Lectures on Gaussian Processes

Lectures on Gaussian Processes PDF

Author: Mikhail Lifshits

Publisher: Springer Science & Business Media

Published: 2012-01-11

Total Pages: 129

ISBN-13: 3642249396

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Gaussian processes can be viewed as a far-reaching infinite-dimensional extension of classical normal random variables. Their theory presents a powerful range of tools for probabilistic modelling in various academic and technical domains such as Statistics, Forecasting, Finance, Information Transmission, Machine Learning - to mention just a few. The objective of these Briefs is to present a quick and condensed treatment of the core theory that a reader must understand in order to make his own independent contributions. The primary intended readership are PhD/Masters students and researchers working in pure or applied mathematics. The first chapters introduce essentials of the classical theory of Gaussian processes and measures with the core notions of reproducing kernel, integral representation, isoperimetric property, large deviation principle. The brevity being a priority for teaching and learning purposes, certain technical details and proofs are omitted. The later chapters touch important recent issues not sufficiently reflected in the literature, such as small deviations, expansions, and quantization of processes. In university teaching, one can build a one-semester advanced course upon these Briefs.​

Gaussian Processes for Machine Learning

Gaussian Processes for Machine Learning PDF

Author: Carl Edward Rasmussen

Publisher: MIT Press

Published: 2005-11-23

Total Pages: 266

ISBN-13: 026218253X

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A comprehensive and self-contained introduction to Gaussian processes, which provide a principled, practical, probabilistic approach to learning in kernel machines. Gaussian processes (GPs) provide a principled, practical, probabilistic approach to learning in kernel machines. GPs have received increased attention in the machine-learning community over the past decade, and this book provides a long-needed systematic and unified 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. The book deals with the supervised-learning problem for both regression and classification, and includes detailed algorithms. A wide variety of covariance (kernel) functions are presented and their properties discussed. Model selection is discussed both from a Bayesian and a classical perspective. Many connections to other well-known techniques from machine learning and statistics are discussed, including support-vector machines, neural networks, splines, regularization networks, relevance vector machines and others. Theoretical issues including learning curves and the PAC-Bayesian framework are treated, and several approximation methods for learning with large datasets are discussed. The book contains illustrative examples and exercises, and code and datasets are available on the Web. Appendixes provide mathematical background and a discussion of Gaussian Markov processes.

Advanced Lectures on Machine Learning

Advanced Lectures on Machine Learning PDF

Author: Olivier Bousquet

Publisher: Springer

Published: 2011-03-22

Total Pages: 246

ISBN-13: 3540286500

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Machine Learning has become a key enabling technology for many engineering applications, investigating scientific questions and theoretical problems alike. To stimulate discussions and to disseminate new results, a summer school series was started in February 2002, the documentation of which is published as LNAI 2600. This book presents revised lectures of two subsequent summer schools held in 2003 in Canberra, Australia, and in Tübingen, Germany. The tutorial lectures included are devoted to statistical learning theory, unsupervised learning, Bayesian inference, and applications in pattern recognition; they provide in-depth overviews of exciting new developments and contain a large number of references. Graduate students, lecturers, researchers and professionals alike will find this book a useful resource in learning and teaching machine learning.

Zeros of Gaussian Analytic Functions and Determinantal Point Processes

Zeros of Gaussian Analytic Functions and Determinantal Point Processes PDF

Author: John Ben Hough

Publisher: American Mathematical Soc.

Published: 2009

Total Pages: 170

ISBN-13: 0821843737

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Examines in some depth two important classes of point processes, determinantal processes and 'Gaussian zeros', i.e., zeros of random analytic functions with Gaussian coefficients. This title presents a primer on modern techniques on the interface of probability and analysis.

Switching and Learning in Feedback Systems

Switching and Learning in Feedback Systems PDF

Author: Roderick Murray-Smith

Publisher: Springer

Published: 2005-01-27

Total Pages: 353

ISBN-13: 3540305602

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A central theme in the study of dynamic systems is the modelling and control of uncertain systems. While ‘uncertainty’ has long been a strong motivating factor behind many techniques developed in the modelling, control, statistics and mathematics communities, the past decade, in particular, has witnessed remarkable progress in this area with the emergence of a number of powerful newmethodsforbothmodellingandcontrollinguncertaindynamicsystems. The speci?c objective of this book is to describe and review some of these exciting new approaches within a single volume. Our approach was to invite some of the leading researchers in this area to contribute to this book by submitting both tutorial papers on their speci?c area of research, and to submit more focussed research papers to document some of the latest results in the area. We feel that collecting some of the main results together in this manner is particularly important as many of the important ideas that emerged in the past decade were derived in a variety of academic disciplines. By providing both tutorial and researchpaperswehopetobeabletoprovidetheinterestedreaderwithsu?cient background to appreciate some of the main concepts from a variety of related, but nevertheless distinct ?elds, and to provide a ?avor of how these results are currently being used to cope with ‘uncertainty. ’ It is our sincere hope that the availability of these results within a single volume will lead to further cro- fertilization of ideas and act as a spark for further research in this important area of applied mathematics.

High-Dimensional Probability

High-Dimensional Probability PDF

Author: Roman Vershynin

Publisher: Cambridge University Press

Published: 2018-09-27

Total Pages: 299

ISBN-13: 1108415199

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An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Efficient Reinforcement Learning Using Gaussian Processes

Efficient Reinforcement Learning Using Gaussian Processes PDF

Author: Marc Peter Deisenroth

Publisher: KIT Scientific Publishing

Published: 2010

Total Pages: 226

ISBN-13: 3866445695

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This book examines Gaussian processes in both model-based reinforcement learning (RL) and inference in nonlinear dynamic systems.First, we introduce PILCO, a fully Bayesian approach for efficient RL in continuous-valued state and action spaces when no expert knowledge is available. PILCO takes model uncertainties consistently into account during long-term planning to reduce model bias. Second, we propose principled algorithms for robust filtering and smoothing in GP dynamic systems.

Lectures on the Poisson Process

Lectures on the Poisson Process PDF

Author: Günter Last

Publisher: Cambridge University Press

Published: 2017-10-26

Total Pages: 315

ISBN-13: 1107088011

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A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.

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