Advertisement
| computational optimal transport with applications to data science: Computational Optimal Transport Gabriel Peyre, Marco Cuturi, 2019-02-12 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. |
| computational optimal transport with applications to data science: Computational Optimal Transport Gabriel Peyré, 2019 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. |
| computational optimal transport with applications to data science: Optimal Transport Cédric Villani, 2008-10-26 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 with applications to data science: Algorithms for Optimization Mykel J. Kochenderfer, Tim A. Wheeler, 2019-03-12 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. |
| computational optimal transport with applications to data science: Optimal Transport for Applied Mathematicians Filippo Santambrogio, 2015-10-17 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. |
| computational optimal transport with applications to data science: Data Intensive Computing Applications for Big Data M. Mittal, V.E. Balas, D.J. Hemanth, 2018-01-31 The book ‘Data Intensive Computing Applications for Big Data’ discusses the technical concepts of big data, data intensive computing through machine learning, soft computing and parallel computing paradigms. It brings together researchers to report their latest results or progress in the development of the above mentioned areas. Since there are few books on this specific subject, the editors aim to provide a common platform for researchers working in this area to exhibit their novel findings. The book is intended as a reference work for advanced undergraduates and graduate students, as well as multidisciplinary, interdisciplinary and transdisciplinary research workers and scientists on the subjects of big data and cloud/parallel and distributed computing, and explains didactically many of the core concepts of these approaches for practical applications. It is organized into 24 chapters providing a comprehensive overview of big data analysis using parallel computing and addresses the complete data science workflow in the cloud, as well as dealing with privacy issues and the challenges faced in a data-intensive cloud computing environment. The book explores both fundamental and high-level concepts, and will serve as a manual for those in the industry, while also helping beginners to understand the basic and advanced aspects of big data and cloud computing. |
| computational optimal transport with applications to data science: Handbook of Machine Learning for Computational Optimization Vishal Jain, Sapna Juneja, Abhinav Juneja, Ramani Kannan, 2021-11-02 Technology is moving at an exponential pace in this era of computational intelligence. Machine learning has emerged as one of the most promising tools used to challenge and think beyond current limitations. This handbook will provide readers with a leading edge to improving their products and processes through optimal and smarter machine learning techniques. This handbook focuses on new machine learning developments that can lead to newly developed applications. It uses a predictive and futuristic approach, which makes machine learning a promising tool for processes and sustainable solutions. It also promotes newer algorithms that are more efficient and reliable for new dimensions in discovering other applications, and then goes on to discuss the potential in making better use of machines in order to ensure optimal prediction, execution, and decision-making. Individuals looking for machine learning-based knowledge will find interest in this handbook. The readership ranges from undergraduate students of engineering and allied courses to researchers, professionals, and application designers. |
| computational optimal transport with applications to data science: An Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flows Alessio Figalli, Federico Glaudo, 2023-05-15 This book provides a self-contained introduction to optimal transport, and it is intended as a starting point for any researcher who wants to enter into this beautiful subject. The presentation focuses on the essential topics of the theory: Kantorovich duality, existence and uniqueness of optimal transport maps, Wasserstein distances, the JKO scheme, Otto's calculus, and Wasserstein gradient flows. At the end, a presentation of some selected applications of optimal transport is given. Suitable for a course at the graduate level, the book also includes an appendix with a series of exercises along with their solutions. The second edition contains a number of additions, such as a new section on the Brunn–Minkowski inequality, new exercises, and various corrections throughout the text. |
| computational optimal transport with applications to data science: An Invitation to Statistics in Wasserstein Space Victor M. Panaretos, Yoav Zemel, 2020-03-10 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. |
| computational optimal transport with applications to data science: Flux-Corrected Transport Dmitri Kuzmin, Rainald Löhner, Stefan Turek, 2014-05-09 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 optimal transport with applications to data science: Machine Learning: Theory and Applications , 2013-05-16 Statistical learning and analysis techniques have become extremely important today, given the tremendous growth in the size of heterogeneous data collections and the ability to process it even from physically distant locations. Recent advances made in the field of machine learning provide a strong framework for robust learning from the diverse corpora and continue to impact a variety of research problems across multiple scientific disciplines. The aim of this handbook is to familiarize beginners as well as experts with some of the recent techniques in this field.The Handbook is divided in two sections: Theory and Applications, covering machine learning, data analytics, biometrics, document recognition and security. - Very relevant to current research challenges faced in various fields - Self-contained reference to machine learning - Emphasis on applications-oriented techniques |
