Download or read book Gaussian Process Regression Analysis for Functional Data written by Jian Qing Shi and published by CRC Press. This book was released on 2011-07-01 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gaussian Process Regression Analysis for Functional Data presents nonparametric statistical methods for functional regression analysis, specifically the methods based on a Gaussian process prior in a functional space. The authors focus on problems involving functional response variables and mixed covariates of functional and scalar variables. Covering the basics of Gaussian process regression, the first several chapters discuss functional data analysis, theoretical aspects based on the asymptotic properties of Gaussian process regression models, and new methodological developments for high dimensional data and variable selection. The remainder of the text explores advanced topics of functional regression analysis, including novel nonparametric statistical methods for curve prediction, curve clustering, functional ANOVA, and functional regression analysis of batch data, repeated curves, and non-Gaussian data. Many flexible models based on Gaussian processes provide efficient ways of model learning, interpreting model structure, and carrying out inference, particularly when dealing with large dimensional functional data. This book shows how to use these Gaussian process regression models in the analysis of functional data. Some MATLAB® and C codes are available on the first author’s website.

Download or read book Gaussian Process Regression Analysis for Functional Data written by Jian Qing Shi and published by CRC Press. This book was released on 2011-07-01 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gaussian Process Regression Analysis for Functional Data presents nonparametric statistical methods for functional regression analysis, specifically the methods based on a Gaussian process prior in a functional space. The authors focus on problems involving functional response variables and mixed covariates of functional and scalar variables.Coveri

Download or read book Functional and High Dimensional Statistics and Related Fields written by Germán Aneiros and published by Springer Nature. This book was released on 2020-06-19 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the latest research on the statistical analysis of functional, high-dimensional and other complex data, addressing methodological and computational aspects, as well as real-world applications. It covers topics like classification, confidence bands, density estimation, depth, diagnostic tests, dimension reduction, estimation on manifolds, high- and infinite-dimensional statistics, inference on functional data, networks, operatorial statistics, prediction, regression, robustness, sequential learning, small-ball probability, smoothing, spatial data, testing, and topological object data analysis, and includes applications in automobile engineering, criminology, drawing recognition, economics, environmetrics, medicine, mobile phone data, spectrometrics and urban environments. The book gathers selected, refereed contributions presented at the Fifth International Workshop on Functional and Operatorial Statistics (IWFOS) in Brno, Czech Republic. The workshop was originally to be held on June 24-26, 2020, but had to be postponed as a consequence of the COVID-19 pandemic. Initiated by the Working Group on Functional and Operatorial Statistics at the University of Toulouse in 2008, the IWFOS workshops provide a forum to discuss the latest trends and advances in functional statistics and related fields, and foster the exchange of ideas and international collaboration in the field.

Download or read book Gaussian Processes for Machine Learning written by Carl Edward Rasmussen and published by MIT Press. This book was released on 2005-11-23 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive and self-contained introduction to Gaussian processes, which provide a principled, practical, probabilistic approach to learning in kernel machines. Gaussian processes (GPs) provide a principled, practical, probabilistic approach to learning in kernel machines. GPs have received increased attention in the machine-learning community over the past decade, and this book provides a long-needed systematic and unified treatment of theoretical and practical aspects of GPs in machine learning. The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics. The book deals with the supervised-learning problem for both regression and classification, and includes detailed algorithms. A wide variety of covariance (kernel) functions are presented and their properties discussed. Model selection is discussed both from a Bayesian and a classical perspective. Many connections to other well-known techniques from machine learning and statistics are discussed, including support-vector machines, neural networks, splines, regularization networks, relevance vector machines and others. Theoretical issues including learning curves and the PAC-Bayesian framework are treated, and several approximation methods for learning with large datasets are discussed. The book contains illustrative examples and exercises, and code and datasets are available on the Web. Appendixes provide mathematical background and a discussion of Gaussian Markov processes.

