Advanced Mean Field Methods PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Advanced Mean Field Methods PDF full book. Access full book title Advanced Mean Field Methods by Manfred Opper. Download full books in PDF and EPUB format.
Author: Manfred Opper
Publisher: MIT Press
ISBN: 9780262150545
Category : Computers
Languages : en
Pages : 300
Get Book Here
Book Description
This book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling. A major problem in modern probabilistic modeling is the huge computational complexity involved in typical calculations with multivariate probability distributions when the number of random variables is large. Because exact computations are infeasible in such cases and Monte Carlo sampling techniques may reach their limits, there is a need for methods that allow for efficient approximate computations. One of the simplest approximations is based on the mean field method, which has a long history in statistical physics. The method is widely used, particularly in the growing field of graphical models. Researchers from disciplines such as statistical physics, computer science, and mathematical statistics are studying ways to improve this and related methods and are exploring novel application areas. Leading approaches include the variational approach, which goes beyond factorizable distributions to achieve systematic improvements; the TAP (Thouless-Anderson-Palmer) approach, which incorporates correlations by including effective reaction terms in the mean field theory; and the more general methods of graphical models. Bringing together ideas and techniques from these diverse disciplines, this book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling.
Author: Manfred Opper
Publisher: MIT Press
ISBN: 9780262150545
Category : Computers
Languages : en
Pages : 300
Get Book Here
Book Description
This book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling. A major problem in modern probabilistic modeling is the huge computational complexity involved in typical calculations with multivariate probability distributions when the number of random variables is large. Because exact computations are infeasible in such cases and Monte Carlo sampling techniques may reach their limits, there is a need for methods that allow for efficient approximate computations. One of the simplest approximations is based on the mean field method, which has a long history in statistical physics. The method is widely used, particularly in the growing field of graphical models. Researchers from disciplines such as statistical physics, computer science, and mathematical statistics are studying ways to improve this and related methods and are exploring novel application areas. Leading approaches include the variational approach, which goes beyond factorizable distributions to achieve systematic improvements; the TAP (Thouless-Anderson-Palmer) approach, which incorporates correlations by including effective reaction terms in the mean field theory; and the more general methods of graphical models. Bringing together ideas and techniques from these diverse disciplines, this book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling.
Author: Nikolas Provatas
Publisher: John Wiley & Sons
ISBN: 3527632379
Category : Computers
Languages : en
Pages : 323
Get Book Here
Book Description
This comprehensive and self-contained, one-stop source discusses phase-field methodology in a fundamental way, explaining advanced numerical techniques for solving phase-field and related continuum-field models. It also presents numerical techniques used to simulate various phenomena in a detailed, step-by-step way, such that readers can carry out their own code developments. Features many examples of how the methods explained can be used in materials science and engineering applications.
Author: Vladimir M Kolomietz
Publisher: World Scientific
ISBN: 9811211795
Category : Science
Languages : en
Pages : 586
Get Book Here
Book Description
This book describes recent theoretical and experimental developments in the study of static and dynamic properties of atomic nuclei, many-body systems of strongly interacting neutrons and protons. The theoretical approach is based on the concept of the mean field, describing the motion of a nucleon in terms of a self-consistent single-particle potential well which approximates the interactions of a nucleon with all the other nucleons. The theoretical approaches also go beyond the mean-field approximation by including the effects of two-body collisions.The self-consistent mean-field approximation is derived using the effective nucleon-nucleon Skyrme-type interaction. The many-body problem is described next in terms of the Wigner phase space of the one-body density, which provides a basis for semi-classical approximations and leads to kinetic equations. Results of static properties of nuclei and properties associated with small amplitude dynamics are also presented. Relaxation processes, due to nucleon-nucleon collisions, are discussed next, followed by instability and large amplitude motion of excited nuclei. Lastly, the book ends with the dynamics of hot nuclei. The concepts and methods developed in this book can be used for describing properties of other many-body systems.
Author: Naoki Katoh
Publisher: Springer Nature
ISBN: 9811640955
Category : Computers
Languages : en
Pages : 403
Get Book Here
Book Description
This open access book gives an overview of cutting-edge work on a new paradigm called the “sublinear computation paradigm,” which was proposed in the large multiyear academic research project “Foundations of Innovative Algorithms for Big Data.” That project ran from October 2014 to March 2020, in Japan. To handle the unprecedented explosion of big data sets in research, industry, and other areas of society, there is an urgent need to develop novel methods and approaches for big data analysis. To meet this need, innovative changes in algorithm theory for big data are being pursued. For example, polynomial-time algorithms have thus far been regarded as “fast,” but if a quadratic-time algorithm is applied to a petabyte-scale or larger big data set, problems are encountered in terms of computational resources or running time. To deal with this critical computational and algorithmic bottleneck, linear, sublinear, and constant time algorithms are required. The sublinear computation paradigm is proposed here in order to support innovation in the big data era. A foundation of innovative algorithms has been created by developing computational procedures, data structures, and modelling techniques for big data. The project is organized into three teams that focus on sublinear algorithms, sublinear data structures, and sublinear modelling. The work has provided high-level academic research results of strong computational and algorithmic interest, which are presented in this book. The book consists of five parts: Part I, which consists of a single chapter on the concept of the sublinear computation paradigm; Parts II, III, and IV review results on sublinear algorithms, sublinear data structures, and sublinear modelling, respectively; Part V presents application results. The information presented here will inspire the researchers who work in the field of modern algorithms.