| computational optimal transport with applications to data science: Gradient Flows Luigi Ambrosio, Nicola Gigli, Giuseppe Savare, 2008-10-29 The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other. |
| computational optimal transport with applications to data science: Scattered Data Approximation Holger Wendland, 2004-12-13 Many practical applications require the reconstruction of a multivariate function from discrete, unstructured data. This book gives a self-contained, complete introduction into this subject. It concentrates on truly meshless methods such as radial basis functions, moving least squares, and partitions of unity. The book starts with an overview on typical applications of scattered data approximation, coming from surface reconstruction, fluid-structure interaction, and the numerical solution of partial differential equations. It then leads the reader from basic properties to the current state of research, addressing all important issues, such as existence, uniqueness, approximation properties, numerical stability, and efficient implementation. Each chapter ends with a section giving information on the historical background and hints for further reading. Complete proofs are included, making this perfectly suited for graduate courses on multivariate approximation and it can be used to support courses in computer-aided geometric design, and meshless methods for partial differential equations. |
| computational optimal transport with applications to data science: Computational Combinatorial Optimization Michael Jünger, Denis Naddef, 2001-11-21 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. |
| computational optimal transport with applications to data science: Data Analytics for Intelligent Transportation Systems Mashrur Chowdhury, Kakan Dey, Amy Apon, 2024-11-02 Data Analytics for Intelligent Transportation Systems provides in-depth coverage of data-enabled methods for analyzing intelligent transportation systems (ITS), including the tools needed to implement these methods using big data analytics and other computing techniques. The book examines the major characteristics of connected transportation systems, along with the fundamental concepts of how to analyze the data they produce. It explores collecting, archiving, processing, and distributing the data, designing data infrastructures, data management and delivery systems, and the required hardware and software technologies. It presents extensive coverage of existing and forthcoming intelligent transportation systems and data analytics technologies. All fundamentals/concepts presented in this book are explained in the context of ITS. Users will learn everything from the basics of different ITS data types and characteristics to how to evaluate alternative data analytics for different ITS applications. They will discover how to design effective data visualizations, tactics on the planning process, and how to evaluate alternative data analytics for different connected transportation applications, along with key safety and environmental applications for both commercial and passenger vehicles, data privacy and security issues, and the role of social media data in traffic planning. Data Analytics for Intelligent Transportation Systems will prepare an educated ITS workforce and tool builders to make the vision for safe, reliable, and environmentally sustainable intelligent transportation systems a reality. It serves as a primary or supplemental textbook for upper-level undergraduate and graduate ITS courses and a valuable reference for ITS practitioners. - Utilizes real ITS examples to facilitate a quicker grasp of materials presented - Contains contributors from both leading academic and commercial domains - Explains how to design effective data visualizations, tactics on the planning process, and how to evaluate alternative data analytics for different connected transportation applications - Includes exercise problems in each chapter to help readers apply and master the learned fundamentals, concepts, and techniques - New to the second edition: Two new chapters on Quantum Computing in Data Analytics and Society and Environment in ITS Data Analytics |
| computational optimal transport with applications to data science: Computational Geometry Franco P. Preparata, Michael I. Shamos, 2012-12-06 From the reviews: This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry. ... ... The book is well organized and lucidly written; a timely contribution by two founders of the field. It clearly demonstrates that computational geometry in the plane is now a fairly well-understood branch of computer science and mathematics. It also points the way to the solution of the more challenging problems in dimensions higher than two. #Mathematical Reviews#1 ... This remarkable book is a comprehensive and systematic study on research results obtained especially in the last ten years. The very clear presentation concentrates on basic ideas, fundamental combinatorial structures, and crucial algorithmic techniques. The plenty of results is clever organized following these guidelines and within the framework of some detailed case studies. A large number of figures and examples also aid the understanding of the material. Therefore, it can be highly recommended as an early graduate text but it should prove also to be essential to researchers and professionals in applied fields of computer-aided design, computer graphics, and robotics. #Biometrical Journal#2 |