Download or read book Handbook of Bayesian Variable Selection written by Mahlet G. Tadesse and published by CRC Press. This book was released on 2021-12-24 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian variable selection has experienced substantial developments over the past 30 years with the proliferation of large data sets. Identifying relevant variables to include in a model allows simpler interpretation, avoids overfitting and multicollinearity, and can provide insights into the mechanisms underlying an observed phenomenon. Variable selection is especially important when the number of potential predictors is substantially larger than the sample size and sparsity can reasonably be assumed. The Handbook of Bayesian Variable Selection provides a comprehensive review of theoretical, methodological and computational aspects of Bayesian methods for variable selection. The topics covered include spike-and-slab priors, continuous shrinkage priors, Bayes factors, Bayesian model averaging, partitioning methods, as well as variable selection in decision trees and edge selection in graphical models. The handbook targets graduate students and established researchers who seek to understand the latest developments in the field. It also provides a valuable reference for all interested in applying existing methods and/or pursuing methodological extensions. Features: Provides a comprehensive review of methods and applications of Bayesian variable selection. Divided into four parts: Spike-and-Slab Priors; Continuous Shrinkage Priors; Extensions to various Modeling; Other Approaches to Bayesian Variable Selection. Covers theoretical and methodological aspects, as well as worked out examples with R code provided in the online supplement. Includes contributions by experts in the field. Supported by a website with code, data, and other supplementary material

Download or read book Corrosion of Aluminium written by Christian Vargel and published by Elsevier. This book was released on 2004-10-02 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: Corrosion of Aluminium highlights the practical and general aspects of the corrosion of aluminium alloys with many illustrations and references. In addition to that, the first chapter allows the reader who is not very familiar with aluminium to understand the metallurgical, chemical and physical features of the aluminium alloys. The author Christian Vargel, has adopted a practitioner approach, based on the expertise and experience gained from a 40 year career in aluminium corrosion This approach is most suitable for assessing the corrosion resistance of aluminium- an assessment which is one of the main conditions for the development of many uses of aluminium in transport, construction, power transmission etc. - 600 bibliographic references provide a comprehensive guide to over 100 years of related study - Providing practical applications to the reader across many industries - Accessible to both the beginner and the expert

Download or read book Modelling and Control of Dynamic Systems Using Gaussian Process Models written by Juš Kocijan and published by Springer. This book was released on 2015-11-21 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph opens up new horizons for engineers and researchers in academia and in industry dealing with or interested in new developments in the field of system identification and control. It emphasizes guidelines for working solutions and practical advice for their implementation rather than the theoretical background of Gaussian process (GP) models. The book demonstrates the potential of this recent development in probabilistic machine-learning methods and gives the reader an intuitive understanding of the topic. The current state of the art is treated along with possible future directions for research. Systems control design relies on mathematical models and these may be developed from measurement data. This process of system identification, when based on GP models, can play an integral part of control design in data-based control and its description as such is an essential aspect of the text. The background of GP regression is introduced first with system identification and incorporation of prior knowledge then leading into full-blown control. The book is illustrated by extensive use of examples, line drawings, and graphical presentation of computer-simulation results and plant measurements. The research results presented are applied in real-life case studies drawn from successful applications including: a gas–liquid separator control; urban-traffic signal modelling and reconstruction; and prediction of atmospheric ozone concentration. A MATLAB® toolbox, for identification and simulation of dynamic GP models is provided for download.

Download or read book Regression and Time Series Model Selection written by Allan D. R. McQuarrie and published by World Scientific. This book was released on 1998 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important book describes procedures for selecting a model from a large set of competing statistical models. It includes model selection techniques for univariate and multivariate regression models, univariate and multivariate autoregressive models, nonparametric (including wavelets) and semiparametric regression models, and quasi-likelihood and robust regression models. Information-based model selection criteria are discussed, and small sample and asymptotic properties are presented. The book also provides examples and large scale simulation studies comparing the performances of information-based model selection criteria, bootstrapping, and cross-validation selection methods over a wide range of models.

