An edition of Gaussian processes for machine learning
(2005)
Gaussian processes for machine learning
by Carl Edward Rasmussen
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Gaussian processes (GPs) provide an approach to kernel-machine learning. This book provides a 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. (From the book's web site, http://www.gaussianprocess.org/gpml/ )
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Book Details
Table of Contents
. Table of Contents
. Series Foreword
. Preface
. Symbols and Notation
. 1: Introduction
A Pictorial Introduction to Bayesian Modelling
Roadmap
. 2: Regression
Weight-space View
Function-space View
Varying the Hyperparameters
Decision Theory for Regression
An Example Application
Smoothing, Weight Functions and Equivalent Kernels
History and Related Work
Appendix: Infinite Radial Basis Function Networks
Exercises
. 3 Classification
Classification Problems
Linear Models for Classification
Gaussian Process Classification
The Laplace Approximation for the Binary GP Classifier
Multi-class Laplace Approximation
Expectation Propagation
Experiments
Discussion
Appendix: Moment Derivations
Exercises
. 4 Covariance Functions
Preliminaries
Examples of Covariance Functions
Eigenfunction Analysis of Kernels
Kernels for Non-vectorial Inputs
Exercises
. 5 Model Selection and Adaptation of Hyperparameters
5.1 The Model Selection Problem
5.2 Bayesian Model Selection
5.3 Cross-validation
5.4 Model Selection for GP Regression
5.5 Model Selection for GP Classification
5.6 Exercises
. 6 Relationships between GPs and Other Models
6.1 Reproducing Kernel Hilbert Spaces
6.2 Regularization
6.3 Spline Models
6.4 Support Vector Machines
6.5 Least-Squares Classification
6.6 Relevance Vector Machines
6.7 Exercises
. 7 Theoretical Perspectives
7.1 The Equivalent Kernel
7.2 Asymptotic Analysis
7.3 Average-case Learning Curves
7.4 PAC-Bayesian Analysis
7.5 Comparison with Other Supervised Learning Methods
7.6 Appendix: Learning Curve for the Ornstein-Uhlenbeck Process
7.7 Exercises
. 8 Approximation Methods for Large Datasets
8.1 Reduced-rank Approximations of the Gram Matrix
8.2 Greedy Approximation
8.3 Approximations for GPR with Fixed Hyperparameters
8.4 Approximations for GPC with Fixed Hyperparameters
8.5 Approximating the Marginal Likelihood and its Derivatives
8.6 Appendix: Equivalence of SR and GPR using the Nyström Approximate Kernel
8.7 Exercises
. 9 Further Issues and Conclusions
9.1 Multiple Outputs
9.2 Noise Models with Dependencies
9.3 Non-Gaussian Likelihoods
9.4 Derivative Observations
9.5 Prediction with Uncertain Inputs
9.6 Mixtures of Gaussian Processes
9.7 Global Optimization
9.8 Evaluation of Integrals
9.9 Student's t Process
9.10 Invariances
9.11 Latent Variable Models
9.12 Conclusions and Future Directions
. A Mathematical Background
. B Gaussian Markov Processes
. C Datasets and Code
. Bibliography
. Author Index
. Subject Index
Edition Notes
Includes bibliographical references and indexes.
Classifications
The Physical Object
ID Numbers
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| June 30, 2019 | Edited by MARC Bot | import existing book |
| December 5, 2010 | Edited by Open Library Bot | Added subjects from MARC records. |
| April 28, 2010 | Edited by Open Library Bot | Linked existing covers to the work. |
| December 10, 2009 | Created by WorkBot | add works page |