Gaussian processes for machine learning
By: Carl Edward Rasmussen, Christopher K.I. Williams.
Contributors: Williams, Christopher K. I.
Series: Adaptive computation and machine learning
Publisher: MIT Press
Published: 2006
Place of publication: Cambridge, Mass
Language: eng
Number of pages: 272
Subjects: Gaussian processes -- Data processing.; Machine learning -- Mathematical models.
Description: 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/ )
Notes: Includes bibliographical references and indexes.
Table of contents: title: . Table of Contents; title: . Series Foreword; title: . Preface; title: . Symbols and Notation; title: . 1: Introduction; title: A Pictorial Introduction to Bayesian Modelling; title: Roadmap; title: . 2: Regression; title: Weight-space View; title: Function-space View; title: Varying the Hyperparameters; title: Decision Theory for Regression; title: An Example Application; title: Smoothing, Weight Functions and Equivalent Kernels; title: History and Related Work; title: Appendix: Infinite Radial Basis Function Networks; title: Exercises; title: . 3 Classification; title: Classification Problems; title: Linear Models for Classification; title: Gaussian Process Classification; title: The Laplace Approximation for the Binary GP Classifier; title: Multi-class Laplace Approximation; title: Expectation Propagation; title: Experiments; title: Discussion; title: Appendix: Moment Derivations; title: Exercises; title: . 4 Covariance Functions; title: Preliminaries; title: Examples of Covariance Functions; title: Eigenfunction Analysis of Kernels; title: Kernels for Non-vectorial Inputs; title: Exercises; title: . 5 Model Selection and Adaptation of Hyperparameters; title: 5.1 The Model Selection Problem; title: 5.2 Bayesian Model Selection; title: 5.3 Cross-validation; title: 5.4 Model Selection for GP Regression; title: 5.5 Model Selection for GP Classification; title: 5.6 Exercises; title: .  6 Relationships between GPs and Other Models; title: 6.1 Reproducing Kernel Hilbert Spaces; title: 6.2 Regularization; title: 6.3 Spline Models; title: 6.4 Support Vector Machines; title: 6.5 Least-Squares Classification; title: 6.6 Relevance Vector Machines; title: 6.7 Exercises; title: .  7 Theoretical Perspectives; title: 7.1 The Equivalent Kernel; title: 7.2 Asymptotic Analysis; title: 7.3 Average-case Learning Curves; title: 7.4 PAC-Bayesian Analysis; title: 7.5 Comparison with Other Supervised Learning Methods; title: 7.6 Appendix: Learning Curve for the Ornstein-Uhlenbeck Process; title: 7.7 Exercises; title: .  8 Approximation Methods for Large Datasets; title: 8.1 Reduced-rank Approximations of the Gram Matrix; title: 8.2 Greedy Approximation; title: 8.3 Approximations for GPR with Fixed Hyperparameters; title: 8.4 Approximations for GPC with Fixed Hyperparameters; title: 8.5 Approximating the Marginal Likelihood and its Derivatives; title: 8.6 Appendix: Equivalence of SR and GPR using the Nyström Approximate Kernel; title: 8.7 Exercises; title: . 9 Further Issues and Conclusions; title: 9.1 Multiple Outputs; title: 9.2 Noise Models with Dependencies; title: 9.3 Non-Gaussian Likelihoods; title: 9.4 Derivative Observations; title: 9.5 Prediction with Uncertain Inputs; title: 9.6 Mixtures of Gaussian Processes; title: 9.7 Global Optimization; title: 9.8 Evaluation of Integrals; title: 9.9 Student's t Process; title: 9.10 Invariances; title: 9.11 Latent Variable Models; title: 9.12 Conclusions and Future Directions; title: .  A Mathematical Background; title: .  B Gaussian Markov Processes; title: .  C Datasets and Code; title: .  Bibliography; title: .  Author Index; title: .  Subject Index