Lectures On Gaussian Processes

Author : Mikhail Lifshits
Publisher : Springer Science & Business Media
Page : 129 pages
File Size : 45,6 Mb
Release : 2012-01-11
Category : Mathematics
ISBN : 9783642249396

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Lectures on Gaussian Processes by Mikhail Lifshits Pdf

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.​

Author : Carl Edward Rasmussen,Christopher K. I. Williams
Publisher : MIT Press
Page : 266 pages
File Size : 50,6 Mb
Release : 2005-11-23
Category : Computers
ISBN : 9780262182539

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Gaussian Processes for Machine Learning by Carl Edward Rasmussen,Christopher K. I. Williams Pdf

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.

Author : Robert J. Adler
Publisher : IMS
Page : 198 pages
File Size : 50,5 Mb
Release : 1990
Category : Mathematics
ISBN : 094060017X

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An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes by Robert J. Adler Pdf

Author : Olivier Bousquet,Ulrike von Luxburg,Gunnar Rätsch
Publisher : Springer
Page : 246 pages
File Size : 50,7 Mb
Release : 2011-03-22
Category : Computers
ISBN : 9783540286509

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Advanced Lectures on Machine Learning by Olivier Bousquet,Ulrike von Luxburg,Gunnar Rätsch Pdf

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.

Author : Roderick Murray-Smith
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 43,8 Mb
Release : 2005-01-31
Category : Computers
ISBN : 9783540244578

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Switching and Learning in Feedback Systems by Roderick Murray-Smith Pdf

This book presents the outcome of the European Summer School on Multi-agent Control, held in Maynooth, Ireland in September 2003. The past decade witnessed remarkable progress in the area of dynamic systems with the emergence of a number of powerful methods for both modeling and controlling uncertain dynamic systems. The first two parts of this book present tutorial lectures by leading researchers in the area introducing the reader to recent achievements on switching and control and on Gaussian processes. The third part is devoted to the presentation of original research contributions in the area; among the topics addressed are car control, bounding algorithms, networked control systems, the theory of linear systems, Bayesian modeling, and surveying multiagent systems.

Author : Robert J. Adler
Publisher : Unknown
Page : 160 pages
File Size : 41,7 Mb
Release : 2008*
Category : Gaussian processes
ISBN : OCLC:276370560

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An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes by Robert J. Adler Pdf

This e-book is the product of Project Euclid and its mission to advance scholarly communication in the field of theoretical and applied mathematics and statistics. Project Euclid was developed and deployed by the Cornell University Library and is jointly managed by Cornell and the Duke University Press.

Author : John Ben Hough,Manjunath Krishnapur ,Yuval Peres ,B\'alint Vir\'ag
Publisher : American Mathematical Soc.
Page : 170 pages
File Size : 42,8 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821843734

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Zeros of Gaussian Analytic Functions and Determinantal Point Processes by John Ben Hough,Manjunath Krishnapur ,Yuval Peres ,B\'alint Vir\'ag Pdf

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.

Author : Roland Dobrushin,Piet Groeneboom,Michel Ledoux
Publisher : Springer
Page : 308 pages
File Size : 44,7 Mb
Release : 2006-11-13
Category : Mathematics
ISBN : 9783540496359

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Lectures on Probability Theory and Statistics by Roland Dobrushin,Piet Groeneboom,Michel Ledoux Pdf

Author : Marc Peter Deisenroth
Publisher : KIT Scientific Publishing
Page : 226 pages
File Size : 52,6 Mb
Release : 2010
Category : Electronic computers. Computer science
ISBN : 9783866445697

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Efficient Reinforcement Learning Using Gaussian Processes by Marc Peter Deisenroth Pdf

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.

Author : Takeyuki Hida,Si Si
Publisher : World Scientific
Page : 281 pages
File Size : 53,6 Mb
Release : 2008
Category : Mathematics
ISBN : 9789812812049

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Lectures on White Noise Functionals by Takeyuki Hida,Si Si Pdf

White noise analysis is an advanced stochastic calculus that has developed extensively since three decades ago. It has two main characteristics. One is the notion of generalized white noise functionals, the introduction of which is oriented by the line of advanced analysis, and they have made much contribution to the fields in science enormously. The other characteristic is that the white noise analysis has an aspect of infinite dimensional harmonic analysis arising from the infinite dimensional rotation group. With the help of this rotation group, the white noise analysis has explored new areas of mathematics and has extended the fields of applications.

