Gaussian Processes for Machine Learning

Gaussian Processes for Machine Learning

Author: Carl Edward Rasmussen

Publisher: MIT Press

Published: 2005-11-23

Total Pages: 266

ISBN-13: 026218253X

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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.


Design and Optimization for 5G Wireless Communications

Design and Optimization for 5G Wireless Communications

Author: Haesik Kim

Publisher: John Wiley & Sons

Published: 2020-03-19

Total Pages: 424

ISBN-13: 1119494443

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This book offers a technical background to the design and optimization of wireless communication systems, covering optimization algorithms for wireless and 5G communication systems design. The book introduces the design and optimization systems which target capacity, latency, and connection density; including Enhanced Mobile Broadband Communication (eMBB), Ultra-Reliable and Low Latency Communication (URLL), and Massive Machine Type Communication (mMTC). The book is organized into two distinct parts: Part I, mathematical methods and optimization algorithms for wireless communications are introduced, providing the reader with the required mathematical background. In Part II, 5G communication systems are designed and optimized using the mathematical methods and optimization algorithms.


Estimation of Distribution Algorithms

Estimation of Distribution Algorithms

Author: Pedro LarraƱaga

Publisher: Springer Science & Business Media

Published: 2001-10-31

Total Pages: 424

ISBN-13: 9780792374664

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Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation is devoted to a new paradigm for evolutionary computation, named estimation of distribution algorithms (EDAs). This new class of algorithms generalizes genetic algorithms by replacing the crossover and mutation operators with learning and sampling from the probability distribution of the best individuals of the population at each iteration of the algorithm. Working in such a way, the relationships between the variables involved in the problem domain are explicitly and effectively captured and exploited. This text constitutes the first compilation and review of the techniques and applications of this new tool for performing evolutionary computation. Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation is clearly divided into three parts. Part I is dedicated to the foundations of EDAs. In this part, after introducing some probabilistic graphical models - Bayesian and Gaussian networks - a review of existing EDA approaches is presented, as well as some new methods based on more flexible probabilistic graphical models. A mathematical modeling of discrete EDAs is also presented. Part II covers several applications of EDAs in some classical optimization problems: the travelling salesman problem, the job scheduling problem, and the knapsack problem. EDAs are also applied to the optimization of some well-known combinatorial and continuous functions. Part III presents the application of EDAs to solve some problems that arise in the machine learning field: feature subset selection, feature weighting in K-NN classifiers, rule induction, partial abductive inference in Bayesian networks, partitional clustering, and the search for optimal weights in artificial neural networks. Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation is a useful and interesting tool for researchers working in the field of evolutionary computation and for engineers who face real-world optimization problems. This book may also be used by graduate students and researchers in computer science. `... I urge those who are interested in EDAs to study this well-crafted book today.' David E. Goldberg, University of Illinois Champaign-Urbana.


Finite Mixture Models

Finite Mixture Models

Author: Geoffrey McLachlan

Publisher: John Wiley & Sons

Published: 2004-03-22

Total Pages: 419

ISBN-13: 047165406X

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An up-to-date, comprehensive account of major issues in finitemixture modeling This volume provides an up-to-date account of the theory andapplications of modeling via finite mixture distributions. With anemphasis on the applications of mixture models in both mainstreamanalysis and other areas such as unsupervised pattern recognition,speech recognition, and medical imaging, the book describes theformulations of the finite mixture approach, details itsmethodology, discusses aspects of its implementation, andillustrates its application in many common statisticalcontexts. Major issues discussed in this book include identifiabilityproblems, actual fitting of finite mixtures through use of the EMalgorithm, properties of the maximum likelihood estimators soobtained, assessment of the number of components to be used in themixture, and the applicability of asymptotic theory in providing abasis for the solutions to some of these problems. The author alsoconsiders how the EM algorithm can be scaled to handle the fittingof mixture models to very large databases, as in data miningapplications. This comprehensive, practical guide: * Provides more than 800 references-40% published since 1995 * Includes an appendix listing available mixture software * Links statistical literature with machine learning and patternrecognition literature * Contains more than 100 helpful graphs, charts, and tables Finite Mixture Models is an important resource for both applied andtheoretical statisticians as well as for researchers in the manyareas in which finite mixture models can be used to analyze data.


Introduction to Graphical Modelling

Introduction to Graphical Modelling

Author: David Edwards

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 342

ISBN-13: 1461204933

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A useful introduction to this topic for both students and researchers, with an emphasis on applications and practicalities rather than on a formal development. It is based on the popular software package for graphical modelling, MIM, freely available for downloading from the Internet. Following a description of some of the basic ideas of graphical modelling, subsequent chapters describe particular families of models, including log-linear models, Gaussian models, and models for mixed discrete and continuous variables. Further chapters cover hypothesis testing and model selection. Chapters 7 and 8 are new to this second edition and describe the use of directed, chain, and other graphs, complete with a summary of recent work on causal inference.


