Combining Soft Computing And Statistical Methods In Data Analysis

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Combining Soft Computing and Statistical Methods in Data Analysis

Author : Christian Borgelt
Publisher : Springer Science & Business Media
ISBN 13 : 3642147461
Total Pages : 640 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Combining Soft Computing and Statistical Methods in Data Analysis by : Christian Borgelt

Download or read book Combining Soft Computing and Statistical Methods in Data Analysis written by Christian Borgelt and published by Springer Science & Business Media. This book was released on 2010-10-12 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last forty years there has been a growing interest to extend probability theory and statistics and to allow for more flexible modelling of imprecision, uncertainty, vagueness and ignorance. The fact that in many real-life situations data uncertainty is not only present in the form of randomness (stochastic uncertainty) but also in the form of imprecision/fuzziness is but one point underlining the need for a widening of statistical tools. Most such extensions originate in a "softening" of classical methods, allowing, in particular, to work with imprecise or vague data, considering imprecise or generalized probabilities and fuzzy events, etc. About ten years ago the idea of establishing a recurrent forum for discussing new trends in the before-mentioned context was born and resulted in the first International Conference on Soft Methods in Probability and Statistics (SMPS) that was held in Warsaw in 2002. In the following years the conference took place in Oviedo (2004), in Bristol (2006) and in Toulouse (2008). In the current edition the conference returns to Oviedo. This edited volume is a collection of papers presented at the SMPS 2010 conference held in Mieres and Oviedo. It gives a comprehensive overview of current research into the fusion of soft methods with probability and statistics.

Towards Advanced Data Analysis by Combining Soft Computing and Statistics

Author : Christian Borgelt
Publisher : Springer
ISBN 13 : 3642302785
Total Pages : 378 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Towards Advanced Data Analysis by Combining Soft Computing and Statistics by : Christian Borgelt

Download or read book Towards Advanced Data Analysis by Combining Soft Computing and Statistics written by Christian Borgelt and published by Springer. This book was released on 2012-08-29 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Soft computing, as an engineering science, and statistics, as a classical branch of mathematics, emphasize different aspects of data analysis. Soft computing focuses on obtaining working solutions quickly, accepting approximations and unconventional approaches. Its strength lies in its flexibility to create models that suit the needs arising in applications. In addition, it emphasizes the need for intuitive and interpretable models, which are tolerant to imprecision and uncertainty. Statistics is more rigorous and focuses on establishing objective conclusions based on experimental data by analyzing the possible situations and their (relative) likelihood. It emphasizes the need for mathematical methods and tools to assess solutions and guarantee performance. Combining the two fields enhances the robustness and generalizability of data analysis methods, while preserving the flexibility to solve real-world problems efficiently and intuitively.

Synergies of Soft Computing and Statistics for Intelligent Data Analysis

Author : Rudolf Kruse
Publisher : Springer Science & Business Media
ISBN 13 : 3642330428
Total Pages : 555 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Synergies of Soft Computing and Statistics for Intelligent Data Analysis by : Rudolf Kruse

Download or read book Synergies of Soft Computing and Statistics for Intelligent Data Analysis written by Rudolf Kruse and published by Springer Science & Business Media. This book was released on 2012-09-13 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years there has been a growing interest to extend classical methods for data analysis. The aim is to allow a more flexible modeling of phenomena such as uncertainty, imprecision or ignorance. Such extensions of classical probability theory and statistics are useful in many real-life situations, since uncertainties in data are not only present in the form of randomness --- various types of incomplete or subjective information have to be handled. About twelve years ago the idea of strengthening the dialogue between the various research communities in the field of data analysis was born and resulted in the International Conference Series on Soft Methods in Probability and Statistics (SMPS). This book gathers contributions presented at the SMPS'2012 held in Konstanz, Germany. Its aim is to present recent results illustrating new trends in intelligent data analysis. It gives a comprehensive overview of current research into the fusion of soft computing methods with probability and statistics. Synergies of both fields might improve intelligent data analysis methods in terms of robustness to noise and applicability to larger datasets, while being able to efficiently obtain understandable solutions of real-world problems.