Author : Vladimir I. Piterbarg
Publisher : American Mathematical Soc.
Page : 222 pages
File Size : 49,9 Mb
Release : 2012-03-28
Category : Mathematics
ISBN : 9780821883310

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Asymptotic Methods in the Theory of Gaussian Processes and Fields by Vladimir I. Piterbarg Pdf

This book is devoted to a systematic analysis of asymptotic behavior of distributions of various typical functionals of Gaussian random variables and fields. The text begins with an extended introduction, which explains fundamental ideas and sketches the basic methods fully presented later in the book. Good approximate formulas and sharp estimates of the remainders are obtained for a large class of Gaussian and similar processes. The author devotes special attention to the development of asymptotic analysis methods, emphasizing the method of comparison, the double-sum method and the method of moments. The author has added an extended introduction and has significantly revised the text for this translation, particularly the material on the double-sum method.

Author : Takeyuki Hida,Masuyuki Hitsuda
Publisher : American Mathematical Soc.
Page : 208 pages
File Size : 42,8 Mb
Release : 2024-07-02
Category : Mathematics
ISBN : 0821887637

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Gaussian Processes by Takeyuki Hida,Masuyuki Hitsuda Pdf

Aimed at students and researchers in mathematics, communications engineering, and economics, this book describes the probabilistic structure of a Gaussian process in terms of its canonical representation (or its innovation process). Multiple Markov properties of a Gaussian process and equivalence problems of Gaussian processes are clearly presented. The authors' approach is unique, involving causality in time evolution and information-theoretic aspects. Because the book is self-contained and only requires background in the fundamentals of probability theory and measure theory, it would be suitable as a textbook at the senior undergraduate or graduate level.

Author : Günter Last,Mathew Penrose
Publisher : Cambridge University Press
Page : 315 pages
File Size : 48,9 Mb
Release : 2017-10-26
Category : Mathematics
ISBN : 9781107088016

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Lectures on the Poisson Process by Günter Last,Mathew Penrose Pdf

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

Author : Richard McElreath
Publisher : CRC Press
Page : 488 pages
File Size : 46,8 Mb
Release : 2018-01-03
Category : Mathematics
ISBN : 9781315362618

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Statistical Rethinking by Richard McElreath Pdf

Statistical Rethinking: A Bayesian Course with Examples in R and Stan builds readers’ knowledge of and confidence in statistical modeling. Reflecting the need for even minor programming in today’s model-based statistics, the book pushes readers to perform step-by-step calculations that are usually automated. This unique computational approach ensures that readers understand enough of the details to make reasonable choices and interpretations in their own modeling work. The text presents generalized linear multilevel models from a Bayesian perspective, relying on a simple logical interpretation of Bayesian probability and maximum entropy. It covers from the basics of regression to multilevel models. The author also discusses measurement error, missing data, and Gaussian process models for spatial and network autocorrelation. By using complete R code examples throughout, this book provides a practical foundation for performing statistical inference. Designed for both PhD students and seasoned professionals in the natural and social sciences, it prepares them for more advanced or specialized statistical modeling. Web Resource The book is accompanied by an R package (rethinking) that is available on the author’s website and GitHub. The two core functions (map and map2stan) of this package allow a variety of statistical models to be constructed from standard model formulas.

Author : I.A. Ibragimov,Y.A. Rozanov
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 48,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461262756

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Gaussian Random Processes by I.A. Ibragimov,Y.A. Rozanov Pdf

The book deals mainly with three problems involving Gaussian stationary processes. The first problem consists of clarifying the conditions for mutual absolute continuity (equivalence) of probability distributions of a "random process segment" and of finding effective formulas for densities of the equiva lent distributions. Our second problem is to describe the classes of spectral measures corresponding in some sense to regular stationary processes (in par ticular, satisfying the well-known "strong mixing condition") as well as to describe the subclasses associated with "mixing rate". The third problem involves estimation of an unknown mean value of a random process, this random process being stationary except for its mean, i. e. , it is the problem of "distinguishing a signal from stationary noise". Furthermore, we give here auxiliary information (on distributions in Hilbert spaces, properties of sam ple functions, theorems on functions of a complex variable, etc. ). Since 1958 many mathematicians have studied the problem of equivalence of various infinite-dimensional Gaussian distributions (detailed and sys tematic presentation of the basic results can be found, for instance, in [23]). In this book we have considered Gaussian stationary processes and arrived, we believe, at rather definite solutions. The second problem mentioned above is closely related with problems involving ergodic theory of Gaussian dynamic systems as well as prediction theory of stationary processes.