Computational Optimal Transport

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Computational Optimal Transport

Gabriel Peyre,Marco Cuturi
Computational Optimal Transport Book PDF

Author : Gabriel Peyre,Marco Cuturi
Publisher : Foundations and Trends(r) in M
Page : 272 pages
File Size : 45,5 Mb
Release : 2019-02-12
Category : Computers
ISBN : 1680835505

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Computational Optimal Transport by Gabriel Peyre,Marco Cuturi Pdf

The goal of Optimal Transport (OT) is to define geometric tools that are useful to compare probability distributions. Their use dates back to 1781. Recent years have witnessed a new revolution in the spread of OT, thanks to the emergence of approximate solvers that can scale to sizes and dimensions that are relevant to data sciences. Thanks to this newfound scalability, OT is being increasingly used to unlock various problems in imaging sciences (such as color or texture processing), computer vision and graphics (for shape manipulation) or machine learning (for regression, classification and density fitting). This monograph reviews OT with a bias toward numerical methods and their applications in data sciences, and sheds lights on the theoretical properties of OT that make it particularly useful for some of these applications. Computational Optimal Transport presents an overview of the main theoretical insights that support the practical effectiveness of OT before explaining how to turn these insights into fast computational schemes. Written for readers at all levels, the authors provide descriptions of foundational theory at two-levels. Generally accessible to all readers, more advanced readers can read the specially identified more general mathematical expositions of optimal transport tailored for discrete measures. Furthermore, several chapters deal with the interplay between continuous and discrete measures, and are thus targeting a more mathematically-inclined audience. This monograph will be a valuable reference for researchers and students wishing to get a thorough understanding of Computational Optimal Transport, a mathematical gem at the interface of probability, analysis and optimization.

Optimal Transport

Cédric Villani
Optimal Transport Book PDF

Author : Cédric Villani
Publisher : Springer Science & Business Media
Page : 970 pages
File Size : 40,8 Mb
Release : 2008-10-26
Category : Mathematics
ISBN : 9783540710509

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Optimal Transport by Cédric Villani Pdf

At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and John Mather launched a revolution in the venerable field of optimal transport founded by G. Monge in the 18th century, which has made breathtaking forays into various other domains of mathematics ever since. The author presents a broad overview of this area, supplying complete and self-contained proofs of all the fundamental results of the theory of optimal transport at the appropriate level of generality. Thus, the book encompasses the broad spectrum ranging from basic theory to the most recent research results. PhD students or researchers can read the entire book without any prior knowledge of the field. A comprehensive bibliography with notes that extensively discuss the existing literature underlines the book’s value as a most welcome reference text on this subject.

Computational Optimal Transport

Gabriel Peyré
Computational Optimal Transport Book PDF

Author : Gabriel Peyré
Publisher : Unknown
Page : 262 pages
File Size : 53,7 Mb
Release : 2019
Category : Electronic
ISBN : 1680835513

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Computational Optimal Transport by Gabriel Peyré Pdf

This book will be a valuable reference for researchers and students wishing to get a thorough understanding of Computational Optimal Transport, a mathematical gem at the interface of probability, analysis and optimization.

Optimal Transport Methods in Economics

Alfred Galichon
Optimal Transport Methods in Economics Book PDF

Author : Alfred Galichon
Publisher : Princeton University Press
Page : 184 pages
File Size : 52,9 Mb
Release : 2018-08-14
Category : Business & Economics
ISBN : 9780691183466

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Optimal Transport Methods in Economics by Alfred Galichon Pdf