Federal Statistics, Multiple Data Sources, and Privacy Protection

Author : National Academies of Sciences, Engineering, and Medicine
Publisher : National Academies Press
ISBN 13 : 0309465370
Total Pages : 195 pages
Book Rating : 4.3/5 (94 download)

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Book Synopsis Federal Statistics, Multiple Data Sources, and Privacy Protection by : National Academies of Sciences, Engineering, and Medicine

Download or read book Federal Statistics, Multiple Data Sources, and Privacy Protection written by National Academies of Sciences, Engineering, and Medicine and published by National Academies Press. This book was released on 2018-01-27 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: The environment for obtaining information and providing statistical data for policy makers and the public has changed significantly in the past decade, raising questions about the fundamental survey paradigm that underlies federal statistics. New data sources provide opportunities to develop a new paradigm that can improve timeliness, geographic or subpopulation detail, and statistical efficiency. It also has the potential to reduce the costs of producing federal statistics. The panel's first report described federal statistical agencies' current paradigm, which relies heavily on sample surveys for producing national statistics, and challenges agencies are facing; the legal frameworks and mechanisms for protecting the privacy and confidentiality of statistical data and for providing researchers access to data, and challenges to those frameworks and mechanisms; and statistical agencies access to alternative sources of data. The panel recommended a new approach for federal statistical programs that would combine diverse data sources from government and private sector sources and the creation of a new entity that would provide the foundational elements needed for this new approach, including legal authority to access data and protect privacy. This second of the panel's two reports builds on the analysis, conclusions, and recommendations in the first one. This report assesses alternative methods for implementing a new approach that would combine diverse data sources from government and private sector sources, including describing statistical models for combining data from multiple sources; examining statistical and computer science approaches that foster privacy protections; evaluating frameworks for assessing the quality and utility of alternative data sources; and various models for implementing the recommended new entity. Together, the two reports offer ideas and recommendations to help federal statistical agencies examine and evaluate data from alternative sources and then combine them as appropriate to provide the country with more timely, actionable, and useful information for policy makers, businesses, and individuals.

Strengthening Links Between Data Analysis and Soft Computing

Author : Przemyslaw Grzegorzewski
Publisher : Springer
ISBN 13 : 3319107658
Total Pages : 294 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Strengthening Links Between Data Analysis and Soft Computing by : Przemyslaw Grzegorzewski

Download or read book Strengthening Links Between Data Analysis and Soft Computing written by Przemyslaw Grzegorzewski and published by Springer. This book was released on 2014-09-10 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers contributions presented at the 7th International Conference on Soft Methods in Probability and Statistics SMPS 2014, held in Warsaw (Poland) on September 22-24, 2014. Its aim is to present recent results illustrating new trends in intelligent data analysis. It gives a comprehensive overview of current research into the fusion of soft computing methods with probability and statistics. Synergies of both fields might improve intelligent data analysis methods in terms of robustness to noise and applicability to larger datasets, while being able to efficiently obtain understandable solutions of real-world problems.

Soft Methods for Data Science

Author : Maria Brigida Ferraro
Publisher : Springer
ISBN 13 : 3319429728
Total Pages : 535 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Soft Methods for Data Science by : Maria Brigida Ferraro

Download or read book Soft Methods for Data Science written by Maria Brigida Ferraro and published by Springer. This book was released on 2016-08-30 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume is a collection of peer reviewed papers presented at the 8th International Conference on Soft Methods in Probability and Statistics (SMPS 2016) held in Rome (Italy). The book is dedicated to Data science which aims at developing automated methods to analyze massive amounts of data and to extract knowledge from them. It shows how Data science employs various programming techniques and methods of data wrangling, data visualization, machine learning, probability and statistics. The soft methods proposed in this volume represent a collection of tools in these fields that can also be useful for data science.