| computational optimal transport with applications to data science: Mobility Patterns, Big Data and Transport Analytics Constantinos Antoniou, Loukas Dimitriou, Francisco Pereira, 2025-06-01 Mobility Patterns, Big Data and Transport Analytics: Tools and Applications for Modeling, Second Edition provides a guide to the new analytical framework and its relation to big data, focusing on capturing, predicting, visualizing and controlling mobility patterns-a key aspect of transportation modeling. It features prominent international experts who provide overviews on new analytical frameworks, applications and concepts in mobility analysis and transportation systems. The fields covered by this book are evolving rapidly and this new edition updates the existing material and provides new chapters that reflect recent developments in the field (such as the emergence of active, transfer and reinforcement learning). Users will find a detailed, mobility ‘structural’ analysis and a look at the extensive behavioral characteristics of transport, observability requirements and limitations for realistic transportation applications, and transportation systems analysis that are related to complex processes and phenomena. It bridges the gap between big data, data science, and transportation systems analysis with a study of big data’s impact on mobility and an introduction to the tools necessary to apply new techniques. |
| computational optimal transport with applications to data science: Optimal Transport Gershon Wolansky, 2021-01-18 The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Editor-in-Chief J rgen Appell, W rzburg, Germany Honorary and Advisory Editors Catherine Bandle, Basel, Switzerland Alain Bensoussan, Richardson, Texas, USA Avner Friedman, Columbus, Ohio, USA Umberto Mosco, Worcester, Massachusetts, USA Louis Nirenberg, New York, USA Alfonso Vignoli, Rome, Italy Editorial Board Manuel del Pino, Bath, UK, and Santiago, Chile Mikio Kato, Nagano, Japan Wojciech Kryszewski, Toruń, Poland Vicenţiu D. Rădulescu, Krak w, Poland Simeon Reich, Haifa, Israel Please submit book proposals to J rgen Appell. Titles in planning include Lucio Damascelli and Filomena Pacella, Morse Index of Solutions of Nonlinear Elliptic Equations (2019) Tomasz W. Dlotko and Yejuan Wang, Critical Parabolic-Type Problems (2019) Rafael Ortega, Periodic Differential Equations in the Plane: A Topological Perspective (2019) Ireneo Peral Alonso and Fernando Soria, Elliptic and Parabolic Equations Involving the Hardy-Leray Potential (2020) Cyril Tintarev, Profile Decompositions and Cocompactness: Functional-Analytic Theory of Concentration Compactness (2020) Takashi Suzuki, Semilinear Elliptic Equations: Classical and Modern Theories (2021) |
| computational optimal transport with applications to data science: Optimal Transport Methods in Economics Alfred Galichon, 2018-08-14 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 |
| computational optimal transport with applications to data science: Mathematics of Big Data Jeremy Kepner, Hayden Jananthan, 2018-08-07 The first book to present the common mathematical foundations of big data analysis across a range of applications and technologies. Today, the volume, velocity, and variety of data are increasing rapidly across a range of fields, including Internet search, healthcare, finance, social media, wireless devices, and cybersecurity. Indeed, these data are growing at a rate beyond our capacity to analyze them. The tools—including spreadsheets, databases, matrices, and graphs—developed to address this challenge all reflect the need to store and operate on data as whole sets rather than as individual elements. This book presents the common mathematical foundations of these data sets that apply across many applications and technologies. Associative arrays unify and simplify data, allowing readers to look past the differences among the various tools and leverage their mathematical similarities in order to solve the hardest big data challenges. The book first introduces the concept of the associative array in practical terms, presents the associative array manipulation system D4M (Dynamic Distributed Dimensional Data Model), and describes the application of associative arrays to graph analysis and machine learning. It provides a mathematically rigorous definition of associative arrays and describes the properties of associative arrays that arise from this definition. Finally, the book shows how concepts of linearity can be extended to encompass associative arrays. Mathematics of Big Data can be used as a textbook or reference by engineers, scientists, mathematicians, computer scientists, and software engineers who analyze big data. |
| computational optimal transport with applications to data science: Topics in Optimal Transportation Cédric Villani, 2021-08-25 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. |
| computational optimal transport with applications to data science: Artificial Intelligence, Evolutionary Computing and Metaheuristics Xin-She Yang, 2012-07-27 Alan Turing pioneered many research areas such as artificial intelligence, computability, heuristics and pattern formation. Nowadays at the information age, it is hard to imagine how the world would be without computers and the Internet. Without Turing's work, especially the core concept of Turing Machine at the heart of every computer, mobile phone and microchip today, so many things on which we are so dependent would be impossible. 2012 is the Alan Turing year -- a centenary celebration of the life and work of Alan Turing. To celebrate Turing's legacy and follow the footsteps of this brilliant mind, we take this golden opportunity to review the latest developments in areas of artificial intelligence, evolutionary computation and metaheuristics, and all these areas can be traced back to Turing's pioneer work. Topics include Turing test, Turing machine, artificial intelligence, cryptography, software testing, image processing, neural networks, nature-inspired algorithms such as bat algorithm and cuckoo search, and multiobjective optimization and many applications. These reviews and chapters not only provide a timely snapshot of the state-of-art developments, but also provide inspiration for young researchers to carry out potentially ground-breaking research in the active, diverse research areas in artificial intelligence, cryptography, machine learning, evolutionary computation, and nature-inspired metaheuristics. This edited book can serve as a timely reference for graduates, researchers and engineers in artificial intelligence, computer sciences, computational intelligence, soft computing, optimization, and applied sciences. |