Optimal Transport Methods in Economics is the first textbook on the subject written especially for students and researchers in economics. Optimal transport theory is used widely to solve problems in mathematics and some areas of the sciences, but it can also be used to understand a range of problems in applied economics, such as the matching between job seekers and jobs, the determinants of real estate prices, and the formation of matrimonial unions. This is the first text to develop clear applications of optimal transport to economic modeling, statistics, and econometrics. It covers the basic results of the theory as well as their relations to linear programming, network flow problems, convex analysis, and computational geometry. Emphasizing computational methods, it also includes programming examples that provide details on implementation. Applications include discrete choice models, models of differential demand, and quantile-based statistical estimation methods, as well as asset pricing models. Authoritative and accessible, Optimal Transport Methods in Economics also features numerous exercises throughout that help you develop your mathematical agility, deepen your computational skills, and strengthen your economic intuition. The first introduction to the subject written especially for economists Includes programming examples Features numerous exercises throughout Ideal for students and researchers alike

Optimal Transport for Applied Mathematicians

Filippo Santambrogio
Optimal Transport for Applied Mathematicians Book PDF

Author : Filippo Santambrogio
Publisher : Birkhäuser
Page : 353 pages
File Size : 55,8 Mb
Release : 2015-10-17
Category : Mathematics
ISBN : 9783319208282

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Optimal Transport for Applied Mathematicians by Filippo Santambrogio Pdf

This monograph presents a rigorous mathematical introduction to optimal transport as a variational problem, its use in modeling various phenomena, and its connections with partial differential equations. Its main goal is to provide the reader with the techniques necessary to understand the current research in optimal transport and the tools which are most useful for its applications. Full proofs are used to illustrate mathematical concepts and each chapter includes a section that discusses applications of optimal transport to various areas, such as economics, finance, potential games, image processing and fluid dynamics. Several topics are covered that have never been previously in books on this subject, such as the Knothe transport, the properties of functionals on measures, the Dacorogna-Moser flow, the formulation through minimal flows with prescribed divergence formulation, the case of the supremal cost, and the most classical numerical methods. Graduate students and researchers in both pure and applied mathematics interested in the problems and applications of optimal transport will find this to be an invaluable resource.

Algorithms for Optimization

Mykel J. Kochenderfer,Tim A. Wheeler
Algorithms for Optimization Book PDF

Author : Mykel J. Kochenderfer,Tim A. Wheeler
Publisher : MIT Press
Page : 521 pages
File Size : 42,9 Mb
Release : 2019-03-12
Category : Computers
ISBN : 9780262039420

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Algorithms for Optimization by Mykel J. Kochenderfer,Tim A. Wheeler Pdf

A comprehensive introduction to optimization with a focus on practical algorithms for the design of engineering systems. This book offers a comprehensive introduction to optimization with a focus on practical algorithms. The book approaches optimization from an engineering perspective, where the objective is to design a system that optimizes a set of metrics subject to constraints. Readers will learn about computational approaches for a range of challenges, including searching high-dimensional spaces, handling problems where there are multiple competing objectives, and accommodating uncertainty in the metrics. Figures, examples, and exercises convey the intuition behind the mathematical approaches. The text provides concrete implementations in the Julia programming language. Topics covered include derivatives and their generalization to multiple dimensions; local descent and first- and second-order methods that inform local descent; stochastic methods, which introduce randomness into the optimization process; linear constrained optimization, when both the objective function and the constraints are linear; surrogate models, probabilistic surrogate models, and using probabilistic surrogate models to guide optimization; optimization under uncertainty; uncertainty propagation; expression optimization; and multidisciplinary design optimization. Appendixes offer an introduction to the Julia language, test functions for evaluating algorithm performance, and mathematical concepts used in the derivation and analysis of the optimization methods discussed in the text. The book can be used by advanced undergraduates and graduate students in mathematics, statistics, computer science, any engineering field, (including electrical engineering and aerospace engineering), and operations research, and as a reference for professionals.