Uncertainty Analysis in Econometrics with Applications

Author : Van-Nam Huynh
Publisher : Springer Science & Business Media
ISBN 13 : 3642354432
Total Pages : 323 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Uncertainty Analysis in Econometrics with Applications by : Van-Nam Huynh

Download or read book Uncertainty Analysis in Econometrics with Applications written by Van-Nam Huynh and published by Springer Science & Business Media. This book was released on 2012-12-14 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike uncertain dynamical systems in physical sciences where models for prediction are somewhat given to us by physical laws, uncertain dynamical systems in economics need statistical models. In this context, modeling and optimization surface as basic ingredients for fruitful applications. This volume concentrates on the current methodology of copulas and maximum entropy optimization. This volume contains main research presentations at the Sixth International Conference of the Thailand Econometrics Society held at the Faculty of Economics, Chiang Mai University, Thailand, during January 10-11, 2013. It consists of keynote addresses, theoretical and applied contributions. These contributions to Econometrics are somewhat centered around the theme of Copulas and Maximum Entropy Econometrics. The method of copulas is applied to a variety of economic problems where multivariate model building and correlation analysis are needed. As for the art of choosing copulas in practical problems, the principle of maximum entropy surfaces as a potential way to do so. The state-of-the-art of Maximum Entropy Econometrics is presented in the first keynote address, while the second keynote address focusses on testing stationarity in economic time series data.

Building Bridges between Soft and Statistical Methodologies for Data Science

Author : Luis A. García-Escudero
Publisher : Springer Nature
ISBN 13 : 3031155092
Total Pages : 421 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Building Bridges between Soft and Statistical Methodologies for Data Science by : Luis A. García-Escudero

Download or read book Building Bridges between Soft and Statistical Methodologies for Data Science written by Luis A. García-Escudero and published by Springer Nature. This book was released on 2022-08-24 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nowadays, data analysis is becoming an appealing topic due to the emergence of new data types, dimensions, and sources. This motivates the development of probabilistic/statistical approaches and tools to cope with these data. Different communities of experts, namely statisticians, mathematicians, computer scientists, engineers, econometricians, and psychologists are more and more interested in facing this challenge. As a consequence, there is a clear need to build bridges between all these communities for Data Science. This book contains more than fifty selected recent contributions aiming to establish the above referred bridges. These contributions address very different and relevant aspects such as imprecise probabilities, information theory, random sets and random fuzzy sets, belief functions, possibility theory, dependence modelling and copulas, clustering, depth concepts, dimensionality reduction of complex data and robustness.

Fuzziness and Medicine: Philosophical Reflections and Application Systems in Health Care

Author : Rudolf Seising
Publisher : Springer
ISBN 13 : 3642365272
Total Pages : 451 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Fuzziness and Medicine: Philosophical Reflections and Application Systems in Health Care by : Rudolf Seising

Download or read book Fuzziness and Medicine: Philosophical Reflections and Application Systems in Health Care written by Rudolf Seising and published by Springer. This book was released on 2013-03-01 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of contributions written by philosophers and scientists active in different fields, such as mathematics, logics, social sciences, computer sciences and linguistics. They comment on and discuss various parts of and subjects and propositions introduced in the Handbook of Analytical Philosophy of Medicine from Kadem Sadegh-Zadeh, published by Springer in 2012. This volume reports on the fruitful exchange and debate that arose in the fuzzy community upon the publication of the Handbook. This was not only very much appreciated by the community but also seen as a critical starting point for beginning a new discussion. The results of this discussion, which involved many different perspectives from science and the humanities and was warmly encouraged by Kadem Sadegh-Zadeh himself, are accurately reported in this volume, which is intended to be a critical companion to Kadem Sadegh-Zadeh ́s handbook. Rudolf Seising is currently an adjunct researcher at the European Centre for Soft Computing in Mieres, Asturias (Spain) and a college lecturer at the Faculty of History and Arts, at the Ludwig Maximilians University of Munich (Germany). Marco Elio Tabacchi is currently the Scientific Director of the Italian National Research & Survey Organization Demopolis, and a research assistant in the Soft Computing Group at University of Palermo (Italy).

