Functional and Shape Data Analysis

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Author: Anuj Srivastava,Eric P. Klassen

Publisher: Springer

ISBN: 1493940201

Category: Mathematics

Page: 447

View: 8241

This textbook for courses on function data analysis and shape data analysis describes how to define, compare, and mathematically represent shapes, with a focus on statistical modeling and inference. It is aimed at graduate students in analysis in statistics, engineering, applied mathematics, neuroscience, biology, bioinformatics, and other related areas. The interdisciplinary nature of the broad range of ideas covered—from introductory theory to algorithmic implementations and some statistical case studies—is meant to familiarize graduate students with an array of tools that are relevant in developing computational solutions for shape and related analyses. These tools, gleaned from geometry, algebra, statistics, and computational science, are traditionally scattered across different courses, departments, and disciplines; Functional and Shape Data Analysis offers a unified, comprehensive solution by integrating the registration problem into shape analysis, better preparing graduate students for handling future scientific challenges. Recently, a data-driven and application-oriented focus on shape analysis has been trending. This text offers a self-contained treatment of this new generation of methods in shape analysis of curves. Its main focus is shape analysis of functions and curves—in one, two, and higher dimensions—both closed and open. It develops elegant Riemannian frameworks that provide both quantification of shape differences and registration of curves at the same time. Additionally, these methods are used for statistically summarizing given curve data, performing dimension reduction, and modeling observed variability. It is recommended that the reader have a background in calculus, linear algebra, numerical analysis, and computation.

Graphs in Biomedical Image Analysis, Computational Anatomy and Imaging Genetics

First International Workshop, GRAIL 2017, 6th International Workshop, MFCA 2017, and Third International Workshop, MICGen 2017, Held in Conjunction with MICCAI 2017, Québec City, QC, Canada, September 10–14, 2017, Proceedings

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Author: M. Jorge Cardoso,Tal Arbel,Enzo Ferrante,Xavier Pennec,Adrian V. Dalca,Sarah Parisot,Sarang Joshi,Nematollah K. Batmanghelich,Aristeidis Sotiras,Mads Nielsen,Mert R. Sabuncu,Tom Fletcher,Li Shen,Stanley Durrleman,Stefan Sommer

Publisher: Springer

ISBN: 331967675X

Category: Computers

Page: 250

View: 611

This book constitutes the refereed joint proceedings of the First International Workshop on Graphs in Biomedical Image Analysis, GRAIL 2017, the 6th International Workshop on Mathematical Foundations of Computational Anatomy, MFCA 2017, and the Third International Workshop on Imaging Genetics, MICGen 2017, held in conjunction with the 20th International Conference on Medical Imaging and Computer-Assisted Intervention, MICCAI 2017, in Québec City, QC, Canada, in September 2017. The 7 full papers presented at GRAIL 2017, the 10 full papers presented at MFCA 2017, and the 5 full papers presented at MICGen 2017 were carefully reviewed and selected. The GRAIL papers cover a wide range of graph based medical image analysis methods and applications, including probabilistic graphical models, neuroimaging using graph representations, machine learning for diagnosis prediction, and shape modeling. The MFCA papers deal with theoretical developments in non-linear image and surface registration in the context of computational anatomy. The MICGen papers cover topics in the field of medical genetics, computational biology and medical imaging.

Missing and Modified Data in Nonparametric Estimation

With R Examples

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Author: Sam Efromovich

Publisher: CRC Press

ISBN: 1351679848

Category: Mathematics

Page: 448

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This book presents a systematic and unified approach for modern nonparametric treatment of missing and modified data via examples of density and hazard rate estimation, nonparametric regression, filtering signals, and time series analysis. All basic types of missing at random and not at random, biasing, truncation, censoring, and measurement errors are discussed, and their treatment is explained. Ten chapters of the book cover basic cases of direct data, biased data, nondestructive and destructive missing, survival data modified by truncation and censoring, missing survival data, stationary and nonstationary time series and processes, and ill-posed modifications. The coverage is suitable for self-study or a one-semester course for graduate students with a prerequisite of a standard course in introductory probability. Exercises of various levels of difficulty will be helpful for the instructor and self-study. The book is primarily about practically important small samples. It explains when consistent estimation is possible, and why in some cases missing data should be ignored and why others must be considered. If missing or data modification makes consistent estimation impossible, then the author explains what type of action is needed to restore the lost information. The book contains more than a hundred figures with simulated data that explain virtually every setting, claim, and development. The companion R software package allows the reader to verify, reproduce and modify every simulation and used estimators. This makes the material fully transparent and allows one to study it interactively. Sam Efromovich is the Endowed Professor of Mathematical Sciences and the Head of the Actuarial Program at the University of Texas at Dallas. He is well known for his work on the theory and application of nonparametric curve estimation and is the author of Nonparametric Curve Estimation: Methods, Theory, and Applications. Professor Sam Efromovich is a Fellow of the Institute of Mathematical Statistics and the American Statistical Association.

