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 Explorations in Monte Carlo Methods written by Ronald W. Shonkwiler and published by Springer Nature. This book was released on with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bayesian Learning for Neural Networks written by Radford M. Neal and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Artificial "neural networks" are widely used as flexible models for classification and regression applications, but questions remain about how the power of these models can be safely exploited when training data is limited. This book demonstrates how Bayesian methods allow complex neural network models to be used without fear of the "overfitting" that can occur with traditional training methods. Insight into the nature of these complex Bayesian models is provided by a theoretical investigation of the priors over functions that underlie them. A practical implementation of Bayesian neural network learning using Markov chain Monte Carlo methods is also described, and software for it is freely available over the Internet. Presupposing only basic knowledge of probability and statistics, this book should be of interest to researchers in statistics, engineering, and artificial intelligence.
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 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 2023-02-03 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 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.
Download or read book Exploring Monte Carlo Methods written by William L. Dunn and published by Elsevier. This book was released on 2022-06-07 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring Monte Carlo Methods, Second Edition provides a valuable introduction to the numerical methods that have come to be known as "Monte Carlo." This unique and trusted resource for course use, as well as researcher reference, offers accessible coverage, clear explanations and helpful examples throughout. Building from the basics, the text also includes applications in a variety of fields, such as physics, nuclear engineering, finance and investment, medical modeling and prediction, archaeology, geology and transportation planning. - Provides a comprehensive yet concise treatment of Monte Carlo methods - Uses the famous "Buffon's needle problem" as a unifying theme to illustrate the many aspects of Monte Carlo methods - Includes numerous exercises and useful appendices on: Certain mathematical functions, Bose Einstein functions, Fermi Dirac functions and Watson functions
Download or read book Database Systems for Advanced Applications written by Shamkant B. Navathe and published by Springer. This book was released on 2016-03-24 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two volume set LNCS 9642 and LNCS 9643 constitutes the refereed proceedings of the 21st International Conference on Database Systems for Advanced Applications, DASFAA 2016, held in Dallas, TX, USA, in April 2016. The 61 full papers presented were carefully reviewed and selected from a total of 183 submissions. The papers cover the following topics: crowdsourcing, data quality, entity identification, data mining and machine learning, recommendation, semantics computing and knowledge base, textual data, social networks, complex queries, similarity computing, graph databases, and miscellaneous, advanced applications.
Download or read book Pseudo Marginal Hamiltonian Monte Carlo with Efficient Importance Sampling written by Kjartan Kloster Osmundsen and published by . This book was released on 2019 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: The joint posterior of latent variables and parameters in Bayesian hierarchical models often has a strong nonlinear dependence structure, thus making it a challenging target for standard Markov-chain Monte-Carlo methods. Pseudo-marginal methods aim at effectively exploring such target distributions, by marginalizing the latent variables using Monte-Carlo integration and directly targeting the marginal posterior of the parameters. We follow this approach and propose a generic pseudo-marginal algorithm for efficiently simulating from the posterior of the parameters. It combines efficient importance sampling, for accurately marginalizing the latent variables, with the recently developed pseudo-marginal Hamiltonian Monte Carlo approach. We illustrate our algorithm in applications to dynamic state space models, where it shows a very high simulation efficiency even in challenging scenarios with complex dependence structures.
Download or read book Gradient Flows written by Luigi Ambrosio and published by Springer Science & Business Media. This book was released on 2008-10-29 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other.
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 Case Studies in Applied Bayesian Data Science written by Kerrie L. Mengersen and published by Springer Nature. This book was released on 2020-05-28 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting a range of substantive applied problems within Bayesian Statistics along with their Bayesian solutions, this book arises from a research program at CIRM in France in the second semester of 2018, which supported Kerrie Mengersen as a visiting Jean-Morlet Chair and Pierre Pudlo as the local Research Professor. The field of Bayesian statistics has exploded over the past thirty years and is now an established field of research in mathematical statistics and computer science, a key component of data science, and an underpinning methodology in many domains of science, business and social science. Moreover, while remaining naturally entwined, the three arms of Bayesian statistics, namely modelling, computation and inference, have grown into independent research fields. While the research arms of Bayesian statistics continue to grow in many directions, they are harnessed when attention turns to solving substantive applied problems. Each such problem set has its own challenges and hence draws from the suite of research a bespoke solution. The book will be useful for both theoretical and applied statisticians, as well as practitioners, to inspect these solutions in the context of the problems, in order to draw further understanding, awareness and inspiration.