| computational optimal transport with applications to data science: Artificial Intelligence in Healthcare Adam Bohr, Kaveh Memarzadeh, 2020-06-21 Artificial Intelligence (AI) in Healthcare is more than a comprehensive introduction to artificial intelligence as a tool in the generation and analysis of healthcare data. The book is split into two sections where the first section describes the current healthcare challenges and the rise of AI in this arena. The ten following chapters are written by specialists in each area, covering the whole healthcare ecosystem. First, the AI applications in drug design and drug development are presented followed by its applications in the field of cancer diagnostics, treatment and medical imaging. Subsequently, the application of AI in medical devices and surgery are covered as well as remote patient monitoring. Finally, the book dives into the topics of security, privacy, information sharing, health insurances and legal aspects of AI in healthcare. - Highlights different data techniques in healthcare data analysis, including machine learning and data mining - Illustrates different applications and challenges across the design, implementation and management of intelligent systems and healthcare data networks - Includes applications and case studies across all areas of AI in healthcare data |
| computational optimal transport with applications to data science: Mass Transportation Problems Svetlozar T. Rachev, Ludger Rüschendorf, 2006-05-17 The first comprehensive account of the theory of mass transportation problems and its applications. In Volume I, the authors systematically develop the theory with emphasis on the Monge-Kantorovich mass transportation and the Kantorovich-Rubinstein mass transshipment problems. They then discuss a variety of different approaches towards solving these problems and exploit the rich interrelations to several mathematical sciences - from functional analysis to probability theory and mathematical economics. The second volume is devoted to applications of the above problems to topics in applied probability, theory of moments and distributions with given marginals, queuing theory, risk theory of probability metrics and its applications to various fields, among them general limit theorems for Gaussian and non-Gaussian limiting laws, stochastic differential equations and algorithms, and rounding problems. Useful to graduates and researchers in theoretical and applied probability, operations research, computer science, and mathematical economics, the prerequisites for this book are graduate level probability theory and real and functional analysis. |
| computational optimal transport with applications to data science: Data Science for Transport Charles Fox, 2018-02-27 The quantity, diversity and availability of transport data is increasing rapidly, requiring new skills in the management and interrogation of data and databases. Recent years have seen a new wave of 'big data', 'Data Science', and 'smart cities' changing the world, with the Harvard Business Review describing Data Science as the sexiest job of the 21st century. Transportation professionals and researchers need to be able to use data and databases in order to establish quantitative, empirical facts, and to validate and challenge their mathematical models, whose axioms have traditionally often been assumed rather than rigorously tested against data. This book takes a highly practical approach to learning about Data Science tools and their application to investigating transport issues. The focus is principally on practical, professional work with real data and tools, including business and ethical issues. Transport modeling practice was developed in a data poor world, and many of our current techniques and skills are building on that sparsity. In a new data rich world, the required tools are different and the ethical questions around data and privacy are definitely different. I am not sure whether current professionals have these skills; and I am certainly not convinced that our current transport modeling tools will survive in a data rich environment. This is an exciting time to be a data scientist in the transport field. We are trying to get to grips with the opportunities that big data sources offer; but at the same time such data skills need to be fused with an understanding of transport, and of transport modeling. Those with these combined skills can be instrumental at providing better, faster, cheaper data for transport decision- making; and ultimately contribute to innovative, efficient, data driven modeling techniques of the future. It is not surprising that this course, this book, has been authored by the Institute for Transport Studies. To do this well, you need a blend of academic rigor and practical pragmatism. There are few educational or research establishments better equipped to do that than ITS Leeds. - Tom van Vuren, Divisional Director, Mott MacDonald WSP is proud to be a thought leader in the world of transport modelling, planning and economics, and has a wide range of opportunities for people with skills in these areas. The evidence base and forecasts we deliver to effectively implement strategies and schemes are ever more data and technology focused a trend we have helped shape since the 1970's, but with particular disruption and opportunity in recent years. As a result of these trends, and to suitably skill the next generation of transport modellers, we asked the world-leading Institute for Transport Studies, to boost skills in these areas, and they have responded with a new MSc programme which you too can now study via this book. - Leighton Cardwell, Technical Director, WSP. From processing and analysing large datasets, to automation of modelling tasks sometimes requiring different software packages to talk to each other, to data