Applied Functional Data Analysis

Methods and Case Studies

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Author: J.O. Ramsay,B.W. Silverman

Publisher: Springer

ISBN: 0387224653

Category: Mathematics

Page: 191

View: 7804

This book contains the ideas of functional data analysis by a number of case studies. The case studies are accessible to research workers in a wide range of disciplines. Every reader should gain not only a specific understanding of the methods of functional data analysis, but more importantly a general insight into the underlying patterns of thought. There is an associated web site with MATLABr and S?PLUSr implementations of the methods discussed.

Geometry Driven Statistics

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Author: Ian L. Dryden,John T. Kent

Publisher: John Wiley & Sons

ISBN: 1118866576

Category: Mathematics

Page: 432

View: 6042

A timely collection of advanced, original material in the area of statistical methodology motivated by geometric problems, dedicated to the influential work of Kanti V. Mardia This volume celebrates Kanti V. Mardia′s long and influential career in statistics. A common theme unifying much of Mardia s work is the importance of geometry in statistics, and to highlight the areas emphasized in his research this book brings together 16 contributions from high–profile researchers in the field. Geometry Driven Statistics covers a wide range of application areas including directional data, shape analysis, spatial data, climate science, fingerprints, image analysis, computer vision and bioinformatics. The book will appeal to statisticians and others with an interest in data motivated by geometric considerations. Summarizing the state of the art, examining some new developments and presenting a vision for the future, Geometry Driven Statistics will enable the reader to broaden knowledge of important research areas in statistics and gain a new appreciation of the work and influence of Kanti V. Mardia.

Recent Advances in Functional Data Analysis and Related Topics

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Author: Frédéric Ferraty

Publisher: Springer Science & Business Media

ISBN: 9783790827361

Category: Mathematics

Page: 322

View: 9247

New technologies allow us to handle increasingly large datasets, while monitoring devices are becoming ever more sophisticated. This high-tech progress produces statistical units sampled over finer and finer grids. As the measurement points become closer, the data can be considered as observations varying over a continuum. This intrinsic continuous data (called functional data) can be found in various fields of science, including biomechanics, chemometrics, econometrics, environmetrics, geophysics, medicine, etc. The failure of standard multivariate statistics to analyze such functional data has led the statistical community to develop appropriate statistical methodologies, called Functional Data Analysis (FDA). Today, FDA is certainly one of the most motivating and popular statistical topics due to its impact on crucial societal issues (health, environment, etc). This is why the FDA statistical community is rapidly growing, as are the statistical developments . Therefore, it is necessary to organize regular meetings in order to provide a state-of-art review of the recent advances in this fascinating area. This book collects selected and extended papers presented at the second International Workshop of Functional and Operatorial Statistics (Santander, Spain, 16-18 June, 2011), in which many outstanding experts on FDA will present the most relevant advances in this pioneering statistical area. Undoubtedly, these proceedings will be an essential resource for academic researchers, master students, engineers, and practitioners not only in statistics but also in numerous related fields of application.

Elementare Wahrscheinlichkeitstheorie und stochastische Prozesse

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Author: Kai L. Chung

Publisher: Springer-Verlag

ISBN: 3642670334

Category: Mathematics

Page: 346

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Aus den Besprechungen: "Unter den zahlreichen Einführungen in die Wahrscheinlichkeitsrechnung bildet dieses Buch eine erfreuliche Ausnahme. Der Stil einer lebendigen Vorlesung ist über Niederschrift und Übersetzung hinweg erhalten geblieben. In jedes Kapitel wird sehr anschaulich eingeführt. Sinn und Nützlichkeit der mathematischen Formulierungen werden den Lesern nahegebracht. Die wichtigsten Zusammenhänge sind als mathematische Sätze klar formuliert." #FREQUENZ#1

Data mining

praktische Werkzeuge und Techniken für das maschinelle Lernen

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Author: Ian H. Witten,Eibe Frank

Publisher: N.A

ISBN: 9783446215337

Category:

Page: 386

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The Statistical Theory of Shape

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Author: Christopher G. Small