Computation and Big Data for Transport

Pedro Diez,Pekka Neittaanmäki,Jacques Periaux,Tero Tuovinen,Jordi Pons-Prats
Computation and Big Data for Transport Book PDF

Author : Pedro Diez,Pekka Neittaanmäki,Jacques Periaux,Tero Tuovinen,Jordi Pons-Prats
Publisher : Springer Nature
Page : 252 pages
File Size : 44,7 Mb
Release : 2020-02-28
Category : Technology & Engineering
ISBN : 9783030377526

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Computation and Big Data for Transport by Pedro Diez,Pekka Neittaanmäki,Jacques Periaux,Tero Tuovinen,Jordi Pons-Prats Pdf

This book gathers the outcomes of the second ECCOMAS CM3 Conference series on transport, which addressed the main challenges and opportunities that computation and big data represent for transport and mobility in the automotive, logistics, aeronautics and marine-maritime fields. Through a series of plenary lectures and mini-forums with lectures followed by question-and-answer sessions, the conference explored potential solutions and innovations to improve transport and mobility in surface and air applications. The book seeks to answer the question of how computational research in transport can provide innovative solutions to Green Transportation challenges identified in the ambitious Horizon 2020 program. In particular, the respective papers present the state of the art in transport modeling, simulation and optimization in the fields of maritime, aeronautics, automotive and logistics research. In addition, the content includes two white papers on transport challenges and prospects. Given its scope, the book will be of interest to students, researchers, engineers and practitioners whose work involves the implementation of Intelligent Transport Systems (ITS) software for the optimal use of roads, including safety and security, traffic and travel data, surface and air traffic management, and freight logistics.

An Invitation to Statistics in Wasserstein Space

Victor M. Panaretos,Yoav Zemel
An Invitation to Statistics in Wasserstein Space Book PDF

Author : Victor M. Panaretos,Yoav Zemel
Publisher : Springer Nature
Page : 157 pages
File Size : 53,6 Mb
Release : 2020-03-10
Category : Mathematics
ISBN : 9783030384388

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An Invitation to Statistics in Wasserstein Space by Victor M. Panaretos,Yoav Zemel Pdf

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.

Flux-Corrected Transport

Dmitri Kuzmin,Rainald Löhner,Stefan Turek
Flux Corrected Transport Book PDF

Author : Dmitri Kuzmin,Rainald Löhner,Stefan Turek
Publisher : Springer Science & Business Media
Page : 462 pages
File Size : 49,6 Mb
Release : 2012-04-02
Category : Science
ISBN : 9789400740372

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Flux-Corrected Transport by Dmitri Kuzmin,Rainald Löhner,Stefan Turek Pdf

Addressing students and researchers as well as Computational Fluid Dynamics practitioners, this book is the most comprehensive review of high-resolution schemes based on the principle of Flux-Corrected Transport (FCT). The foreword by J.P. Boris and historical note by D.L. Book describe the development of the classical FCT methodology for convection-dominated transport problems, while the design philosophy behind modern FCT schemes is explained by S.T. Zalesak. The subsequent chapters present various improvements and generalizations proposed over the past three decades. In this new edition, recent results are integrated into existing chapters in order to describe significant advances since the publication of the first edition. Also, 3 new chapters were added in order to cover the following topics: algebraic flux correction for finite elements, iterative and linearized FCT schemes, TVD-like flux limiters, acceleration of explicit and implicit solvers, mesh adaptation, failsafe limiting for systems of conservation laws, flux-corrected interpolation (remapping), positivity preservation in RANS turbulence models, and the use of FCT as an implicit subgrid scale model for large eddy simulations.

Computational Complexity and Feasibility of Data Processing and Interval Computations

V. Kreinovich,A.V. Lakeyev,J. Rohn,P.T. Kahl
Computational Complexity and Feasibility of Data Processing and Interval Computations Book PDF

Author : V. Kreinovich,A.V. Lakeyev,J. Rohn,P.T. Kahl
Publisher : Springer Science & Business Media
Page : 460 pages
File Size : 48,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475727937

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Computational Complexity and Feasibility of Data Processing and Interval Computations by V. Kreinovich,A.V. Lakeyev,J. Rohn,P.T. Kahl Pdf