Quantitative Logic and Soft Computing

Author : Bing-Yuan Cao
Publisher : Springer Science & Business Media
ISBN 13 : 3642156606
Total Pages : 810 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Quantitative Logic and Soft Computing by : Bing-Yuan Cao

Download or read book Quantitative Logic and Soft Computing written by Bing-Yuan Cao and published by Springer Science & Business Media. This book was released on 2010-10-14 with total page 810 pages. Available in PDF, EPUB and Kindle. Book excerpt: Admittedly, the notion “intelligence or intelligent computing” has been around us for several decades, implicitly indicating any non-conventional methods of solving complex system problems such as expert systems and intelligent control techniques that mimic human skill and replace human operators for automation. Various kinds of intelligent methods have been suggested, phenomenological or ontological, and we have been witnessing quite successful applications. On the other hand, “Soft Computing Techniques” is the concept coined by Lot? Zadeh, referring to “a set of approaches of computing which parallels the remarkable ability of the human mind to reason and learn in an environment of uncertainty, imprecision and partial truth. ” Such a notion is well contrasted with the conventionalbinary logic based hard c- puting and has been effectively utilized with the guiding principle of “exploiting the tolerance for uncertainty,imprecision and partial truth to achieve tractability, - bustness and low solution cost. ” The soft computing techniques are often employed as the technical entities in a tool box with tools being FL, ANN, Rough Set, GA etc. Based on one’s intuition and experience, an engineer can build and realize hum- like systems by smartly mixing proper technical tools effectivelyand ef?ciently in a wide range of ?elds. For some time, the soft computing techniques are also referred to as intelligent computing tools.

Fuzzy Approaches for Soft Computing and Approximate Reasoning: Theories and Applications

Author : Marie-Jeanne Lesot
Publisher : Springer Nature
ISBN 13 : 3030543412
Total Pages : 305 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Fuzzy Approaches for Soft Computing and Approximate Reasoning: Theories and Applications by : Marie-Jeanne Lesot

Download or read book Fuzzy Approaches for Soft Computing and Approximate Reasoning: Theories and Applications written by Marie-Jeanne Lesot and published by Springer Nature. This book was released on 2020-10-26 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers cutting-edge papers in the area of Computational Intelligence, presented by specialists, and covering all major trends in the research community in order to provide readers with a rich primer. It presents an overview of various soft computing topics and approximate reasoning-based approaches, both from theoretical and applied perspectives. Numerous topics are covered: fundamentals aspects of fuzzy sets theory, reasoning approaches (interpolative, analogical, similarity-based), decision and optimization theory, fuzzy databases, soft machine learning, summarization, interpretability and XAI. Moreover, several application-based papers are included, e.g. on image processing, semantic web and intelligent tutoring systems. This book is dedicated to Bernadette Bouchon-Meunier in honor of her achievements in Computational Intelligence, which, throughout her career, have included profuse and diverse collaborations, both thematically and geographically.

Soft Computing Models in Industrial and Environmental Applications, 6th International Conference SOCO 2011

Author : Emilio Corchado
Publisher : Springer Science & Business Media
ISBN 13 : 3642196446
Total Pages : 620 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Soft Computing Models in Industrial and Environmental Applications, 6th International Conference SOCO 2011 by : Emilio Corchado

Download or read book Soft Computing Models in Industrial and Environmental Applications, 6th International Conference SOCO 2011 written by Emilio Corchado and published by Springer Science & Business Media. This book was released on 2011-03-04 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of Advances in Intelligent and Soft Computing contains accepted papers presented at SOCO 2011 held in the beautiful and historic city of Salamanca, Spain, April 2011. This volume presents the papers accepted for the 2011 edition, both for the main event and the Special Sessions. SOCO 2011 Special Sessions are a very useful tool in order to complement the regular program with new or emerging topics of particular interest to the participating community. Four special sessions were organized related to relevant topics as: Optimization and Control in Industry, Speech Processing and Soft Computing, Systems, Man & Cybernetics and Soft Computing for Medical Applications.

Data Science for Financial Econometrics

Author : Nguyen Ngoc Thach
Publisher : Springer Nature
ISBN 13 : 3030488535
Total Pages : 633 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Data Science for Financial Econometrics by : Nguyen Ngoc Thach

Download or read book Data Science for Financial Econometrics written by Nguyen Ngoc Thach and published by Springer Nature. This book was released on 2020-11-13 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an overview of state-of-the-art econometric techniques, with a special emphasis on financial econometrics. There is a major need for such techniques, since the traditional way of designing mathematical models – based on researchers’ insights – can no longer keep pace with the ever-increasing data flow. To catch up, many application areas have begun relying on data science, i.e., on techniques for extracting models from data, such as data mining, machine learning, and innovative statistics. In terms of capitalizing on data science, many application areas are way ahead of economics. To close this gap, the book provides examples of how data science techniques can be used in economics. Corresponding techniques range from almost traditional statistics to promising novel ideas such as quantum econometrics. Given its scope, the book will appeal to students and researchers interested in state-of-the-art developments, and to practitioners interested in using data science techniques.