Publisher: Springer Science & Business Media

ISBN: 1461240328

Category: Mathematics

Page: 230

View: 9090

In general terms, the shape of an object, data set, or image can be de fined as the total of all information that is invariant under translations, rotations, and isotropic rescalings. Thus two objects can be said to have the same shape if they are similar in the sense of Euclidean geometry. For example, all equilateral triangles have the same shape, and so do all cubes. In applications, bodies rarely have exactly the same shape within measure ment error. In such cases the variation in shape can often be the subject of statistical analysis. The last decade has seen a considerable growth in interest in the statis tical theory of shape. This has been the result of a synthesis of a number of different areas and a recognition that there is considerable common ground among these areas in their study of shape variation. Despite this synthesis of disciplines, there are several different schools of statistical shape analysis. One of these, the Kendall school of shape analysis, uses a variety of mathe matical tools from differential geometry and probability, and is the subject of this book. The book does not assume a particularly strong background by the reader in these subjects, and so a brief introduction is provided to each of these topics. Anyone who is unfamiliar with this material is advised to consult a more complete reference. As the literature on these subjects is vast, the introductory sections can be used as a brief guide to the literature.

Progress in Advanced Structural and Functional Materials Design

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Author: Tomoyuki Kakeshita

Publisher: Springer Science & Business Media

ISBN: 4431540644

Category: Technology & Engineering

Page: 290

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This book describes clearly various research topics investigated for these 10 years in the Research Center of Advanced Structural and Functional Materials Design in Osaka University, Japan. Every chapter is aimed at understanding most advanced researches in materials science by describing its fundamentals and details as much as possible. Since both general explanations and cutting-edge commentaries are given for each topic in this book, it provides a lot of useful information for ordinary readers as well as materials scientists & engineers who wish to understand the future development in materials science fields of metals, alloys, ceramics, semiconductors etc. In particular, this book deals with special fusion area of structural and functional materials such as medical bone materials, of which contents are very unique features as materials science textbook.

Spatio-temporal Image Analysis for Longitudinal and Time-Series Image Data

Third International Workshop, STIA 2014, Held in Conjunction with MICCAI 2014, Boston, MA, USA, September 18, 2014, Revised Selected Papers

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Author: Stanley Durrleman,Tom Fletcher,Guido Gerig,Marc Niethammer,Xavier Pennec

Publisher: Springer

ISBN: 3319149059

Category: Computers

Page: 89

View: 8848

This book constitutes the thoroughly refereed post-conference proceedings of the Third International Workshop on Spatio-temporal Image Analysis for Longitudinal and Time-Series Image Data, STIA 2014, held in conjunction with MICCAI 2014 in Boston, MA, USA, in September 2014. The 7 papers presented in this volume were carefully reviewed and selected from 15 submissions. They are organized in topical sections named: longitudinal registration and shape modeling, longitudinal modeling, reconstruction from longitudinal data, and 4D image processing.

Fuzzy-Clusteranalyse

Verfahren für die Bilderkennung, Klassifizierung und Datenanalyse

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Author: Frank Höppner,Rudolf Kruse,Frank Klawonn

Publisher: Springer-Verlag

ISBN: 3322868362

Category: Technology & Engineering

Page: 280

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Dieses Buch ist das Standardwerk zu einem neuen Bereich der angewandten Fuzzy-Technologie, der Fuzzy-Clusteranalyse. Diese beinhaltet Verfahren der Mustererkennung zur Gruppierung und Strukturierung von Daten. Dabei werden im Gegensatz zu klassischen Clustering-Techniken die Daten nicht eindeutig zu Klassen zugeordnet, sondern Zugehörigkeitsgrade bestimmt, so daß die Fuzzy-Verfahren robust gegenüber gestörten oder verrauschten Daten sind und fließende Klassenübergänge handhaben können. Dieses Werk gibt eine methodische Einführung in die zahlreichen Fuzzy-Clustering-Algorithmen mit ihren Anwendungen in den Bereichen Datenanalyse, Erzeugung von Regeln für Fuzzy-Regler, Klassifikations- und Approximationsprobleme sowie eine ausführliche Darstellung des Shell-Clustering zur Erkennung von geometrischen Konturen in Bildern.

