Gaussian Processes for Machine Learning


Author: Carl Edward Rasmussen,Christopher K. I. Williams
Publisher: Mit Press
ISBN: 9780262182539
Category: Computers
Page: 248
View: 1666

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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.

Machine Learning

A Probabilistic Perspective
Author: Kevin P. Murphy
Publisher: MIT Press
ISBN: 0262018020
Category: Computers
Page: 1067
View: 3846

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A comprehensive introduction to machine learning that uses probabilistic models and inference as a unifying approach.

Gaussian Process Regression Analysis for Functional Data


Author: Jian Qing Shi,Taeryon Choi
Publisher: CRC Press
ISBN: 1439837740
Category: Mathematics
Page: 216
View: 4281

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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.

Gaussian Processes, Function Theory, and the Inverse Spectral Problem


Author: Harry Dym,Henry P. McKean
Publisher: Courier Corporation
ISBN: 048646279X
Category: Mathematics
Page: 333
View: 6647

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This text offers background in function theory, Hardy functions, and probability as preparation for surveys of Gaussian processes, strings and spectral functions, and strings and spaces of integral functions. It addresses the relationship between the past and the future of a real, one-dimensional, stationary Gaussian process. 1976 edition.

Learning with Kernels

Support Vector Machines, Regularization, Optimization, and Beyond
Author: Bernhard Schölkopf,Alexander J. Smola
Publisher: MIT Press
ISBN: 9780262194754
Category: Computers
Page: 626
View: 9401

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A comprehensive introduction to Support Vector Machines and related kernel methods.

Lectures on Gaussian Processes


Author: Mikhail Lifshits
Publisher: Springer Science & Business Media
ISBN: 3642249396
Category: Mathematics
Page: 121
View: 9773

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Gaussian processes can be viewed as a far-reaching infinite-dimensional extension of classical normal random variables. Their theory presents a powerful range of tools for probabilistic modelling in various academic and technical domains such as Statistics, Forecasting, Finance, Information Transmission, Machine Learning - to mention just a few. The objective of these Briefs is to present a quick and condensed treatment of the core theory that a reader must understand in order to make his own independent contributions. The primary intended readership are PhD/Masters students and researchers working in pure or applied mathematics. The first chapters introduce essentials of the classical theory of Gaussian processes and measures with the core notions of reproducing kernel, integral representation, isoperimetric property, large deviation principle. The brevity being a priority for teaching and learning purposes, certain technical details and proofs are omitted. The later chapters touch important recent issues not sufficiently reflected in the literature, such as small deviations, expansions, and quantization of processes. In university teaching, one can build a one-semester advanced course upon these Briefs.​

Kernel Methods in Computational Biology


Author: Bernhard Schölkopf,Koji Tsuda,Jean-Philippe Vert
Publisher: MIT Press
ISBN: 9780262195096
Category: Computers
Page: 400
View: 9425

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A detailed overview of current research in kernel methods and their application to computational biology.

Bayesian Reasoning and Machine Learning


Author: David Barber
Publisher: Cambridge University Press
ISBN: 0521518148
Category: Computers
Page: 697
View: 6025

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A practical introduction perfect for final-year undergraduate and graduate students without a solid background in linear algebra and calculus.

Mathematical Methods for Neural Network Analysis and Design


Author: Richard M. Golden
Publisher: MIT Press
ISBN: 9780262071741
Category: Computers
Page: 419
View: 2964

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This graduate-level text teaches students how to use a small number of powerful mathematical tools for analyzing and designing a wide variety of artificial neural network (ANN) systems, including their own customized neural networks. Mathematical Methods for Neural Network Analysis and Design offers an original, broad, and integrated approach that explains each tool in a manner that is independent of specific ANN systems. Although most of the methods presented are familiar, their systematic application to neural networks is new. Included are helpful chapter summaries and detailed solutions to over 100 ANN system analysis and design problems. For convenience, many of the proofs of the key theorems have been rewritten so that the entire book uses a relatively uniform notion. This text is unique in several ways. It is organized according to categories of mathematical tools—for investigating the behavior of an ANN system, for comparing (and improving) the efficiency of system computations, and for evaluating its computational goals— that correspond respectively to David Marr's implementational, algorithmic, and computational levels of description. And instead of devoting separate chapters to different types of ANN systems, it analyzes the same group of ANN systems from the perspective of different mathematical methodologies. A Bradford Book

Large-scale Kernel Machines


Author: Léon Bottou
Publisher: MIT Press
ISBN: 0262026252
Category: Computers
Page: 396
View: 4155

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Solutions for learning from large scale datasets, including kernel learning algorithms that scale linearly with the volume of the data and experiments carried out on realistically large datasets.

Bayesian Filtering and Smoothing


Author: Simo Särkkä
Publisher: Cambridge University Press
ISBN: 110703065X
Category: Computers
Page: 254
View: 5981

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A unified Bayesian treatment of the state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models.