Fuzzy Statistical Inferences Based on Fuzzy Random Variables

Author : Gholamreza Hesamian
Publisher : CRC Press
ISBN 13 : 1000539822
Total Pages : 452 pages
Book Rating : 4.0/5 (5 download)

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Book Synopsis Fuzzy Statistical Inferences Based on Fuzzy Random Variables by : Gholamreza Hesamian

Download or read book Fuzzy Statistical Inferences Based on Fuzzy Random Variables written by Gholamreza Hesamian and published by CRC Press. This book was released on 2022-02-24 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the most commonly used techniques for the most statistical inferences based on fuzzy data. It brings together many of the main ideas used in statistical inferences in one place, based on fuzzy information including fuzzy data. This book covers a much wider range of topics than a typical introductory text on fuzzy statistics. It includes common topics like elementary probability, descriptive statistics, hypothesis tests, one-way ANOVA, control-charts, reliability systems and regression models. The reader is assumed to know calculus and a little fuzzy set theory. The conventional knowledge of probability and statistics is required. Key Features: Includes example in Mathematica and MATLAB. Contains theoretical and applied exercises for each section. Presents various popular methods for analyzing fuzzy data. The book is suitable for students and researchers in statistics, social science, engineering, and economics, and it can be used at graduate and P.h.D level.

Guide to Intelligent Data Analysis

Author : Michael R. Berthold
Publisher : Springer Science & Business Media
ISBN 13 : 184882260X
Total Pages : 399 pages
Book Rating : 4.8/5 (488 download)

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Book Synopsis Guide to Intelligent Data Analysis by : Michael R. Berthold

Download or read book Guide to Intelligent Data Analysis written by Michael R. Berthold and published by Springer Science & Business Media. This book was released on 2010-06-23 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Each passing year bears witness to the development of ever more powerful computers, increasingly fast and cheap storage media, and even higher bandwidth data connections. This makes it easy to believe that we can now – at least in principle – solve any problem we are faced with so long as we only have enough data. Yet this is not the case. Although large databases allow us to retrieve many different single pieces of information and to compute simple aggregations, general patterns and regularities often go undetected. Furthermore, it is exactly these patterns, regularities and trends that are often most valuable. To avoid the danger of “drowning in information, but starving for knowledge” the branch of research known as data analysis has emerged, and a considerable number of methods and software tools have been developed. However, it is not these tools alone but the intelligent application of human intuition in combination with computational power, of sound background knowledge with computer-aided modeling, and of critical reflection with convenient automatic model construction, that results in successful intelligent data analysis projects. Guide to Intelligent Data Analysis provides a hands-on instructional approach to many basic data analysis techniques, and explains how these are used to solve data analysis problems. Topics and features: guides the reader through the process of data analysis, following the interdependent steps of project understanding, data understanding, data preparation, modeling, and deployment and monitoring; equips the reader with the necessary information in order to obtain hands-on experience of the topics under discussion; provides a review of the basics of classical statistics that support and justify many data analysis methods, and a glossary of statistical terms; includes numerous examples using R and KNIME, together with appendices introducing the open source software; integrates illustrations and case-study-style examples to support pedagogical exposition. This practical and systematic textbook/reference for graduate and advanced undergraduate students is also essential reading for all professionals who face data analysis problems. Moreover, it is a book to be used following one’s exploration of it. Dr. Michael R. Berthold is Nycomed-Professor of Bioinformatics and Information Mining at the University of Konstanz, Germany. Dr. Christian Borgelt is Principal Researcher at the Intelligent Data Analysis and Graphical Models Research Unit of the European Centre for Soft Computing, Spain. Dr. Frank Höppner is Professor of Information Systems at Ostfalia University of Applied Sciences, Germany. Dr. Frank Klawonn is a Professor in the Department of Computer Science and Head of the Data Analysis and Pattern Recognition Laboratory at Ostfalia University of Applied Sciences, Germany. He is also Head of the Bioinformatics and Statistics group at the Helmholtz Centre for Infection Research, Braunschweig, Germany.

