Download or read book Monte Carlo Methods written by Adrian Barbu and published by Springer Nature. This book was released on 2020-02-24 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book seeks to bridge the gap between statistics and computer science. It provides an overview of Monte Carlo methods, including Sequential Monte Carlo, Markov Chain Monte Carlo, Metropolis-Hastings, Gibbs Sampler, Cluster Sampling, Data Driven MCMC, Stochastic Gradient descent, Langevin Monte Carlo, Hamiltonian Monte Carlo, and energy landscape mapping. Due to its comprehensive nature, the book is suitable for developing and teaching graduate courses on Monte Carlo methods. To facilitate learning, each chapter includes several representative application examples from various fields. The book pursues two main goals: (1) It introduces researchers to applying Monte Carlo methods to broader problems in areas such as Computer Vision, Computer Graphics, Machine Learning, Robotics, Artificial Intelligence, etc.; and (2) it makes it easier for scientists and engineers working in these areas to employ Monte Carlo methods to enhance their research.
Download or read book Hamiltonian Monte Carlo Methods in Machine Learning written by Tshilidzi Marwala and published by Elsevier. This book was released on 2023-03 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hamiltonian Monte Carlo Methods in Machine Learning introduces methods for optimal tuning of HMC parameters, along with an introduction of Shadow and Non-canonical HMC methods with improvements and speedup. Lastly, the authors address the critical issues of variance reduction for parameter estimates of numerous HMC based samplers. The book offers a comprehensive introduction to Hamiltonian Monte Carlo methods and provides a cutting-edge exposition of the current pathologies of HMC-based methods in both tuning, scaling and sampling complex real-world posteriors. These are mainly in the scaling of inference (e.g., Deep Neural Networks), tuning of performance-sensitive sampling parameters and high sample autocorrelation. Other sections provide numerous solutions to potential pitfalls, presenting advanced HMC methods with applications in renewable energy, finance and image classification for biomedical applications. Readers will get acquainted with both HMC sampling theory and algorithm implementation.
Download or read book Hamiltonian Monte Carlo Methods in Machine Learning written by Tshilidzi Marwala and published by Elsevier. This book was released on 2023-02-03 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hamiltonian Monte Carlo Methods in Machine Learning introduces methods for optimal tuning of HMC parameters, along with an introduction of Shadow and Non-canonical HMC methods with improvements and speedup. Lastly, the authors address the critical issues of variance reduction for parameter estimates of numerous HMC based samplers. The book offers a comprehensive introduction to Hamiltonian Monte Carlo methods and provides a cutting-edge exposition of the current pathologies of HMC-based methods in both tuning, scaling and sampling complex real-world posteriors. These are mainly in the scaling of inference (e.g., Deep Neural Networks), tuning of performance-sensitive sampling parameters and high sample autocorrelation. Other sections provide numerous solutions to potential pitfalls, presenting advanced HMC methods with applications in renewable energy, finance and image classification for biomedical applications. Readers will get acquainted with both HMC sampling theory and algorithm implementation. Provides in-depth analysis for conducting optimal tuning of Hamiltonian Monte Carlo (HMC) parameters Presents readers with an introduction and improvements on Shadow HMC methods as well as non-canonical HMC methods Demonstrates how to perform variance reduction for numerous HMC-based samplers Includes source code from applications and algorithms
Download or read book Monte Carlo Methods written by Adrian G. Barbu and published by . This book was released on 2020 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book seeks to bridge the gap between statistics and computer science. It provides an overview of Monte Carlo methods, including Sequential Monte Carlo, Markov Chain Monte Carlo, Metropolis-Hastings, Gibbs Sampler, Cluster Sampling, Data Driven MCMC, Stochastic Gradient descent, Langevin Monte Carlo, Hamiltonian Monte Carlo, and energy landscape mapping. Due to its comprehensive nature, the book is suitable for developing and teaching graduate courses on Monte Carlo methods. To facilitate learning, each chapter includes several representative application examples from various fields. The book pursues two main goals: (1) It introduces researchers to applying Monte Carlo methods to broader problems in areas such as Computer Vision, Computer Graphics, Machine Learning, Robotics, Artificial Intelligence, etc.; and (2) it makes it easier for scientists and engineers working in these areas to employ Monte Carlo methods to enhance their research.--
Download or read book Machine learning using approximate inference written by Christian Andersson Naesseth and published by Linköping University Electronic Press. This book was released on 2018-11-27 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: Automatic decision making and pattern recognition under uncertainty are difficult tasks that are ubiquitous in our everyday life. The systems we design, and technology we develop, requires us to coherently represent and work with uncertainty in data. Probabilistic models and probabilistic inference gives us a powerful framework for solving this problem. Using this framework, while enticing, results in difficult-to-compute integrals and probabilities when conditioning on the observed data. This means we have a need for approximate inference, methods that solves the problem approximately using a systematic approach. In this thesis we develop new methods for efficient approximate inference in probabilistic models. There are generally two approaches to approximate inference, variational methods and Monte Carlo methods. In Monte Carlo methods we use a large number of random samples to approximate the integral of interest. With variational methods, on the other hand, we turn the integration problem into that of an optimization problem. We develop algorithms of both types and bridge the gap between them. First, we present a self-contained tutorial to the popular sequential Monte Carlo (SMC) class of methods. Next, we propose new algorithms and applications based on SMC for approximate inference in probabilistic graphical models. We derive nested sequential Monte Carlo, a new algorithm particularly well suited for inference in a large class of high-dimensional probabilistic models. Then, inspired by similar ideas we derive interacting particle Markov chain Monte Carlo to make use of parallelization to speed up approximate inference for universal probabilistic programming languages. After that, we show how we can make use of the rejection sampling process when generating gamma distributed random variables to speed up variational inference. Finally, we bridge the gap between SMC and variational methods by developing variational sequential Monte Carlo, a new flexible family of variational approximations.