visualization, SYSTRA employs a range of techniques and tools to provide our clients with deeper insights and effective solutions. This book does an excellent job in giving you the skills to manage, interrogate and analyse databases, and develop powerful presentations. Another important publication from ITS Leeds. - Fitsum Teklu, Associate Director (Modelling & Appraisal) SYSTRA Ltd Urban planning has relied for decades on statistical and computational practices that have little to do with mainstream data science. Information is still often used as evidence on the impact of new infrastructure even when it hardly contains any valid evidence. This book is an extremely welcome effort to provide young professionals with the skills needed to analyse how cities and transport networks actually work. The book is also highly relevant to anyone who will later want to build digital solutions to optimise urban travel based on emerging data sources. - Yaron Hollander, author of Transport Modelling for a Complete Beginner |
| computational optimal transport with applications to data science: Optimal Transport and Applications to Geometric Optics Cristian E. Gutiérrez, 2024-01-10 This book concerns the theory of optimal transport (OT) and its applications to solving problems in geometric optics. It is a self-contained presentation including a detailed analysis of the Monge problem, the Monge-Kantorovich problem, the transshipment problem, and the network flow problem. A chapter on Monge-Ampère measures is included containing also exercises. A detailed analysis of the Wasserstein metric is also carried out. For the applications to optics, the book describes the necessary background concerning light refraction, solving both far-field and near-field refraction problems, and indicates lines of current research in this area. Researchers in the fields of mathematical analysis, optimal transport, partial differential equations (PDEs), optimization, and optics will find this book valuable. It is also suitable for graduate students studying mathematics, physics, and engineering. The prerequisites for this book include a solid understanding of measure theory and integration, as well as basic knowledge of functional analysis. |
| computational optimal transport with applications to data science: Advanced Mathematical Applications in Data Science Biswadip Basu Mallik, Kirti Verma, Rahul Kar, Ashok Kumar Shaw, 2023-08-24 Advanced Mathematical Applications in Data Science comprehensively explores the crucial role mathematics plays in the field of data science. Each chapter is contributed by scientists, researchers, and academicians. The 13 chapters cover a range of mathematical concepts utilized in data science, enabling readers to understand the intricate connection between mathematics and data analysis. The book covers diverse topics, including, machine learning models, the Kalman filter, data modeling, artificial neural networks, clustering techniques, and more, showcasing the application of advanced mathematical tools for effective data processing and analysis. With a strong emphasis on real-world applications, the book offers a deeper understanding of the foundational principles behind data analysis and its numerous interdisciplinary applications. This reference is an invaluable resource for graduate students, researchers, academicians, and learners pursuing a research career in mathematical computing or completing advanced data science courses. Key Features: Comprehensive coverage of advanced mathematical concepts and techniques in data science Contributions from established scientists, researchers, and academicians Real-world case studies and practical applications of mathematical methods Focus on diverse areas, such as image classification, carbon emission assessment, customer churn prediction, and healthcare data analysis In-depth exploration of data science's connection with mathematics, computer science, and artificial intelligence Scholarly references for each chapter Suitable for readers with high school-level mathematical knowledge, making it accessible to a broad audience in academia and industry. |
| computational optimal transport with applications to data science: Data-Driven Solutions to Transportation Problems Yinhai Wang, Ziqiang Zeng, 2018-12-05 Data-Driven Solutions to Transportation Problems explores the fundamental principle of analyzing different types of transportation-related data using methodologies such as the data fusion model, the big data mining approach, computer vision-enabled traffic sensing data analysis, and machine learning. The book examines the state-of-the-art in data-enabled methodologies, technologies and applications in transportation. Readers will learn how to solve problems relating to energy efficiency under connected vehicle environments, urban travel behavior, trajectory data-based travel pattern identification, public transportation analysis, traffic signal control efficiency, optimizing traffic networks network, and much more. |
| computational optimal transport with applications to data science: Data Analysis and Applications 3 Andreas Makrides, Alex Karagrigoriou, Christos H. Skiadas, 2020-06-16 Data analysis as an area of importance has grown exponentially, especially during the past couple of decades. This can be attributed to a rapidly growing computer industry and the wide applicability of computational techniques, in conjunction with new advances of analytic tools. This being the case, the need for literature that addresses this is self-evident. New publications are appearing, covering the need for information from all fields of science and engineering, thanks to the universal relevance of data analysis and statistics packages. This book is a collective work by a number of leading scientists, analysts, engineers, mathematicians and statisticians who have been working at the forefront of data analysis. The chapters included in this volume represent a cross-section of current concerns and research interests in these scientific areas. The material is divided into two parts: Computational Data Analysis, and Classification Data Analysis, with methods for both - providing the reader with both theoretical and applied information on data analysis methods, models and techniques and appropriate applications. |