Statistical Analysis of Financial Data in R

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Author: René Carmona

Publisher: Springer Science & Business Media

ISBN: 1461487889

Category: Business & Economics

Page: 588

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Although there are many books on mathematical finance, few deal with the statistical aspects of modern data analysis as applied to financial problems. This textbook fills this gap by addressing some of the most challenging issues facing financial engineers. It shows how sophisticated mathematics and modern statistical techniques can be used in the solutions of concrete financial problems. Concerns of risk management are addressed by the study of extreme values, the fitting of distributions with heavy tails, the computation of values at risk (VaR), and other measures of risk. Principal component analysis (PCA), smoothing, and regression techniques are applied to the construction of yield and forward curves. Time series analysis is applied to the study of temperature options and nonparametric estimation. Nonlinear filtering is applied to Monte Carlo simulations, option pricing and earnings prediction. This textbook is intended for undergraduate students majoring in financial engineering, or graduate students in a Master in finance or MBA program. It is sprinkled with practical examples using market data, and each chapter ends with exercises. Practical examples are solved in the R computing environment. They illustrate problems occurring in the commodity, energy and weather markets, as well as the fixed income, equity and credit markets. The examples, experiments and problem sets are based on the library Rsafd developed for the purpose of the text. The book should help quantitative analysts learn and implement advanced statistical concepts. Also, it will be valuable for researchers wishing to gain experience with financial data, implement and test mathematical theories, and address practical issues that are often ignored or underestimated in academic curricula. This is the new, fully-revised edition to the book Statistical Analysis of Financial Data in S-Plus. René Carmona is the Paul M. Wythes '55 Professor of Engineering and Finance at Princeton University in the department of Operations Research and Financial Engineering, and Director of Graduate Studies of the Bendheim Center for Finance. His publications include over one hundred articles and eight books in probability and statistics. He was elected Fellow of the Institute of Mathematical Statistics in 1984, and of the Society for Industrial and Applied Mathematics in 2010. He is on the editorial board of several peer-reviewed journals and book series. Professor Carmona has developed computer programs for teaching statistics and research in signal analysis and financial engineering. He has worked for many years on energy, the commodity markets and more recently in environmental economics, and he is recognized as a leading researcher and expert in these areas.

Topologie I

Erster Band. Grundbegriffe der Mengentheoretischen Topologie Topologie der Komplexe · Topologische Invarianzsätze und Anschliessende Begriffsbildungen · Verschlingungen im n-Dimensionalen Euklidischen Raum Stetige Abbildungen von Polyedern

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Author: Paul Alexandroff,H. Hopf

Publisher: Springer-Verlag

ISBN: 3662020211

Category: Mathematics

Page: 638

View: 8971

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Wahrscheinlichkeit

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Author: Alʹbert Nikolaevich Shiri︠a︡ev,Hans Jürgen Engelbert

Publisher: N.A

ISBN: N.A

Category: Probabilities

Page: 592

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New Developments in Classification and Data Analysis

Proceedings of the Meeting of the Classification and Data Analysis Group (CLADAG) of the Italian Statistical Society, University of Bologna, September 22-24, 2003

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Author: Classification Group of SIS. Meeting,Società Italiana di Statistica Classification and Data Analysis Group

Publisher: Springer Science & Business Media

ISBN: 9783540238096

Category: Business & Economics

Page: 369

View: 8611

The volume presents new developments in data analysis and classification. Particular attention is devoted to clustering, discrimination, data analysis and statistics, as well as applications in biology, finance and social sciences. The reader will find theory and algorithms on recent technical and methodological developments and many application papers showing the empirical usefulness of the newly developed solutions.

A Probabilistic Framework for Point-Based Shape Modeling in Medical Image Analysis

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Author: Heike Hufnagel

Publisher: Springer Science & Business Media

ISBN: 3834886009

Category: Technology & Engineering

Page: 147

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Heike Hufnagel develops a mathematically sound statistical shape model. Due to the particular attributes of the model, the challenging integration of explicit and implicit representations can be performed in an elegant mathematical formulation, thus combining the advantages of both explicit model and implicit segmentation method.

Advances in Intelligent Data Analysis

4th International Conference, IDA 2001, Cascais, Portugal, September 13-15, 2001. Proceedings

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Author: International Data Analysis (IDA). International conference (