Download or read book Markov Chain Monte Carlo Methods for Machine Learning written by Nando De Freitas and published by . This book was released on 2003 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Markov Chain Monte Carlo written by Steve Brooks and published by CRC Press. This book was released on 2011-05-10 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their popularization in the 1990s, Markov chain Monte Carlo (MCMC) methods have revolutionized statistical computing and have had an especially profound impact on the practice of Bayesian statistics. Furthermore, MCMC methods have enabled the development and use of intricate models in an astonishing array of disciplines as diverse as fisherie
Download or read book MCMC from Scratch written by Masanori Hanada and published by Springer Nature. This book was released on 2022-10-20 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook explains the fundamentals of Markov Chain Monte Carlo (MCMC) without assuming advanced knowledge of mathematics and programming. MCMC is a powerful technique that can be used to integrate complicated functions or to handle complicated probability distributions. MCMC is frequently used in diverse fields where statistical methods are important – e.g. Bayesian statistics, quantum physics, machine learning, computer science, computational biology, and mathematical economics. This book aims to equip readers with a sound understanding of MCMC and enable them to write simulation codes by themselves. The content consists of six chapters. Following Chap. 2, which introduces readers to the Monte Carlo algorithm and highlights the advantages of MCMC, Chap. 3 presents the general aspects of MCMC. Chap. 4 illustrates the essence of MCMC through the simple example of the Metropolis algorithm. In turn, Chap. 5 explains the HMC algorithm, Gibbs sampling algorithm and Metropolis-Hastings algorithm, discussing their pros, cons and pitfalls. Lastly, Chap. 6 presents several applications of MCMC. Including a wealth of examples and exercises with solutions, as well as sample codes and further math topics in the Appendix, this book offers a valuable asset for students and beginners in various fields.
Download or read book Special Issue Markov Chain Monte Carlo Methods for Machine Learning written by Nando de Freitas and published by . This book was released on 2003 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Markov Chain Monte Carlo Methods in Quantum Field Theories written by Anosh Joseph and published by Springer Nature. This book was released on 2020-04-16 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This primer is a comprehensive collection of analytical and numerical techniques that can be used to extract the non-perturbative physics of quantum field theories. The intriguing connection between Euclidean Quantum Field Theories (QFTs) and statistical mechanics can be used to apply Markov Chain Monte Carlo (MCMC) methods to investigate strongly coupled QFTs. The overwhelming amount of reliable results coming from the field of lattice quantum chromodynamics stands out as an excellent example of MCMC methods in QFTs in action. MCMC methods have revealed the non-perturbative phase structures, symmetry breaking, and bound states of particles in QFTs. The applications also resulted in new outcomes due to cross-fertilization with research areas such as AdS/CFT correspondence in string theory and condensed matter physics. The book is aimed at advanced undergraduate students and graduate students in physics and applied mathematics, and researchers in MCMC simulations and QFTs. At the end of this book the reader will be able to apply the techniques learned to produce more independent and novel research in the field.
Download or read book Sequential Monte Carlo Methods in Practice written by Arnaud Doucet and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo methods are revolutionizing the on-line analysis of data in many fileds. They have made it possible to solve numerically many complex, non-standard problems that were previously intractable. This book presents the first comprehensive treatment of these techniques.