| computational optimal transport with applications to data science: ECAI 2023 K. Gal, A. Nowé, G.J. Nalepa, 2023-10-18 Artificial intelligence, or AI, now affects the day-to-day life of almost everyone on the planet, and continues to be a perennial hot topic in the news. This book presents the proceedings of ECAI 2023, the 26th European Conference on Artificial Intelligence, and of PAIS 2023, the 12th Conference on Prestigious Applications of Intelligent Systems, held from 30 September to 4 October 2023 and on 3 October 2023 respectively in Kraków, Poland. Since 1974, ECAI has been the premier venue for presenting AI research in Europe, and this annual conference has become the place for researchers and practitioners of AI to discuss the latest trends and challenges in all subfields of AI, and to demonstrate innovative applications and uses of advanced AI technology. ECAI 2023 received 1896 submissions – a record number – of which 1691 were retained for review, ultimately resulting in an acceptance rate of 23%. The 390 papers included here, cover topics including machine learning, natural language processing, multi agent systems, and vision and knowledge representation and reasoning. PAIS 2023 received 17 submissions, of which 10 were accepted after a rigorous review process. Those 10 papers cover topics ranging from fostering better working environments, behavior modeling and citizen science to large language models and neuro-symbolic applications, and are also included here. Presenting a comprehensive overview of current research and developments in AI, the book will be of interest to all those working in the field. |
| computational optimal transport with applications to data science: Optimal Transportation and Applications Luigi Ambrosio, Luis A. Caffarelli, Yann Brenier, Giuseppe Buttazzo, Cédric Villani, 2003-01-01 Leading researchers in the field of Optimal Transportation, with different views and perspectives, contribute to this Summer School volume: Monge-Ampère and Monge-Kantorovich theory, shape optimization and mass transportation are linked, among others, to applications in fluid mechanics granular material physics and statistical mechanics, emphasizing the attractiveness of the subject from both a theoretical and applied point of view. The volume is designed to become a guide to researchers willing to enter into this challenging and useful theory. |
| computational optimal transport with applications to data science: Handbook of Uncertainty Quantification Roger Ghanem, David Higdon, Howman Owhadi, 2016-05-08 The topic of Uncertainty Quantification (UQ) has witnessed massive developments in response to the promise of achieving risk mitigation through scientific prediction. It has led to the integration of ideas from mathematics, statistics and engineering being used to lend credence to predictive assessments of risk but also to design actions (by engineers, scientists and investors) that are consistent with risk aversion. The objective of this Handbook is to facilitate the dissemination of the forefront of UQ ideas to their audiences. We recognize that these audiences are varied, with interests ranging from theory to application, and from research to development and even execution. |
| computational optimal transport with applications to data science: Nonlinear Programming Lorenz T. Biegler, 2010-01-01 This book addresses modern nonlinear programming (NLP) concepts and algorithms, especially as they apply to challenging applications in chemical process engineering. The author provides a firm grounding in fundamental NLP properties and algorithms, and relates them to real-world problem classes in process optimization, thus making the material understandable and useful to chemical engineers and experts in mathematical optimization. |
| computational optimal transport with applications to data science: Convex Analysis and Monotone Operator Theory in Hilbert Spaces Heinz H. Bauschke, Patrick L. Combettes, 2017-02-28 This reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, machine learning, physics, decision sciences, economics, and inverse problems. The second edition of Convex Analysis and Monotone Operator Theory in Hilbert Spaces greatly expands on the first edition, containing over 140 pages of new material, over 270 new results, and more than 100 new exercises. It features a new chapter on proximity operators including two sections on proximity operators of matrix functions, in addition to several new sections distributed throughout the original chapters. Many existing results have been improved, and the list of references has been updated. Heinz H. Bauschke is a Full Professor of Mathematics at the Kelowna campus of the University of British Columbia, Canada. Patrick L. Combettes, IEEE Fellow, was on the faculty of the City University of New York and of Université Pierre et Marie Curie – Paris 6 before joining North Carolina State University as a Distinguished Professor of Mathematics in 2016. |
| computational optimal transport with applications to data science: Geometric Science of Information Frank Nielsen, Frédéric Barbaresco, 2021-07-10 This book constitutes the proceedings of the 5th International Conference on Geometric Science of Information, GSI 2021, held in Paris, France, in July 2021. The 98 papers presented in this volume were carefully reviewed and selected from 125 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications. The papers are organized in the following topics: Probability and statistics on Riemannian Manifolds; sub-Riemannian geometry and neuromathematics; shapes spaces; geometry of quantum states; geometric and structure preserving discretizations; information geometry in physics; Lie group machine learning; geometric and symplectic methods for hydrodynamical models; harmonic analysis on Lie groups; statistical manifold and Hessian information geometry; geometric mechanics; deformed entropy, cross-entropy, and relative entropy; transformation information geometry; statistics, information and topology; geometric deep learning; topological and geometrical structures in neurosciences; computational information geometry; manifold and optimization; divergence statistics; optimal transport and learning; and geometric structures in thermodynamics and statistical physics. |
