Gaussian Processes for Machine Learning

Carl Edward Rasmussen and Christopher K. I. Williams
MIT Press, 2006. ISBN-10 0-262-18253-X, ISBN-13 978-0-262-18253-9.

This book is © Copyright 2006 by Massachusetts Institute of Technology. The MIT Press have kindly agreed to allow us to make the book available on the web. The web version of the book corresponds to the 2nd printing. You can buy the book for a list price of 36.00 US$ or 23.95 UK£.

The whole book as a single pdf file.

List of contents and individual chapters in pdf format

Table of Contents
Series Foreword
Symbols and Notation
1 Introduction
1.1 A Pictorial Introduction to Bayesian Modelling
1.2 Roadmap
2 Regression
2.1 Weight-space View
2.2 Function-space View
2.3 Varying the Hyperparameters
2.4 Decision Theory for Regression
2.5 An Example Application
2.6 Smoothing, Weight Functions and Equivalent Kernels
2.7 History and Related Work
2.8 Appendix: Infinite Radial Basis Function Networks
2.9 Exercises
3 Classification
3.1 Classification Problems
3.2 Linear Models for Classification
3.3 Gaussian Process Classification
3.4 The Laplace Approximation for the Binary GP Classifier
3.5 Multi-class Laplace Approximation
3.6 Expectation Propagation
3.7 Experiments
3.8 Discussion
3.9 Appendix: Moment Derivations
3.10 Exercises
4 Covariance Functions
4.1 Preliminaries
4.2 Examples of Covariance Functions
4.3 Eigenfunction Analysis of Kernels
4.4 Kernels for Non-vectorial Inputs
4.5 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
Author Index
Subject Index

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