Download or read book Learning Kernel Classifiers written by Ralf Herbrich and published by MIT Press. This book was released on 2001-12-07 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: An overview of the theory and application of kernel classification methods. Linear classifiers in kernel spaces have emerged as a major topic within the field of machine learning. The kernel technique takes the linear classifier—a limited, but well-established and comprehensively studied model—and extends its applicability to a wide range of nonlinear pattern-recognition tasks such as natural language processing, machine vision, and biological sequence analysis. This book provides the first comprehensive overview of both the theory and algorithms of kernel classifiers, including the most recent developments. It begins by describing the major algorithmic advances: kernel perceptron learning, kernel Fisher discriminants, support vector machines, relevance vector machines, Gaussian processes, and Bayes point machines. Then follows a detailed introduction to learning theory, including VC and PAC-Bayesian theory, data-dependent structural risk minimization, and compression bounds. Throughout, the book emphasizes the interaction between theory and algorithms: how learning algorithms work and why. The book includes many examples, complete pseudo code of the algorithms presented, and an extensive source code library.

Download or read book Advanced Mean Field Methods written by Manfred Opper and published by MIT Press. This book was released on 2001 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling. A major problem in modern probabilistic modeling is the huge computational complexity involved in typical calculations with multivariate probability distributions when the number of random variables is large. Because exact computations are infeasible in such cases and Monte Carlo sampling techniques may reach their limits, there is a need for methods that allow for efficient approximate computations. One of the simplest approximations is based on the mean field method, which has a long history in statistical physics. The method is widely used, particularly in the growing field of graphical models. Researchers from disciplines such as statistical physics, computer science, and mathematical statistics are studying ways to improve this and related methods and are exploring novel application areas. Leading approaches include the variational approach, which goes beyond factorizable distributions to achieve systematic improvements; the TAP (Thouless-Anderson-Palmer) approach, which incorporates correlations by including effective reaction terms in the mean field theory; and the more general methods of graphical models. Bringing together ideas and techniques from these diverse disciplines, this book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling.

Download or read book Statistical Foundations of Data Science written by Jianqing Fan and published by CRC Press. This book was released on 2020-09-21 with total page 942 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Foundations of Data Science gives a thorough introduction to commonly used statistical models, contemporary statistical machine learning techniques and algorithms, along with their mathematical insights and statistical theories. It aims to serve as a graduate-level textbook and a research monograph on high-dimensional statistics, sparsity and covariance learning, machine learning, and statistical inference. It includes ample exercises that involve both theoretical studies as well as empirical applications. The book begins with an introduction to the stylized features of big data and their impacts on statistical analysis. It then introduces multiple linear regression and expands the techniques of model building via nonparametric regression and kernel tricks. It provides a comprehensive account on sparsity explorations and model selections for multiple regression, generalized linear models, quantile regression, robust regression, hazards regression, among others. High-dimensional inference is also thoroughly addressed and so is feature screening. The book also provides a comprehensive account on high-dimensional covariance estimation, learning latent factors and hidden structures, as well as their applications to statistical estimation, inference, prediction and machine learning problems. It also introduces thoroughly statistical machine learning theory and methods for classification, clustering, and prediction. These include CART, random forests, boosting, support vector machines, clustering algorithms, sparse PCA, and deep learning.

Download or read book Economic Analysis of the Digital Economy written by Avi Goldfarb and published by University of Chicago Press. This book was released on 2015-05-08 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is a small and growing literature that explores the impact of digitization in a variety of contexts, but its economic consequences, surprisingly, remain poorly understood. This volume aims to set the agenda for research in the economics of digitization, with each chapter identifying a promising area of research. "Economics of Digitization "identifies urgent topics with research already underway that warrant further exploration from economists. In addition to the growing importance of digitization itself, digital technologies have some features that suggest that many well-studied economic models may not apply and, indeed, so many aspects of the digital economy throw normal economics in a loop. "Economics of Digitization" will be one of the first to focus on the economic implications of digitization and to bring together leading scholars in the economics of digitization to explore emerging research.

Download or read book Uncertainty Quantification and Model Calibration written by Jan Peter Hessling and published by BoD – Books on Demand. This book was released on 2017-07-05 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty quantification may appear daunting for practitioners due to its inherent complexity but can be intriguing and rewarding for anyone with mathematical ambitions and genuine concern for modeling quality. Uncertainty quantification is what remains to be done when too much credibility has been invested in deterministic analyses and unwarranted assumptions. Model calibration describes the inverse operation targeting optimal prediction and refers to inference of best uncertain model estimates from experimental calibration data. The limited applicability of most state-of-the-art approaches to many of the large and complex calculations made today makes uncertainty quantification and model calibration major topics open for debate, with rapidly growing interest from both science and technology, addressing subtle questions such as credible predictions of climate heating.