| computational optimal transport with applications to data science: Introduction to HPC with MPI for Data Science Frank Nielsen, 2016-02-03 This gentle introduction to High Performance Computing (HPC) for Data Science using the Message Passing Interface (MPI) standard has been designed as a first course for undergraduates on parallel programming on distributed memory models, and requires only basic programming notions. Divided into two parts the first part covers high performance computing using C++ with the Message Passing Interface (MPI) standard followed by a second part providing high-performance data analytics on computer clusters. In the first part, the fundamental notions of blocking versus non-blocking point-to-point communications, global communications (like broadcast or scatter) and collaborative computations (reduce), with Amdalh and Gustafson speed-up laws are described before addressing parallel sorting and parallel linear algebra on computer clusters. The common ring, torus and hypercube topologies of clusters are then explained and global communication procedures on these topologies are studied. This first part closes with the MapReduce (MR) model of computation well-suited to processing big data using the MPI framework. In the second part, the book focuses on high-performance data analytics. Flat and hierarchical clustering algorithms are introduced for data exploration along with how to program these algorithms on computer clusters, followed by machine learning classification, and an introduction to graph analytics. This part closes with a concise introduction to data core-sets that let big data problems be amenable to tiny data problems. Exercises are included at the end of each chapter in order for students to practice the concepts learned, and a final section contains an overall exam which allows them to evaluate how well they have assimilated the material covered in the book. |
| computational optimal transport with applications to data science: Probabilistic Machine Learning Kevin P. Murphy, 2022-03-01 A detailed and up-to-date introduction to machine learning, presented through the unifying lens of probabilistic modeling and Bayesian decision theory. This book offers a detailed and up-to-date introduction to machine learning (including deep learning) through the unifying lens of probabilistic modeling and Bayesian decision theory. The book covers mathematical background (including linear algebra and optimization), basic supervised learning (including linear and logistic regression and deep neural networks), as well as more advanced topics (including transfer learning and unsupervised learning). End-of-chapter exercises allow students to apply what they have learned, and an appendix covers notation. Probabilistic Machine Learning grew out of the author’s 2012 book, Machine Learning: A Probabilistic Perspective. More than just a simple update, this is a completely new book that reflects the dramatic developments in the field since 2012, most notably deep learning. In addition, the new book is accompanied by online Python code, using libraries such as scikit-learn, JAX, PyTorch, and Tensorflow, which can be used to reproduce nearly all the figures; this code can be run inside a web browser using cloud-based notebooks, and provides a practical complement to the theoretical topics discussed in the book. This introductory text will be followed by a sequel that covers more advanced topics, taking the same probabilistic approach. |
| computational optimal transport with applications to data science: Advances on Mathematical Modeling and Optimization with Its Applications Gunjan Mukherjee, Biswadip Basu Mallik, Rahul Kar, Aryan Chaudhary, 2024-03-28 Advances on Mathematical Modeling and Optimization with Its Applications discusses optimization, equality, and inequality constraints and their application in the versatile optimizing domain. It further covers non-linear optimization methods such as global optimization, and gradient-based non-linear optimization, and their applications. Discusses important topics including multi-component differential equations, geometric partial differential equations, and computational neural systems Covers linear integer programming and network design problems, along with an application of the mixed integer problems Discusses constrained and unconstrained optimization, equality, and inequality constraints, and their application in the versatile optimizing domain Elucidates the application of statistical models, probability models, and transfer learning concepts Showcases the importance of multi-attribute decision modeling in the domain of image processing and soft computing The text is primarily for senior undergraduate and graduate students, and academic researchers in the fields of mathematics, statistics, and computer science. |
| computational optimal transport with applications to data science: Lectures on Optimal Transport Luigi Ambrosio, Elia Brué, Daniele Semola, 2021-07-22 This textbook is addressed to PhD or senior undergraduate students in mathematics, with interests in analysis, calculus of variations, probability and optimal transport. It originated from the teaching experience of the first author in the Scuola Normale Superiore, where a course on optimal transport and its applications has been given many times during the last 20 years. The topics and the tools were chosen at a sufficiently general and advanced level so that the student or scholar interested in a more specific theme would gain from the book the necessary background to explore it. After a large and detailed introduction to classical theory, more specific attention is devoted to applications to geometric and functional inequalities and to partial differential equations. |
