Lectures On Gaussian Processes

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Lectures on Gaussian Processes

Author : Mikhail Lifshits
Publisher : Springer Science & Business Media
ISBN 13 : 3642249396
Total Pages : 129 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Lectures on Gaussian Processes by : Mikhail Lifshits

Download or read book Lectures on Gaussian Processes written by Mikhail Lifshits and published by Springer Science & Business Media. This book was released on 2012-01-11 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lectures on Gaussian Processes

Author : Mikhail Lifshits
Publisher : Springer Science & Business Media
ISBN 13 : 3642249388
Total Pages : 129 pages
Book Rating : 4.6/5 (422 download)

DOWNLOAD NOW!

Book Synopsis Lectures on Gaussian Processes by : Mikhail Lifshits

Download or read book Lectures on Gaussian Processes written by Mikhail Lifshits and published by Springer Science & Business Media. This book was released on 2012-01-13 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Carl Edward Rasmussen
Publisher : MIT Press
ISBN 13 : 026218253X
Total Pages : 266 pages
Book Rating : 4.2/5 (621 download)

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Book Synopsis Gaussian Processes for Machine Learning by : Carl Edward Rasmussen

Download or read book Gaussian Processes for Machine Learning written by Carl Edward Rasmussen and published by MIT Press. This book was released on 2005-11-23 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Zeros of Gaussian Analytic Functions and Determinantal Point Processes

Author : John Ben Hough
Publisher : American Mathematical Soc.
ISBN 13 : 0821843737
Total Pages : 170 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Zeros of Gaussian Analytic Functions and Determinantal Point Processes by : John Ben Hough

Download or read book Zeros of Gaussian Analytic Functions and Determinantal Point Processes written by John Ben Hough and published by American Mathematical Soc.. This book was released on 2009 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Advanced Lectures on Machine Learning

Author : Olivier Bousquet
Publisher : Springer
ISBN 13 : 3540286500
Total Pages : 249 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Advanced Lectures on Machine Learning by : Olivier Bousquet

Download or read book Advanced Lectures on Machine Learning written by Olivier Bousquet and published by Springer. This book was released on 2011-03-22 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes

Author : Robert J. Adler
Publisher : IMS
ISBN 13 : 9780940600171
Total Pages : 198 pages
Book Rating : 4.6/5 (1 download)

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

Download or read book An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes written by Robert J. Adler and published by IMS. This book was released on 1990 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Efficient Reinforcement Learning Using Gaussian Processes

Author : Marc Peter Deisenroth
Publisher : KIT Scientific Publishing
ISBN 13 : 3866445695
Total Pages : 226 pages
Book Rating : 4.8/5 (664 download)

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Book Synopsis Efficient Reinforcement Learning Using Gaussian Processes by : Marc Peter Deisenroth

Download or read book Efficient Reinforcement Learning Using Gaussian Processes written by Marc Peter Deisenroth and published by KIT Scientific Publishing. This book was released on 2010 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Günter Last
Publisher : Cambridge University Press
ISBN 13 : 1107088011
Total Pages : 315 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Lectures on the Poisson Process by : Günter Last

Download or read book Lectures on the Poisson Process written by Günter Last and published by Cambridge University Press. This book was released on 2017-10-26 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.

High-Dimensional Probability

Author : Roman Vershynin
Publisher : Cambridge University Press
ISBN 13 : 1108415199
Total Pages : 299 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis High-Dimensional Probability by : Roman Vershynin

Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Statistical Rethinking

Author : Richard McElreath
Publisher : CRC Press
ISBN 13 : 1315362619
Total Pages : 488 pages
Book Rating : 4.3/5 (153 download)

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Book Synopsis Statistical Rethinking by : Richard McElreath

Download or read book Statistical Rethinking written by Richard McElreath and published by CRC Press. This book was released on 2018-01-03 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Probabilistic Machine Learning

Author : Kevin P. Murphy
Publisher : MIT Press
ISBN 13 : 0262369303
Total Pages : 858 pages
Book Rating : 4.2/5 (623 download)

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Book Synopsis Probabilistic Machine Learning by : Kevin P. Murphy

Download or read book Probabilistic Machine Learning written by Kevin P. Murphy and published by MIT Press. This book was released on 2022-03-01 with total page 858 pages. Available in PDF, EPUB and Kindle. Book excerpt: A detailed and up-to-date introduction to machine learning, presented through the unifying lens of probabilistic modeling and Bayesian decision theory. This book offers a detailed and up-to-date introduction to machine learning (including deep learning) through the unifying lens of probabilistic modeling and Bayesian decision theory. The book covers mathematical background (including linear algebra and optimization), basic supervised learning (including linear and logistic regression and deep neural networks), as well as more advanced topics (including transfer learning and unsupervised learning). End-of-chapter exercises allow students to apply what they have learned, and an appendix covers notation. Probabilistic Machine Learning grew out of the author’s 2012 book, Machine Learning: A Probabilistic Perspective. More than just a simple update, this is a completely new book that reflects the dramatic developments in the field since 2012, most notably deep learning. In addition, the new book is accompanied by online Python code, using libraries such as scikit-learn, JAX, PyTorch, and Tensorflow, which can be used to reproduce nearly all the figures; this code can be run inside a web browser using cloud-based notebooks, and provides a practical complement to the theoretical topics discussed in the book. This introductory text will be followed by a sequel that covers more advanced topics, taking the same probabilistic approach.