Download or read book Riemannian Geometric Statistics in Medical Image Analysis written by Xavier Pennec and published by Academic Press. This book was released on 2019-09-02 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past 15 years, there has been a growing need in the medical image computing community for principled methods to process nonlinear geometric data. Riemannian geometry has emerged as one of the most powerful mathematical and computational frameworks for analyzing such data. Riemannian Geometric Statistics in Medical Image Analysis is a complete reference on statistics on Riemannian manifolds and more general nonlinear spaces with applications in medical image analysis. It provides an introduction to the core methodology followed by a presentation of state-of-the-art methods. Beyond medical image computing, the methods described in this book may also apply to other domains such as signal processing, computer vision, geometric deep learning, and other domains where statistics on geometric features appear. As such, the presented core methodology takes its place in the field of geometric statistics, the statistical analysis of data being elements of nonlinear geometric spaces. The foundational material and the advanced techniques presented in the later parts of the book can be useful in domains outside medical imaging and present important applications of geometric statistics methodology Content includes: The foundations of Riemannian geometric methods for statistics on manifolds with emphasis on concepts rather than on proofs Applications of statistics on manifolds and shape spaces in medical image computing Diffeomorphic deformations and their applications As the methods described apply to domains such as signal processing (radar signal processing and brain computer interaction), computer vision (object and face recognition), and other domains where statistics of geometric features appear, this book is suitable for researchers and graduate students in medical imaging, engineering and computer science. A complete reference covering both the foundations and state-of-the-art methods Edited and authored by leading researchers in the field Contains theory, examples, applications, and algorithms Gives an overview of current research challenges and future applications
Download or read book Exploring Dynamic Hamiltonian Monte Carlo for Bayesian Neural Networks written by Yiu Sing Lau and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "Neural network models have seen tremendous success in predictive tasks in machine learning and artificial intelligence, with some attributing their success to implicit use of Bayesian inference. Stan is a state-of-the-art software for Bayesian statistical computing used mainly in the statistical community, however, it is not optimized for use with neural network models. In this thesis, we replicated much of Stan's No U-Turn sampler in PyTorch and explored its use for sampling from Bayesian neural network models. We were able to explore different samplers, model structures and their sampling and predictive performances on a benchmark classification task. We found that Bayesian inference gives more robust predictive performance compared to their frequentist counterparts in general, but care is needed with the choice of prior and the MCMC sampler. " --
Download or read book Differential Equations Dynamical Systems and Linear Algebra written by Morris W. Hirsch and published by Academic Press. This book was released on 1974-06-28 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. A prominent role is played by the structure theory of linear operators on finite-dimensional vector spaces; the authors have included a self-contained treatment of that subject.
Download or read book Simulating Hamiltonian Dynamics written by Benedict Leimkuhler and published by Cambridge University Press. This book was released on 2004 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric integrators are time-stepping methods, designed such that they exactly satisfy conservation laws, symmetries or symplectic properties of a system of differential equations. In this book the authors outline the principles of geometric integration and demonstrate how they can be applied to provide efficient numerical methods for simulating conservative models. Beginning from basic principles and continuing with discussions regarding the advantageous properties of such schemes, the book introduces methods for the N-body problem, systems with holonomic constraints, and rigid bodies. More advanced topics treated include high-order and variable stepsize methods, schemes for treating problems involving multiple time-scales, and applications to molecular dynamics and partial differential equations. The emphasis is on providing a unified theoretical framework as well as a practical guide for users. The inclusion of examples, background material and exercises enhance the usefulness of the book for self-instruction or as a text for a graduate course on the subject.
Download or read book Machine Learning and Knowledge Discovery in Databases written by Paolo Frasconi and published by Springer. This book was released on 2016-09-03 with total page 850 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three volume set LNAI 9851, LNAI 9852, and LNAI 9853 constitutes the refereed proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases, ECML PKDD 2016, held in Riva del Garda, Italy, in September 2016. The 123 full papers and 16 short papers presented were carefully reviewed and selected from a total of 460 submissions. The papers presented focus on practical and real-world studies of machine learning, knowledge discovery, data mining; innovative prototype implementations or mature systems that use machine learning techniques and knowledge discovery processes in a real setting; recent advances at the frontier of machine learning and data mining with other disciplines. Part I and Part II of the proceedings contain the full papers of the contributions presented in the scientific track and abstracts of the scientific plenary talks. Part III contains the full papers of the contributions presented in the industrial track, short papers describing demonstration, the nectar papers, and the abstracts of the industrial plenary talks.
Download or read book Monte Carlo Strategies in Scientific Computing written by Jun S. Liu and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained and up-to-date treatment of the Monte Carlo method and develops a common framework under which various Monte Carlo techniques can be "standardized" and compared. Given the interdisciplinary nature of the topics and a moderate prerequisite for the reader, this book should be of interest to a broad audience of quantitative researchers such as computational biologists, computer scientists, econometricians, engineers, probabilists, and statisticians. It can also be used as a textbook for a graduate-level course on Monte Carlo methods.