Publisher: Springer Science & Business Media

ISBN: 3540425810

Category: Business & Economics

Page: 384

View: 9451

Wewouldalsoliketoexpressourgratitudetothesponsors:Fundac˜ ¸ao paraaCiˆenciaeaTecnologia,Minist´eriodaCiˆenciaedaTecnologia,Faculdade deCiˆenciaseTecnologia,UniversidadeNovadeLisboa,Funda¸c˜aoCalousteG- benkianandIPEInvestimentoseParticipac˜ ¸oesEmpresariais,S. A. September2001 FrankHo?mann DavidJ. Hand NiallAdams GabrielaGuimaraes DougFisher Organization IDA2001wasorganizedbythedepartmentofComputerScience,NewUniversity ofLisbon. ConferenceCommittee GeneralChair: DouglasFisher(VanderbiltUniversity,USA) ProgramChairs: DavidJ. Hand(ImperialCollege,UK) NiallAdams(ImperialCollege,UK) ConferenceChair: GabrielaGuimaraes(NewUniversityofLisbon,Portugal) PublicityChair: FrankH¨oppner(Univ. ofAppl. SciencesEmden,Germany) PublicationChair: FrankHo?mann(RoyalInstituteofTechnology,Sweden) LocalChair: FernandoMoura-Pires(UniversityofEvora,Portugal) AreaChairs: RobertaSiciliano(UniversityofNaples,Italy) ArnoSiebes(CWI,TheNetherlands) PavelBrazdil(UniversityofPorto,Portugal) ProgramCommittee NiallAdams(ImperialCollege,UK) PieterAdriaans(Syllogic,TheNetherlands) RussellAlmond(EducationalTestingService,USA) ThomasB¨ack(InformatikCentrumDortmund,Germany) RiccardoBellazzi(UniversityofPavia,Italy) MichaelBerthold(Tripos,USA) LiuBing(NationalUniversityofSingapore) PaulCohen(UniversityofMassachusetts,USA) PaulDarius(LeuvenUniversity,Belgium) FazelFamili(NationalResearchCouncil,Canada) DouglasFisher(VanderbiltUniversity,USA) KarlFroeschl(UniversityofVienna,Austria) AlexGammerman(RoyalHolloway,UK) AdolfGrauel(UniversityofPaderborn,Germany) GabrielaGuimaraes(NewUniversityofLisbon,Portugal) LawrenceO. Hall(UniversityofSouthFlorida,USA) FrankHo?mann(RoyalInstituteofTechnology,Sweden) AdeleHowe(ColoradoStateUniversity,USA) Klaus-PeterHuber(SASInstitute,Germany) DavidJensen(UniversityofMassachusetts,USA) JoostKok(LeidenUniversity,TheNetherlands) RudolfKruse(UniversityofMagdeburg,Germany) FrankKlawonn(UniversityofAppliedSciencesEmden,Germany) VIII Organization HansLenz(FreeUniversityofBerlin,Germany) DavidMadigan(Soliloquy,USA) RainerMalaka(EuropeanMediaLaboratory,Germany) HeikkiMannila(Nokia,Finland) FernandoMouraPires(UniversityofEvora,Portugal) SusanaNascimento(UniversityofLisbon,Portugal) WayneOldford(UniversityofWaterloo,Canada) AlbertPrat(TechnicalUniversityofCatalunya,Spain) PeterProtzel(TechnicalUniversityChemnitz,Germany) GiacomodellaRiccia(UniversityofUdine,Italy) RosannaSchiavo(UniversityofVenice,Italy) KaisaSere(AboAkademiUniversity,Finland) RobertaSiciliano(UniversityofNaples,Italy) RosariaSilipo(Nuance,USA) FloorVerdenius(ATO-DLO,TheNetherlands) StefanWrobel(UniversityofMagdeburg,Germany) HuiXiaoLiu(BrunelUniversity,UK) NevinZhang(HongKongUniversityofScienceandTechnology,HongKong) SponsoringInstitutions Fundac˜ ¸aoparaaCiˆenciaeaTecnologia,Minist´eriodaCiˆenciaedaTecnologia FaculdadedeCiˆenciaseTecnologia,UniversidadeNovadeLisboa Fundac˜ ¸aoCalousteGulbenkian IPEInvestimentoseParticipac˜ ¸oesEmpresariais,S. A. TableofContents TheFourthInternationalSymposiumonIntelligentData Analysis FeatureCharacterizationinScienti?cDatasets. . . . . . . . . . . . . . . . . . . . . . . . . 1 ElizabethBradley(UniversityofColorado),NancyCollins(University ofColorado),W. PhilipKegelmeyer(SandiaNationalLaboratories) RelevanceFeedbackintheBayesianNetworkRetrievalModel: AnApproachBasedonTermInstantiation. . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 LuisM. deCampos(UniversityofGranada),JuanM. Fernan ´ dez–Luna (UniversityofJa´en),JuanF. Huete(UniversityofGranada) GeneratingFuzzySummariesfromFuzzyMultidimensionalDatabases. . . . 24 AnneLaurent(Universit´ePierreetMarieCurie) AMixture-of-ExpertsFrameworkforLearningfromImbalancedData Sets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 AndrewEstabrooks(IBM),NathalieJapkowicz(UniversityofOttawa) PredictingTime-VaryingFunctionswithLocalModels. . . . . . . . . . . . . . . . . . 44 AchimLewandowski(ChemnitzUniversity),PeterProtzel(Chemn