Gaussian Hilbert Spaces

Author : Svante Janson
Publisher : Cambridge University Press
ISBN 13 : 0521561280
Total Pages : 358 pages
Book Rating : 4.5/5 (215 download)

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Book Synopsis Gaussian Hilbert Spaces by : Svante Janson

Download or read book Gaussian Hilbert Spaces written by Svante Janson and published by Cambridge University Press. This book was released on 1997-06-12 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats the very special and fundamental mathematical properties that hold for a family of Gaussian (or normal) random variables. Such random variables have many applications in probability theory, other parts of mathematics, statistics and theoretical physics. The emphasis throughout this book is on the mathematical structures common to all these applications. This will be an excellent resource for all researchers whose work involves random variables.

Lectures on Random Lozenge Tilings

Author : Vadim Gorin
Publisher : Cambridge University Press
ISBN 13 : 1108843964
Total Pages : 261 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis Lectures on Random Lozenge Tilings by : Vadim Gorin

Download or read book Lectures on Random Lozenge Tilings written by Vadim Gorin and published by Cambridge University Press. This book was released on 2021-09-09 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book dedicated to reviewing the mathematics of random tilings of large domains on the plane.

Random Processes for Engineers

Author : Bruce Hajek
Publisher : Cambridge University Press
ISBN 13 : 1316241246
Total Pages : 429 pages
Book Rating : 4.3/5 (162 download)

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Book Synopsis Random Processes for Engineers by : Bruce Hajek

Download or read book Random Processes for Engineers written by Bruce Hajek and published by Cambridge University Press. This book was released on 2015-03-12 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: This engaging introduction to random processes provides students with the critical tools needed to design and evaluate engineering systems that must operate reliably in uncertain environments. A brief review of probability theory and real analysis of deterministic functions sets the stage for understanding random processes, whilst the underlying measure theoretic notions are explained in an intuitive, straightforward style. Students will learn to manage the complexity of randomness through the use of simple classes of random processes, statistical means and correlations, asymptotic analysis, sampling, and effective algorithms. Key topics covered include: • Calculus of random processes in linear systems • Kalman and Wiener filtering • Hidden Markov models for statistical inference • The estimation maximization (EM) algorithm • An introduction to martingales and concentration inequalities. Understanding of the key concepts is reinforced through over 100 worked examples and 300 thoroughly tested homework problems (half of which are solved in detail at the end of the book).

Mathematical Analysis and Applications

Author : Michael Ruzhansky
Publisher : John Wiley & Sons
ISBN 13 : 1119414334
Total Pages : 1021 pages
Book Rating : 4.1/5 (194 download)

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Book Synopsis Mathematical Analysis and Applications by : Michael Ruzhansky

Download or read book Mathematical Analysis and Applications written by Michael Ruzhansky and published by John Wiley & Sons. This book was released on 2018-04-11 with total page 1021 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors—a noted team of international researchers in the field— highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields.

Random Graphs, Phase Transitions, and the Gaussian Free Field

Author : Martin T. Barlow
Publisher : Springer Nature
ISBN 13 : 3030320111
Total Pages : 421 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Random Graphs, Phase Transitions, and the Gaussian Free Field by : Martin T. Barlow

Download or read book Random Graphs, Phase Transitions, and the Gaussian Free Field written by Martin T. Barlow and published by Springer Nature. This book was released on 2019-12-03 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2017 PIMS-CRM Summer School in Probability was held at the Pacific Institute for the Mathematical Sciences (PIMS) at the University of British Columbia in Vancouver, Canada, during June 5-30, 2017. It had 125 participants from 20 different countries, and featured two main courses, three mini-courses, and twenty-nine lectures. The lecture notes contained in this volume provide introductory accounts of three of the most active and fascinating areas of research in modern probability theory, especially designed for graduate students entering research: Scaling limits of random trees and random graphs (Christina Goldschmidt) Lectures on the Ising and Potts models on the hypercubic lattice (Hugo Duminil-Copin) Extrema of the two-dimensional discrete Gaussian free field (Marek Biskup) Each of these contributions provides a thorough introduction that will be of value to beginners and experts alike.

Probabilistic Graphical Models

Author : Daphne Koller
Publisher : MIT Press
ISBN 13 : 0262258358
Total Pages : 1270 pages
Book Rating : 4.2/5 (622 download)

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Book Synopsis Probabilistic Graphical Models by : Daphne Koller

Download or read book Probabilistic Graphical Models written by Daphne Koller and published by MIT Press. This book was released on 2009-07-31 with total page 1270 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general framework for constructing and using probabilistic models of complex systems that would enable a computer to use available information for making decisions. Most tasks require a person or an automated system to reason—to reach conclusions based on available information. The framework of probabilistic graphical models, presented in this book, provides a general approach for this task. The approach is model-based, allowing interpretable models to be constructed and then manipulated by reasoning algorithms. These models can also be learned automatically from data, allowing the approach to be used in cases where manually constructing a model is difficult or even impossible. Because uncertainty is an inescapable aspect of most real-world applications, the book focuses on probabilistic models, which make the uncertainty explicit and provide models that are more faithful to reality. Probabilistic Graphical Models discusses a variety of models, spanning Bayesian networks, undirected Markov networks, discrete and continuous models, and extensions to deal with dynamical systems and relational data. For each class of models, the text describes the three fundamental cornerstones: representation, inference, and learning, presenting both basic concepts and advanced techniques. Finally, the book considers the use of the proposed framework for causal reasoning and decision making under uncertainty. The main text in each chapter provides the detailed technical development of the key ideas. Most chapters also include boxes with additional material: skill boxes, which describe techniques; case study boxes, which discuss empirical cases related to the approach described in the text, including applications in computer vision, robotics, natural language understanding, and computational biology; and concept boxes, which present significant concepts drawn from the material in the chapter. Instructors (and readers) can group chapters in various combinations, from core topics to more technically advanced material, to suit their particular needs.