Download or read book Graphical Models for Machine Learning and Digital Communication written by Brendan J. Frey and published by MIT Press. This book was released on 1998 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Content Description. #Includes bibliographical references and index.

Download or read book Flexible Bayesian Regression Modelling written by Yanan Fan and published by Academic Press. This book was released on 2019-10-30 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Flexible Bayesian Regression Modeling is a step-by-step guide to the Bayesian revolution in regression modeling, for use in advanced econometric and statistical analysis where datasets are characterized by complexity, multiplicity, and large sample sizes, necessitating the need for considerable flexibility in modeling techniques. It reviews three forms of flexibility: methods which provide flexibility in their error distribution; methods which model non-central parts of the distribution (such as quantile regression); and finally models that allow the mean function to be flexible (such as spline models). Each chapter discusses the key aspects of fitting a regression model. R programs accompany the methods. This book is particularly relevant to non-specialist practitioners with intermediate mathematical training seeking to apply Bayesian approaches in economics, biology, finance, engineering and medicine. - Introduces powerful new nonparametric Bayesian regression techniques to classically trained practitioners - Focuses on approaches offering both superior power and methodological flexibility - Supplemented with instructive and relevant R programs within the text - Covers linear regression, nonlinear regression and quantile regression techniques - Provides diverse disciplinary case studies for correlation and optimization problems drawn from Bayesian analysis 'in the wild'

Download or read book Handbook of Mixture Analysis written by Sylvia Fruhwirth-Schnatter and published by CRC Press. This book was released on 2019-01-04 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mixture models have been around for over 150 years, and they are found in many branches of statistical modelling, as a versatile and multifaceted tool. They can be applied to a wide range of data: univariate or multivariate, continuous or categorical, cross-sectional, time series, networks, and much more. Mixture analysis is a very active research topic in statistics and machine learning, with new developments in methodology and applications taking place all the time. The Handbook of Mixture Analysis is a very timely publication, presenting a broad overview of the methods and applications of this important field of research. It covers a wide array of topics, including the EM algorithm, Bayesian mixture models, model-based clustering, high-dimensional data, hidden Markov models, and applications in finance, genomics, and astronomy. Features: Provides a comprehensive overview of the methods and applications of mixture modelling and analysis Divided into three parts: Foundations and Methods; Mixture Modelling and Extensions; and Selected Applications Contains many worked examples using real data, together with computational implementation, to illustrate the methods described Includes contributions from the leading researchers in the field The Handbook of Mixture Analysis is targeted at graduate students and young researchers new to the field. It will also be an important reference for anyone working in this field, whether they are developing new methodology, or applying the models to real scientific problems.

Download or read book Bilevel Optimization written by Stephan Dempe and published by Springer Nature. This book was released on 2020-11-23 with total page 679 pages. Available in PDF, EPUB and Kindle. Book excerpt: 2019 marked the 85th anniversary of Heinrich Freiherr von Stackelberg’s habilitation thesis “Marktform und Gleichgewicht,” which formed the roots of bilevel optimization. Research on the topic has grown tremendously since its introduction in the field of mathematical optimization. Besides the substantial advances that have been made from the perspective of game theory, many sub-fields of bilevel optimization have emerged concerning optimal control, multiobjective optimization, energy and electricity markets, management science, security and many more. Each chapter of this book covers a specific aspect of bilevel optimization that has grown significantly or holds great potential to grow, and was written by top experts in the corresponding area. In other words, unlike other works on the subject, this book consists of surveys of different topics on bilevel optimization. Hence, it can serve as a point of departure for students and researchers beginning their research journey or pursuing related projects. It also provides a unique opportunity for experienced researchers in the field to learn about the progress made so far and directions that warrant further investigation. All chapters have been peer-reviewed by experts on mathematical optimization.