Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning): | Guide books

Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)December 2005

Go to Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)

December 2005

Publisher:

The MIT Press

ISBN:978-0-262-18253-9

Published:01 December 2005

Available at Amazon

Bibliometrics

Sections

2005

Abstract

No abstract available.

Cited By

Contributors

Carl Edward Rasmussen
University of Cambridge
- Publication Years1994 - 2024
- Publication counts47
- Citation count3,207
- Available for Download12
- Downloads (cumulative)6,055
- Downloads (12 months)699
- Downloads (6 weeks)123
- Average Downloads per Article505
- Average Citation per Article68
View Full Profile
Christopher K I Williams
- Publication Years2005 - 2005
- Publication counts2
- Citation count2,157
- Available for Download0
- Downloads (cumulative)0
- Downloads (12 months)0
- Downloads (6 weeks)0
- Average Downloads per Article0
- Average Citation per Article1,079
View Full Profile

Index Terms

Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
1. Mathematics of computing
  1. Probability and statistics
2. Theory of computation
  1. Theory and algorithms for application domains
    1. Machine learning theory
      1. Markov decision processes

Reviews

Reviewer: Luminita State

Research in machine learning has come from a number of different areas, including statistics, brain modeling, adaptive control theory, psychological models, artificial intelligence, and evolutionary models. Each of these areas brings to the field different methods and different vocabularies; these are now being assimilated into a more unified discipline. The focus of this book is to present a clear and concise overview of the main ideas of Gaussian processes in a machine learning context. The authors also point out a wide range of connections to existing models in the literature and develop a suitable approximate inference framework as a basis for faster practical algorithms. The book is concerned with supervised learning, that is, the problem of learning input-output mappings from empirical data. The first part, chapters 1 through 5, is devoted to specific topics in the area of Gaussian modeling in supervised learning. The second part covers the connections to other methods, fast approximations, and more specialized properties. Chapter 1 provides an introduction to Bayesian modeling. Chapter 2 analyzes regression, viewed as a supervised learning technique in predicting the values of continuous parameters. It gives a detailed presentation of the basics of the Bayesian linear model and the use of the Bayesian linear model in a higher dimensional feature space that results from projections expressed in terms of a set of basis functions of initial inputs. Chapter 3 investigates several methods of approximate inference for probabilistic classification, viewed as a function approximation problem. The main topics treated here are concerned with the derivation of the Gaussian process regression by generalizing linear regression, the use of the logistic regression as an analog of linear regression in the case of classification problems, and the generalization of the logistic regression to yield Gaussian process classification (GPC). Experimental results in testing GPC, together with their analysis, are provided in the final sections of this chapter. Chapter 4 is devoted to topics related to covariance functions. The first sections of this chapter briefly investigate several classes of covariance functions, such as stationary, squared exponential, Matern class, rational quadratic, and piecewise polynomial with compact support, and some nonstationary covariance functions. The final sections of this chapter are concerned with special topics related to kernels, ways to combine or modify existing covariance functions, eigenfunction analysis of kernels, and the presentation of some special classes of kernels. Chapter 5 provides a detailed treatment of the model selection problem, including the discrete choice of the functional form for the covariance function and the values of the hyperparameters. The problem is approached in terms of different methodologies, Bayesian principles, cross-validation, and the leave-one-out estimator. In the final sections of this chapter, these methods are applied to learning in Gaussian process models for regression and classification. Chapter 6 presents a series of concepts and models related to Gaussian process prediction, such as reproducing kernel Hilbert spaces, regularization theory, and splines. The final sections of this chapter focus on other families of kernel machines that are related to Gaussian process prediction, support vector machines, least-squares classification, and vector machines. Chapter 7 investigates the Gaussian processes from a theoretical point of view. Several conclusions expressed in terms of consistency, equivalence, and orthogonality are derived in order to establish asymptotic properties of Gaussian processes. The final sections of this chapter present a PAC-Bayesian analysis of Gaussian processes for classification and comparison with other supervised learning methods. Chapter 8 presents reduced-rank approximation of the Gram matrix and approximation schemes for Gaussian process regression (GPR); these aim to develop suitable approximation schemes for large datasets. Chapter 9 provides a brief description of other issues related to Gaussian process prediction and a series of comments on related work. The book is an excellent and comprehensive monograph on the topic of Gaussian approaches in machine learning. It is strongly recommended to a large class of readers, including researchers, graduate students, and practitioners in fields related to statistics, artificial intelligence, and pattern recognition. The numerous examples included in the text and the problems suggested as exercises at the end of each chapter are welcome and facilitate the understanding of the content. The list of references includes the most representative work published in this area. Online Computing Reviews Service

Access critical reviews of Computing literature here

Become a reviewer for Computing Reviews.

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Recommendations

Lifelong Machine Learning
Machine Learning: The State of the Art

The two fundamental problems in machine learning (ML) are statistical analysis and algorithm design. The former tells us the principles of the mathematical models that we establish from the observation data. The latter defines the conditions on which ...
Machine Learning: A Technical Approach To Machine Learning For Beginners

Save to Binder