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I. Williams  \nGaussian Processes for Machine Learning  \nAdaptive Computation and Machine Learning  \nThomas Dietterich, Editor  \nChristopher Bishop, David Heckerman, Michael Jordan, and Michael Kearns, Associate Editors  \nBioinformatics: The Machine Learning Approach, Pierre Baldi and S􀀜ren Brunak  \nReinforcement Learning: An Introduction, Richard S. Sutton and Andrew G. Barto  \nGraphical Models for Machine Learning and Digital Communication, Brendan J. Frey  \nLearning in Graphical Models, Michael I. Jordan  \nCausation, Prediction, and Search, second edition, Peter Spirtes, Clark Glymour, and Richard Scheines  \nPrinciples of Data Mining,  \nDavid Hand, Heikki Mannila, and Padhraic Smyth  \nBioinformatics: The Machine Learning Approach, second edition,  \nPierre Baldi and S􀀜ren Brunak  \nLearning Kernel Classi􀀌ers: Theory and Algorithms, Ralf Herbrich  \nLearning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond, Bernhard Sch􀁿olkopf and Alexander J. Smola  \nIntroduction to Machine Learning, Ethem Alpaydin  \nGaussian Processes for Machine Learning,  \nCarl Edward Rasmussen and Christopher K. I. Williams  \nGaussian Processes for Machine Learning  \nCarl Edward Rasmussen Christopher K. I. Williams  \nThe MIT Press Cambridge, Massachusetts London, England  \n􀀍c 2006 Massachusetts Institute of Technology  \nAll rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher.  \nMIT Press books may be purchased at special quantity discounts for business or sales promotional use. For information, please email special   sales@mitpress.mit.edu or write to Special Sales Department, The MIT Press, 55 Hayward Street, Cambridge, MA 02142 .  \nTypeset by the authors using LATEX2\".  \nThis book printed and bound in the United States of America.  \nLibrary of Congress Cataloging-in-Publication Data  \nRasmussen, Carl Edward.  \nGaussian processes for machine learning / Carl Edward Rasmussen, Christopher K. I. Williams.  \n[p. cm. |](p. cm. |) (Adaptive computation and machine learning) Includes bibliographical references and indexes.  \nISBN 0-262-18253-X  \n1. Gaussian processes|Data processing. 2. Machine learning|Mathematical models.  \nI. Williams, Christopher K. I. II. Title. III. Series.  \nQA274.4.R37 2006  \n519.2'3|dc22  \n2005053433  \n10 9 8 7 6 5 4 3 2 1  \nThe actual science of logic is conversant at present only with things either certain, impossible, or entirely doubtful, none of which (fortunately) we have to reason on. Therefore the true logic for this world is the calculus of Probabilities, which takes account of the magnitude of the probability which is, or ought tobe, in a reasonable man's mind.  \n| James Clerk Maxwell [1850]  \nContents  \nSeries Foreword .................................... xi  \nPreface ........................................ xiii  \nSymbols and Notation ................................ xvii  \n1 Introduction 1  \n1.1 A Pictorial Introduction to Bayesian Modelling ............... 3  \n1.2 Roadmap .................................... 5  \n2 Regression 7  \n2.1 Weight-space View ............................... 7  \n2.1.1 The Standard Linear Model ...................... 8  \n2.1.2 Projections of Inputs into Feature Space ............... 11  \n2.2 Function-space View .............................. 13  \n2.3 Varying the Hyperparameters ......................... 19  \n2.4 Decision Theory for Regression ........................ 21  \n2.5 An Example Application ............................ 22  \n2.6 Smoothing, Weight Functions and Equivalent Kernels ........... 24  \n􀀃 2.7 Incorporating Explicit Basis Functions .................... 27  \n2.7.1 Marginal Likelihood .......................... 29  \n2.8 History and Related Work ........................... 29  \n2.9 Exercises ............","cbCaieIsH0KhgKou","https://ap.wps.com/l/cbCaieIsH0KhgKou","pdf",2815417,266,"English","# Contents\n## Series Foreword\n## Preface\n## Symbols and Notation\n## 1 Introduction\n## 2 Regression\n## 3 Classification\n## 4 Covariance functions","[{\"question\":\"What are the main topics covered in the book?\",\"answer\":\"The book covers regression, classification, and covariance functions for Gaussian processes, including key theoretical views and practical examples.\"},{\"question\":\"How does the book approach regression with Gaussian processes?\",\"answer\":\"Regression is treated through weight-space and function-space perspectives, discussion of hyperparameters, smoothing and equivalent kernels, and decision theory for regression.\"},{\"question\":\"What methods are discussed for Gaussian-process classification?\",\"answer\":\"It presents classification problems and several approximation approaches such as Laplace approximation (including multi-class variants) and expectation propagation, along with implementation details and experiments.\"}]","Gaussian Processes for Machine Learning - Adaptive Computation and Machine Learning - series | PDF",1789976105,670]