Probabilistic Graphical Models

Principles and Techniques
Author: Daphne Koller,Nir Friedman
Publisher: MIT Press
ISBN: 0262258358
Category: Computers
Page: 1280
View: 3459

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Most tasks require a person or an automated system to reason -- to reach conclusions based on available information. The framework of probabilistic graphical models, presented in this book, provides a general approach for this task. The approach is model-based, allowing interpretable models to be constructed and then manipulated by reasoning algorithms. These models can also be learned automatically from data, allowing the approach to be used in cases where manually constructing a model is difficult or even impossible. Because uncertainty is an inescapable aspect of most real-world applications, the book focuses on probabilistic models, which make the uncertainty explicit and provide models that are more faithful to reality. Probabilistic Graphical Models discusses a variety of models, spanning Bayesian networks, undirected Markov networks, discrete and continuous models, and extensions to deal with dynamical systems and relational data. For each class of models, the text describes the three fundamental cornerstones: representation, inference, and learning, presenting both basic concepts and advanced techniques. Finally, the book considers the use of the proposed framework for causal reasoning and decision making under uncertainty. The main text in each chapter provides the detailed technical development of the key ideas. Most chapters also include boxes with additional material: skill boxes, which describe techniques; case study boxes, which discuss empirical cases related to the approach described in the text, including applications in computer vision, robotics, natural language understanding, and computational biology; and concept boxes, which present significant concepts drawn from the material in the chapter. Instructors (and readers) can group chapters in various combinations, from core topics to more technically advanced material, to suit their particular needs.

Foundations of Machine Learning


Author: Mehryar Mohri,Afshin Rostamizadeh,Ameet Talwalkar
Publisher: MIT Press
ISBN: 0262304732
Category: Computers
Page: 432
View: 4995

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This graduate-level textbook introduces fundamental concepts and methods in machine learning. It describes several important modern algorithms, provides the theoretical underpinnings of these algorithms, and illustrates key aspects for their application. The authors aim to present novel theoretical tools and concepts while giving concise proofs even for relatively advanced topics. Foundations of Machine Learning fills the need for a general textbook that also offers theoretical details and an emphasis on proofs. Certain topics that are often treated with insufficient attention are discussed in more detail here; for example, entire chapters are devoted to regression, multi-class classification, and ranking. The first three chapters lay the theoretical foundation for what follows, but each remaining chapter is mostly self-contained. The appendix offers a concise probability review, a short introduction to convex optimization, tools for concentration bounds, and several basic properties of matrices and norms used in the book.The book is intended for graduate students and researchers in machine learning, statistics, and related areas; it can be used either as a textbook or as a reference text for a research seminar.

Applied Multivariate Analysis

Using Bayesian and Frequentist Methods of Inference, Second Edition
Author: S. James Press
Publisher: Courier Corporation
ISBN: 0486442365
Category: Mathematics
Page: 671
View: 1168

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Includes practical elements of matrix theory, continuous multivariate distributions and basic multivariate statistics in the normal distribution; regression and the analysis of variance; factor analysis and latent structure analysis; canonical correlations; stable portfolio analysis; classifications and discrimination models; control in the multivariate linear model; and structuring multivariate populations. 1982 edition.

Knowledge Discovery with Support Vector Machines


Author: Lutz H. Hamel
Publisher: John Wiley & Sons
ISBN: 1118211030
Category: Computers
Page: 246
View: 2257

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An easy-to-follow introduction to support vector machines This book provides an in-depth, easy-to-follow introduction to support vector machines drawing only from minimal, carefully motivated technical and mathematical background material. It begins with a cohesive discussion of machine learning and goes on to cover: Knowledge discovery environments Describing data mathematically Linear decision surfaces and functions Perceptron learning Maximum margin classifiers Support vector machines Elements of statistical learning theory Multi-class classification Regression with support vector machines Novelty detection Complemented with hands-on exercises, algorithm descriptions, and data sets, Knowledge Discovery with Support Vector Machines is an invaluable textbook for advanced undergraduate and graduate courses. It is also an excellent tutorial on support vector machines for professionals who are pursuing research in machine learning and related areas.

Pattern Recognition and Machine Learning


Author: Christopher M. Bishop
Publisher: Springer
ISBN: 9781493938438
Category: Computers
Page: 738
View: 6755

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This is the first textbook on pattern recognition to present the Bayesian viewpoint. The book presents approximate inference algorithms that permit fast approximate answers in situations where exact answers are not feasible. It uses graphical models to describe probability distributions when no other books apply graphical models to machine learning. No previous knowledge of pattern recognition or machine learning concepts is assumed. Familiarity with multivariate calculus and basic linear algebra is required, and some experience in the use of probabilities would be helpful though not essential as the book includes a self-contained introduction to basic probability theory.

A First Course in Machine Learning


Author: Simon Rogers,Mark Girolami
Publisher: CRC Press
ISBN: 1498759602
Category: Business & Economics
Page: 305
View: 5523

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A First Course in Machine Learning covers the core mathematical and statistical techniques needed to understand some of the most popular machine learning algorithms. The algorithms presented span the main problem areas within machine learning: classification, clustering and projection. The text gives detailed descriptions and derivations for a small number of algorithms rather than cover many algorithms in less detail. Referenced throughout the text and available on a supporting website (http://bit.ly/firstcourseml), an extensive collection of MATLAB®/Octave scripts enables students to recreate plots that appear in the book and investigate changing model specifications and parameter values. By experimenting with the various algorithms and concepts, students see how an abstract set of equations can be used to solve real problems. Requiring minimal mathematical prerequisites, the classroom-tested material in this text offers a concise, accessible introduction to machine learning. It provides students with the knowledge and confidence to explore the machine learning literature and research specific methods in more detail.