Targeted audience • Specialists in numerical computations, especially in numerical optimiza tion, who are interested in designing algorithms with automatie result ver ification, and who would therefore be interested in knowing how general their algorithms caIi in principle be. • Mathematicians and computer scientists who are interested in the theory 0/ computing and computational complexity, especially computational com plexity of numerical computations. • Students in applied mathematics and computer science who are interested in computational complexity of different numerical methods and in learning general techniques for estimating this computational complexity. The book is written with all explanations and definitions added, so that it can be used as a graduate level textbook. What this book .is about Data processing. In many real-life situations, we are interested in the value of a physical quantity y that is diflicult (or even impossible) to measure directly. For example, it is impossible to directly measure the amount of oil in an oil field or a distance to a star. Since we cannot measure such quantities directly, we measure them indirectly, by measuring some other quantities Xi and using the known relation between y and Xi'S to reconstruct y. The algorithm that transforms the results Xi of measuring Xi into an estimate fj for y is called data processing.

Computational Combinatorial Optimization

Michael Jünger,Denis Naddef
Computational Combinatorial Optimization Book PDF

Author : Michael Jünger,Denis Naddef
Publisher : Springer Science & Business Media
Page : 317 pages
File Size : 53,7 Mb
Release : 2001-11-21
Category : Mathematics
ISBN : 9783540428770

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Computational Combinatorial Optimization by Michael Jünger,Denis Naddef Pdf

This tutorial contains written versions of seven lectures on Computational Combinatorial Optimization given by leading members of the optimization community. The lectures introduce modern combinatorial optimization techniques, with an emphasis on branch and cut algorithms and Lagrangian relaxation approaches. Polyhedral combinatorics as the mathematical backbone of successful algorithms are covered from many perspectives, in particular, polyhedral projection and lifting techniques and the importance of modeling are extensively discussed. Applications to prominent combinatorial optimization problems, e.g., in production and transport planning, are treated in many places; in particular, the book contains a state-of-the-art account of the most successful techniques for solving the traveling salesman problem to optimality.

Topics in Optimal Transportation

Cédric Villani
Topics in Optimal Transportation Book PDF

Author : Cédric Villani
Publisher : American Mathematical Soc.
Page : 370 pages
File Size : 53,9 Mb
Release : 2021-08-25
Category : Education
ISBN : 9781470467265

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Topics in Optimal Transportation by Cédric Villani Pdf

This is the first comprehensive introduction to the theory of mass transportation with its many—and sometimes unexpected—applications. In a novel approach to the subject, the book both surveys the topic and includes a chapter of problems, making it a particularly useful graduate textbook. In 1781, Gaspard Monge defined the problem of “optimal transportation” (or the transferring of mass with the least possible amount of work), with applications to engineering in mind. In 1942, Leonid Kantorovich applied the newborn machinery of linear programming to Monge's problem, with applications to economics in mind. In 1987, Yann Brenier used optimal transportation to prove a new projection theorem on the set of measure preserving maps, with applications to fluid mechanics in mind. Each of these contributions marked the beginning of a whole mathematical theory, with many unexpected ramifications. Nowadays, the Monge-Kantorovich problem is used and studied by researchers from extremely diverse horizons, including probability theory, functional analysis, isoperimetry, partial differential equations, and even meteorology. Originating from a graduate course, the present volume is intended for graduate students and researchers, covering both theory and applications. Readers are only assumed to be familiar with the basics of measure theory and functional analysis.