Copulae in Mathematical and Quantitative Finance

Copulae in Mathematical and Quantitative Finance

Author: Piotr Jaworski

Publisher: Springer Science & Business Media

Published: 2013-06-18

Total Pages: 299

ISBN-13: 3642354076

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Copulas are mathematical objects that fully capture the dependence structure among random variables and hence offer great flexibility in building multivariate stochastic models. Since their introduction in the early 1950s, copulas have gained considerable popularity in several fields of applied mathematics, especially finance and insurance. Today, copulas represent a well-recognized tool for market and credit models, aggregation of risks, and portfolio selection. Historically, the Gaussian copula model has been one of the most common models in credit risk. However, the recent financial crisis has underlined its limitations and drawbacks. In fact, despite their simplicity, Gaussian copula models severely underestimate the risk of the occurrence of joint extreme events. Recent theoretical investigations have put new tools for detecting and estimating dependence and risk (like tail dependence, time-varying models, etc) in the spotlight. All such investigations need to be further developed and promoted, a goal this book pursues. The book includes surveys that provide an up-to-date account of essential aspects of copula models in quantitative finance, as well as the extended versions of talks selected from papers presented at the workshop in Cracow.


High-Dimensional Covariance Estimation

High-Dimensional Covariance Estimation

Author: Mohsen Pourahmadi

Publisher: John Wiley & Sons

Published: 2013-06-24

Total Pages: 204

ISBN-13: 1118034295

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Methods for estimating sparse and large covariance matrices Covariance and correlation matrices play fundamental roles in every aspect of the analysis of multivariate data collected from a variety of fields including business and economics, health care, engineering, and environmental and physical sciences. High-Dimensional Covariance Estimation provides accessible and comprehensive coverage of the classical and modern approaches for estimating covariance matrices as well as their applications to the rapidly developing areas lying at the intersection of statistics and machine learning. Recently, the classical sample covariance methodologies have been modified and improved upon to meet the needs of statisticians and researchers dealing with large correlated datasets. High-Dimensional Covariance Estimation focuses on the methodologies based on shrinkage, thresholding, and penalized likelihood with applications to Gaussian graphical models, prediction, and mean-variance portfolio management. The book relies heavily on regression-based ideas and interpretations to connect and unify many existing methods and algorithms for the task. High-Dimensional Covariance Estimation features chapters on: Data, Sparsity, and Regularization Regularizing the Eigenstructure Banding, Tapering, and Thresholding Covariance Matrices Sparse Gaussian Graphical Models Multivariate Regression The book is an ideal resource for researchers in statistics, mathematics, business and economics, computer sciences, and engineering, as well as a useful text or supplement for graduate-level courses in multivariate analysis, covariance estimation, statistical learning, and high-dimensional data analysis.


Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers

Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers

Author: Stephen Boyd

Publisher: Now Publishers Inc

Published: 2011

Total Pages: 138

ISBN-13: 160198460X

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Surveys the theory and history of the alternating direction method of multipliers, and discusses its applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others.


Solving Large Scale Learning Tasks. Challenges and Algorithms

Solving Large Scale Learning Tasks. Challenges and Algorithms

Author: Stefan Michaelis

Publisher: Springer

Published: 2016-07-02

Total Pages: 397

ISBN-13: 3319417061

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In celebration of Prof. Morik's 60th birthday, this Festschrift covers research areas that Prof. Morik worked in and presents various researchers with whom she collaborated. The 23 refereed articles in this Festschrift volume provide challenges and solutions from theoreticians and practitioners on data preprocessing, modeling, learning, and evaluation. Topics include data-mining and machine-learning algorithms, feature selection and feature generation, optimization as well as efficiency of energy and communication.


Machine Learning and Knowledge Discovery in Databases

Machine Learning and Knowledge Discovery in Databases

Author: Annalisa Appice

Publisher: Springer

Published: 2015-08-28

Total Pages: 802

ISBN-13: 3319235257

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The three volume set LNAI 9284, 9285, and 9286 constitutes the refereed proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases, ECML PKDD 2015, held in Porto, Portugal, in September 2015. The 131 papers presented in these proceedings were carefully reviewed and selected from a total of 483 submissions. These include 89 research papers, 11 industrial papers, 14 nectar papers, 17 demo papers. They were organized in topical sections named: classification, regression and supervised learning; clustering and unsupervised learning; data preprocessing; data streams and online learning; deep learning; distance and metric learning; large scale learning and big data; matrix and tensor analysis; pattern and sequence mining; preference learning and label ranking; probabilistic, statistical, and graphical approaches; rich data; and social and graphs. Part III is structured in industrial track, nectar track, and demo track.