Synergies of Soft Computing and Statistics for Intelligent Data Analysis

Author : Rudolf Kruse
Publisher : Springer
ISBN 13 : 9783642330438
Total Pages : 584 pages
Book Rating : 4.3/5 (34 download)

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Book Synopsis Synergies of Soft Computing and Statistics for Intelligent Data Analysis by : Rudolf Kruse

Download or read book Synergies of Soft Computing and Statistics for Intelligent Data Analysis written by Rudolf Kruse and published by Springer. This book was released on 2012-09-14 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years there has been a growing interest to extend classical methods for data analysis. The aim is to allow a more flexible modeling of phenomena such as uncertainty, imprecision or ignorance. Such extensions of classical probability theory and statistics are useful in many real-life situations, since uncertainties in data are not only present in the form of randomness --- various types of incomplete or subjective information have to be handled. About twelve years ago the idea of strengthening the dialogue between the various research communities in the field of data analysis was born and resulted in the International Conference Series on Soft Methods in Probability and Statistics (SMPS). This book gathers contributions presented at the SMPS'2012 held in Konstanz, Germany. Its aim is to present recent results illustrating new trends in intelligent data analysis. It gives a comprehensive overview of current research into the fusion of soft computing methods with probability and statistics. Synergies of both fields might improve intelligent data analysis methods in terms of robustness to noise and applicability to larger datasets, while being able to efficiently obtain understandable solutions of real-world problems.

The Geometry of Uncertainty

Author : Fabio Cuzzolin
Publisher : Springer Nature
ISBN 13 : 3030631532
Total Pages : 850 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis The Geometry of Uncertainty by : Fabio Cuzzolin

Download or read book The Geometry of Uncertainty written by Fabio Cuzzolin and published by Springer Nature. This book was released on 2020-12-17 with total page 850 pages. Available in PDF, EPUB and Kindle. Book excerpt: The principal aim of this book is to introduce to the widest possible audience an original view of belief calculus and uncertainty theory. In this geometric approach to uncertainty, uncertainty measures can be seen as points of a suitably complex geometric space, and manipulated in that space, for example, combined or conditioned. In the chapters in Part I, Theories of Uncertainty, the author offers an extensive recapitulation of the state of the art in the mathematics of uncertainty. This part of the book contains the most comprehensive summary to date of the whole of belief theory, with Chap. 4 outlining for the first time, and in a logical order, all the steps of the reasoning chain associated with modelling uncertainty using belief functions, in an attempt to provide a self-contained manual for the working scientist. In addition, the book proposes in Chap. 5 what is possibly the most detailed compendium available of all theories of uncertainty. Part II, The Geometry of Uncertainty, is the core of this book, as it introduces the author’s own geometric approach to uncertainty theory, starting with the geometry of belief functions: Chap. 7 studies the geometry of the space of belief functions, or belief space, both in terms of a simplex and in terms of its recursive bundle structure; Chap. 8 extends the analysis to Dempster’s rule of combination, introducing the notion of a conditional subspace and outlining a simple geometric construction for Dempster’s sum; Chap. 9 delves into the combinatorial properties of plausibility and commonality functions, as equivalent representations of the evidence carried by a belief function; then Chap. 10 starts extending the applicability of the geometric approach to other uncertainty measures, focusing in particular on possibility measures (consonant belief functions) and the related notion of a consistent belief function. The chapters in Part III, Geometric Interplays, are concerned with the interplay of uncertainty measures of different kinds, and the geometry of their relationship, with a particular focus on the approximation problem. Part IV, Geometric Reasoning, examines the application of the geometric approach to the various elements of the reasoning chain illustrated in Chap. 4, in particular conditioning and decision making. Part V concludes the book by outlining a future, complete statistical theory of random sets, future extensions of the geometric approach, and identifying high-impact applications to climate change, machine learning and artificial intelligence. The book is suitable for researchers in artificial intelligence, statistics, and applied science engaged with theories of uncertainty. The book is supported with the most comprehensive bibliography on belief and uncertainty theory.