Author: Václav Šmídl
Publisher: Springer Science & Business Media
ISBN: 3540288201
Category : Technology & Engineering
Languages : en
Pages : 241
Get Book Here
Book Description
Treating VB approximation in signal processing, this monograph is for academic and industrial research groups in signal processing, data analysis, machine learning and identification. It reviews distributional approximation, showing that tractable algorithms for parametric model identification can be generated in off-line and on-line contexts.
Author: Daniel Barbara
Publisher: SIAM
ISBN: 9780898715453
Category : Mathematics
Languages : en
Pages : 368
Get Book Here
Book Description
The third SIAM International Conference on Data Mining provided an open forum for the presentation, discussion and development of innovative algorithms, software and theories for data mining applications and data intensive computation. This volume includes 21 research papers.
Author: Ashok N. Srivastava
Publisher: CRC Press
ISBN: 1420059459
Category : Business & Economics
Languages : en
Pages : 330
Get Book Here
Book Description
The Definitive Resource on Text Mining Theory and Applications from Foremost Researchers in the FieldGiving a broad perspective of the field from numerous vantage points, Text Mining: Classification, Clustering, and Applications focuses on statistical methods for text mining and analysis. It examines methods to automatically cluster and classify te
Author: Pierre Del Moral
Publisher: CRC Press
ISBN: 1466504056
Category : Mathematics
Languages : en
Pages : 628
Get Book Here
Book Description
In the last three decades, there has been a dramatic increase in the use of interacting particle methods as a powerful tool in real-world applications of Monte Carlo simulation in computational physics, population biology, computer sciences, and statistical machine learning. Ideally suited to parallel and distributed computation, these advanced particle algorithms include nonlinear interacting jump diffusions; quantum, diffusion, and resampled Monte Carlo methods; Feynman-Kac particle models; genetic and evolutionary algorithms; sequential Monte Carlo methods; adaptive and interacting Markov chain Monte Carlo models; bootstrapping methods; ensemble Kalman filters; and interacting particle filters. Mean Field Simulation for Monte Carlo Integration presents the first comprehensive and modern mathematical treatment of mean field particle simulation models and interdisciplinary research topics, including interacting jumps and McKean-Vlasov processes, sequential Monte Carlo methodologies, genetic particle algorithms, genealogical tree-based algorithms, and quantum and diffusion Monte Carlo methods. Along with covering refined convergence analysis on nonlinear Markov chain models, the author discusses applications related to parameter estimation in hidden Markov chain models, stochastic optimization, nonlinear filtering and multiple target tracking, stochastic optimization, calibration and uncertainty propagations in numerical codes, rare event simulation, financial mathematics, and free energy and quasi-invariant measures arising in computational physics and population biology. This book shows how mean field particle simulation has revolutionized the field of Monte Carlo integration and stochastic algorithms. It will help theoretical probability researchers, applied statisticians, biologists, statistical physicists, and computer scientists work better across their own disciplinary boundaries.
Author: Rajesh P.N. Rao
Publisher: MIT Press
ISBN: 9780262264327
Category : Medical
Languages : en
Pages : 348
Get Book Here
Book Description
A survey of probabilistic approaches to modeling and understanding brain function. Neurophysiological, neuroanatomical, and brain imaging studies have helped to shed light on how the brain transforms raw sensory information into a form that is useful for goal-directed behavior. A fundamental question that is seldom addressed by these studies, however, is why the brain uses the types of representations it does and what evolutionary advantage, if any, these representations confer. It is difficult to address such questions directly via animal experiments. A promising alternative is to use probabilistic principles such as maximum likelihood and Bayesian inference to derive models of brain function. This book surveys some of the current probabilistic approaches to modeling and understanding brain function. Although most of the examples focus on vision, many of the models and techniques are applicable to other modalities as well. The book presents top-down computational models as well as bottom-up neurally motivated models of brain function. The topics covered include Bayesian and information-theoretic models of perception, probabilistic theories of neural coding and spike timing, computational models of lateral and cortico-cortical feedback connections, and the development of receptive field properties from natural signals.
Author: Mario Figueiredo
Publisher: Springer Science & Business Media
ISBN: 3540425233
Category : Computers
Languages : en
Pages : 654
Get Book Here
Book Description
This book constitutes the refereed proceedings of the Third International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition, EMMCVPR 2001, held in Sophia Antipolis, France in September 2001. The 42 revised full papers presented were carefully reviewed and selected from 70 submissions. The book offers topical sections on probabilistic models and estimation; image modeling and synthesis; clustering, grouping, and segmentation; optimization and graphs; and shapes, curves, surfaces, and templates.