Download or read book Introduction to Deep Learning A Beginner s Edition written by Harshitha Raghavan Devarajan and published by INENCE PUBLICATIONS PVT LTD. This book was released on 2024-08-10 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Introduction to Deep Learning: A Beginner’s Edition" is a comprehensive guide designed specifically for newcomers to the field of deep learning. This book provides an accessible introduction to the fundamental concepts, making it an ideal starting point for those who are curious about artificial intelligence and its rapidly expanding applications. The book begins with a clear explanation of what deep learning is and how it differs from traditional machine learning, covering the basics of neural networks and how they are used to recognize patterns and make decisions. One of the key strengths of this book is its practical, hands-on approach. Readers are guided through the process of building, training, and deploying neural networks using popular frameworks like TensorFlow and PyTorch. The step-by-step instructions, along with code snippets, allow even those with little to no programming experience to engage actively with the material. Visual aids, such as diagrams and flowcharts, are used throughout the book to simplify complex topics, making it easier for readers to grasp the inner workings of neural networks. The book also explores real-world applications of deep learning, highlighting its impact across various industries, including healthcare, autonomous vehicles, and natural language processing. By providing context and practical examples, the book demonstrates how deep learning is being used to solve complex problems and transform industries. In addition to the core content, the book includes a glossary of key terms, quizzes, and exercises to reinforce learning. "Introduction to Deep Learning: A Beginner’s Edition" is more than just a textbook; it is a complete learning experience designed to equip beginners with the knowledge and skills needed to embark on a successful journey into the world of deep learning.
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 Scalable Hamiltonian Monte Carlo Via Surrogate Methods written by Cheng Zhang and published by . This book was released on 2017 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: Markov chain Monte Carlo (MCMC) methods have been widely used in Bayesian inference involving intractable probabilistic models. However, simple MCMC algorithms (e.g., random walk Metropolis and Gibbs sampling) are notorious for their lack of computational efficiency in complex, high-dimensional models and poor scaling to large data sets. In recent years, many advanced MCMC methods (e.g., Hamiltonian Monte Carlo and Riemannian Manifold Hamiltonian Monte Carlo) have been proposed that utilize geometrical and statistical quantities from the model in order to explore the target distribution more effectively. The gain in the efficacy of exploration, however, often comes at a significant computational cost which hinders their application to problems with large data sets or complex likelihoods.In practice, it remains challenging to design scalable MCMC algorithms that can balance computational complexity and exploration efficacy well. To address this issue, some recent algorithms rely on stochastic gradient methods by approximating full data gradients using mini-batches of data. In contrast, this thesis focuses on accelerating the computation of MCMC samplers based on various surrogate methods via exploring the regularity of the target distribution.We start with a precomputing strategy that can be used to build efficient surrogates in relatively low-dimension parameter spaces. We then propose a random network surrogate architecture which can effectively capture the collective properties of large data sets or complex models with scalability, flexibility and efficiency. Finally, we provide a variational perspective for our random network surrogate methods and propose an approximate inference framework that combines the advantages of both variational Bayes and Markov chain Monte Carlo methods. The properties and efficiency of our proposed methods are demonstrated on a variety of synthetic and real-world data problems.
Download or read book Full Seismic Waveform Modelling and Inversion written by Andreas Fichtner and published by Springer Science & Business Media. This book was released on 2010-11-16 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent progress in numerical methods and computer science allows us today to simulate the propagation of seismic waves through realistically heterogeneous Earth models with unprecedented accuracy. Full waveform tomography is a tomographic technique that takes advantage of numerical solutions of the elastic wave equation. The accuracy of the numerical solutions and the exploitation of complete waveform information result in tomographic images that are both more realistic and better resolved. This book develops and describes state of the art methodologies covering all aspects of full waveform tomography including methods for the numerical solution of the elastic wave equation, the adjoint method, the design of objective functionals and optimisation schemes. It provides a variety of case studies on all scales from local to global based on a large number of examples involving real data. It is a comprehensive reference on full waveform tomography for advanced students, researchers and professionals.
