning, Marc G. Bellemare, Will Dabney, and Mark Rowland, who spearheaded development of the field, present its key concepts and review some of its many applications. They demonstrate its power to account for many complex, interesting phenomena that arise from interactions with one's environment. The authors present core ideas from classical reinforcement learning to contextualize distributional topics and include mathematical proofs pertaining to major results discussed in the text. They guide the reader through a series of algorithmic and mathematical developments that, in turn, characterize, compute, estimate, and make decisions on the basis of the random return. Practitioners in disciplines as diverse as finance (risk management), computational neuroscience, computational psychiatry, psychology, macroeconomics, and robotics are already using distributional reinforcement learning, paving the way for its expanding applications in mathematical finance, engineering, and the life sciences. More than a mathematical approach, distributional reinforcement learning represents a new perspective on how intelligent agents make predictions and decisions.
Decision And Game Theory For Security
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Author : Fei Fang
language : en
Publisher: Springer Nature
Release Date : 2023-03-12
Decision And Game Theory For Security written by Fei Fang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-12 with Computers categories.
This book constitutes the refereed proceedings of the 13th International Conference on Decision and Game Theory for Security, GameSec 2022, held in October 2022 in Pittsburgh, PA, USA. The 15 full papers presented were carefully reviewed and selected from 39 submissions. The papers are grouped thematically on: deception in security; planning and learning in dynamic environments; security games; adversarial learning and optimization; novel applications and new game models.
Statistics For Mathematicians
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Author : Victor M. Panaretos
language : en
Publisher: Birkhäuser
Release Date : 2016-06-01
Statistics For Mathematicians written by Victor M. Panaretos and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-01 with Mathematics categories.
This textbook provides a coherent introduction to the main concepts and methods of one-parameter statistical inference. Intended for students of Mathematics taking their first course in Statistics, the focus is on Statistics for Mathematicians rather than on Mathematical Statistics. The goal is not to focus on the mathematical/theoretical aspects of the subject, but rather to provide an introduction to the subject tailored to the mindset and tastes of Mathematics students, who are sometimes turned off by the informal nature of Statistics courses. This book can be used as the basis for an elementary semester-long first course on Statistics with a firm sense of direction that does not sacrifice rigor. The deeper goal of the text is to attract the attention of promising Mathematics students.
The Founder S Dilemmas
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Author : Noam Wasserman
language : en
Publisher: Princeton University Press
Release Date : 2013-04
The Founder S Dilemmas written by Noam Wasserman and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04 with Business & Economics categories.
The Founder's Dilemmas examines how early decisions by entrepreneurs can make or break a startup and its team. Drawing on a decade of research, including quantitative data on almost ten thousand founders as well as inside stories of founders like Evan Williams of Twitter and Tim Westergren of Pandora, Noam Wasserman reveals the common pitfalls founders face and how to avoid them.