Handbook of Machine Learning for Computational Optimization

Vishal Jain,Sapna Juneja,Abhinav Juneja,Ramani Kannan
Handbook of Machine Learning for Computational Optimization Book PDF

Author : Vishal Jain,Sapna Juneja,Abhinav Juneja,Ramani Kannan
Publisher : CRC Press
Page : 295 pages
File Size : 42,7 Mb
Release : 2021-11-02
Category : Technology & Engineering
ISBN : 9781000455670

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Handbook of Machine Learning for Computational Optimization by Vishal Jain,Sapna Juneja,Abhinav Juneja,Ramani Kannan Pdf

Focuses on new machine learning developments that can lead to newly developed applications Uses a predictive and futuristic approach which makes Machine Learning a promising tool for business processes and sustainable solutions Promotes newer algorithms which are more efficient and reliable for a new dimension in discovering certain latent domains of applications Discusses the huge potential in making better use of machines in order to ensure optimal prediction, execution, and decision-making Offers many real-time case studies

Modern Statistical Methods for Health Research

Yichuan Zhao,(Din) Ding-Geng Chen
Modern Statistical Methods for Health Research Book PDF

Author : Yichuan Zhao,(Din) Ding-Geng Chen
Publisher : Springer
Page : 0 pages
File Size : 44,7 Mb
Release : 2022-10-15
Category : Medical
ISBN : 3030724395

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Modern Statistical Methods for Health Research by Yichuan Zhao,(Din) Ding-Geng Chen Pdf

This book brings together the voices of leading experts in the frontiers of biostatistics, biomedicine, and the health sciences to discuss the statistical procedures, useful methods, and novel applications in biostatistics research. It also includes discussions of potential future directions of biomedicine and new statistical developments for health research, with the intent of stimulating research and fostering the interactions of scholars across health research related disciplines. Topics covered include: Health data analysis and applications to EHR data Clinical trials, FDR, and applications in health science Big network analytics and its applications in GWAS Survival analysis and functional data analysis Graphical modelling in genomic studies The book will be valuable to data scientists and statisticians who are working in biomedicine and health, other practitioners in the health sciences, and graduate students and researchers in biostatistics and health.

Large-scale Kernel Machines

Léon Bottou,Olivier Chapelle,Dennis Decoste
Large scale Kernel Machines Book PDF

Author : Léon Bottou,Olivier Chapelle,Dennis Decoste
Publisher : MIT Press
Page : 409 pages
File Size : 44,6 Mb
Release : 2007
Category : Computers
ISBN : 9780262026253

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Large-scale Kernel Machines by Léon Bottou,Olivier Chapelle,Dennis Decoste Pdf

Solutions for learning from large scale datasets, including kernel learning algorithms that scale linearly with the volume of the data and experiments carried out on realistically large datasets. Pervasive and networked computers have dramatically reduced the cost of collecting and distributing large datasets. In this context, machine learning algorithms that scale poorly could simply become irrelevant. We need learning algorithms that scale linearly with the volume of the data while maintaining enough statistical efficiency to outperform algorithms that simply process a random subset of the data. This volume offers researchers and engineers practical solutions for learning from large scale datasets, with detailed descriptions of algorithms and experiments carried out on realistically large datasets. At the same time it offers researchers information that can address the relative lack of theoretical grounding for many useful algorithms. After a detailed description of state-of-the-art support vector machine technology, an introduction of the essential concepts discussed in the volume, and a comparison of primal and dual optimization techniques, the book progresses from well-understood techniques to more novel and controversial approaches. Many contributors have made their code and data available online for further experimentation. Topics covered include fast implementations of known algorithms, approximations that are amenable to theoretical guarantees, and algorithms that perform well in practice but are difficult to analyze theoretically. Contributors Léon Bottou, Yoshua Bengio, Stéphane Canu, Eric Cosatto, Olivier Chapelle, Ronan Collobert, Dennis DeCoste, Ramani Duraiswami, Igor Durdanovic, Hans-Peter Graf, Arthur Gretton, Patrick Haffner, Stefanie Jegelka, Stephan Kanthak, S. Sathiya Keerthi, Yann LeCun, Chih-Jen Lin, Gaëlle Loosli, Joaquin Quiñonero-Candela, Carl Edward Rasmussen, Gunnar Rätsch, Vikas Chandrakant Raykar, Konrad Rieck, Vikas Sindhwani, Fabian Sinz, Sören Sonnenburg, Jason Weston, Christopher K. I. Williams, Elad Yom-Tov