| computational optimal transport with applications to data science: ICDSMLA 2021 Amit Kumar, Sabrina Senatore, Vinit Kumar Gunjan, 2023-02-06 This book gathers selected high-impact articles from the 3rd International Conference on Data Science, Machine Learning & Applications 2021. It highlights the latest developments in the areas of artificial intelligence, machine learning, soft computing, human–computer interaction and various data science and machine learning applications. It brings together scientists and researchers from different universities and industries around the world to showcase a broad range of perspectives, practices and technical expertise. |
Optimal Transport Applications to Data Science - uchile.cl
Increased interest in ML community to use optimal transport (OT) methods. NIPS Tutorial on OT. New Book: Computational Optimal Transport (Peyre & Cuturi), FREE online. Classic Book: …
Computational Optimal Transport - Springer
The optimal transport (OT) problem is a clas-sical optimization problem having the form of linear programming. Machine learning appli-cations put forward new computational chal-lenges in …
Computational optimal transport - uni-goettingen.de
Gabriel Peyré, Marco Cuturi: Computational Optimal Transport, Foundations and Trends in Machine Learning, 2019, 11, 355-607, available online: https://optimaltransport.g ithub.io/book/ …
arXiv:2008.02995v3 [stat.ML] 20 May 2021
decade to accelerate the computation for optimal transport methods. In this review, we present some cutting-edge computational optimal transport methods with a focus on the regularization …
ComputationalOptimal Transport - now publishers
nd relevance in data sciences. We give a prominent place to the many generalizations of OT that have been proposed in but a few years, and connect them with related approaches originating …
Multiscale Strategies for Computing Optimal Transport
Optimal transport is the problem of minimizing the cost of moving a source probability distribution to a target probability distribution given a function that assigns costs to moving mass from …
Computational Optimal Transport - MFO
Optimal transport is the mathematical discipline of matching supply to demand while minimizing ship-ping costs. This matching problem becomes extremely challenging as the quantity of …
Optimal Transport in Data Science: Theory and Applications
Optimal Transport Preliminaries Discrete Distributions Pure Assignments and Monge Map Consider N = M and p x = q y = 1/N. Then, the optimal solution is a permutation σ: an invertible …
Course notes on Computational Optimal Transport - GitHub …
These note cours are intended to complement the book [37] with more details on the theory of Optimal Transport. Many parts are extracted from this book, with some additions and re-writing.
Optimal Transport for Structured data - Titouan Vayer
Optimal Transport for Structured data Applications on graphs Titouan Vayer Joint work with Laetitia Chapel, Remi Flamary, Romain Tavenard and Nicolas Courty March 8, 2019 1/38
Efficient Optimal Transport Computation with Medical …
Given two distributions, optimal transport (OT) seeks to move mass of distribution to distribution in a way that minimizes work (or cost). More formally, in the case of 2-Wasserstein distance, we …
Computational Optimal Transport for Machine and Deep …
Course about the computational aspects of optimal transport and its applications. Three practical labs (Python). All details of the course here https://mathurinm.github.io/otml/. 50 % homeworks …
OPTIMAL TRANSPORT AND APPLICATIONS TO MACHINE …
[11] M. Cuturi and G. Peyr e, Computational optimal transport: with applications to data science, Now Publishers, Boston, MA, 2019, ISBN 978-1-68083-550-2; 978-1-68083-551-9. …
Scalable Optimal Transport in High Dimensions for Graph …
In this work we make OT computation for high-dimensional point sets more scalable by introducing two fast and accurate approximations of entropy-regularized optimal transport: …
Learning Cost Functions for Optimal Transport - Mathematics …
Learning the cost function for optimal transport from observed transport plan or its samples has been cast as a bi-level optimization problem. In this paper, we derive an unconstrained convex …
arXiv:2008.02995v2 [stat.ML] 10 Sep 2020
decade to accelerate the computation for optimal transport methods. In this review, we present some cutting-edge computational optimal transport methods with a focus on the regularization …
Optimal Transport Minimization: Crowd Localization on …
Optimal Transport Minimization algorithm, a parameter-free method for crowd localization on density map. OT-M alternates between two steps: M-step: the point map is updated using the …
Approximate Optimal Transport for Continuous Densities with …
Empir-ical results on real applications of image retrieval and synthetic data demonstrate that our Cop-OT can gain more accurate approximations to contin-uous OT values than the state-of-the …
Foundations of Optimal Transport - Computational Optimal …
Optimal mass transport: Signal processing and machine-learning applications. IEEE signal processing magazine, 34(4), 43-59.
Optimal transport for applications in control and esti…
The optimal transport problem is to determine an optimal way to 10 transport one mass distribution to another, where the cost of moving a unit mass depends on …
A Deformable Constraint Transport Network for Optimal …
A Deformable Constraint Transport Network for Optimal Aortic Segmentation From CT Images Weiyuan Lin , Zhifan Gao , Member, IEEE, Hui Liu, and Heye Zhang …
IoT-Based Non-Intrusive Automated Driver Drowsiness …
and public transport applications. It consists of an embedded system, edge computing and cloud computing modules, and a mobile phone application, in an attempt to …
