Algebraic Geometry And Statistical Learning Theory PDF Download
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| Author | : Sumio Watanabe |
| Publisher | : Cambridge University Press |
| Total Pages | : 295 |
| Release | : 2009-08-13 |
| Genre | : Computers |
| ISBN | : 0521864674 |
Download Algebraic Geometry and Statistical Learning Theory Book in PDF, ePub and Kindle
Sure to be influential, Watanabe's book lays the foundations for the use of algebraic geometry in statistical learning theory. Many models/machines are singular: mixture models, neural networks, HMMs, Bayesian networks, stochastic context-free grammars are major examples. The theory achieved here underpins accurate estimation techniques in the presence of singularities.
| Author | : L. Pachter |
| Publisher | : Cambridge University Press |
| Total Pages | : 440 |
| Release | : 2005-08-22 |
| Genre | : Mathematics |
| ISBN | : 9780521857000 |
Download Algebraic Statistics for Computational Biology Book in PDF, ePub and Kindle
This book, first published in 2005, offers an introduction to the application of algebraic statistics to computational biology.
| Author | : Sumio Watanabe |
| Publisher | : CRC Press |
| Total Pages | : 331 |
| Release | : 2018-04-27 |
| Genre | : Mathematics |
| ISBN | : 148223808X |
Download Mathematical Theory of Bayesian Statistics Book in PDF, ePub and Kindle
Mathematical Theory of Bayesian Statistics introduces the mathematical foundation of Bayesian inference which is well-known to be more accurate in many real-world problems than the maximum likelihood method. Recent research has uncovered several mathematical laws in Bayesian statistics, by which both the generalization loss and the marginal likelihood are estimated even if the posterior distribution cannot be approximated by any normal distribution. Features Explains Bayesian inference not subjectively but objectively. Provides a mathematical framework for conventional Bayesian theorems. Introduces and proves new theorems. Cross validation and information criteria of Bayesian statistics are studied from the mathematical point of view. Illustrates applications to several statistical problems, for example, model selection, hyperparameter optimization, and hypothesis tests. This book provides basic introductions for students, researchers, and users of Bayesian statistics, as well as applied mathematicians. Author Sumio Watanabe is a professor of Department of Mathematical and Computing Science at Tokyo Institute of Technology. He studies the relationship between algebraic geometry and mathematical statistics.
| Author | : M.K. Murray |
| Publisher | : Routledge |
| Total Pages | : 164 |
| Release | : 2017-10-19 |
| Genre | : Mathematics |
| ISBN | : 1351455117 |
Download Differential Geometry and Statistics Book in PDF, ePub and Kindle
Several years ago our statistical friends and relations introduced us to the work of Amari and Barndorff-Nielsen on applications of differential geometry to statistics. This book has arisen because we believe that there is a deep relationship between statistics and differential geometry and moreoever that this relationship uses parts of differential geometry, particularly its 'higher-order' aspects not readily accessible to a statistical audience from the existing literature. It is, in part, a long reply to the frequent requests we have had for references on differential geometry! While we have not gone beyond the path-breaking work of Amari and Barndorff- Nielsen in the realm of applications, our book gives some new explanations of their ideas from a first principles point of view as far as geometry is concerned. In particular it seeks to explain why geometry should enter into parametric statistics, and how the theory of asymptotic expansions involves a form of higher-order differential geometry. The first chapter of the book explores exponential families as flat geometries. Indeed the whole notion of using log-likelihoods amounts to exploiting a particular form of flat space known as an affine geometry, in which straight lines and planes make sense, but lengths and angles are absent. We use these geometric ideas to introduce the notion of the second fundamental form of a family whose vanishing characterises precisely the exponential families.
| Author | : Mathias Drton |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 177 |
| Release | : 2009-04-25 |
| Genre | : Mathematics |
| ISBN | : 3764389052 |
Download Lectures on Algebraic Statistics Book in PDF, ePub and Kindle
How does an algebraic geometer studying secant varieties further the understanding of hypothesis tests in statistics? Why would a statistician working on factor analysis raise open problems about determinantal varieties? Connections of this type are at the heart of the new field of "algebraic statistics". In this field, mathematicians and statisticians come together to solve statistical inference problems using concepts from algebraic geometry as well as related computational and combinatorial techniques. The goal of these lectures is to introduce newcomers from the different camps to algebraic statistics. The introduction will be centered around the following three observations: many important statistical models correspond to algebraic or semi-algebraic sets of parameters; the geometry of these parameter spaces determines the behaviour of widely used statistical inference procedures; computational algebraic geometry can be used to study parameter spaces and other features of statistical models.
| Author | : Sumio Watanabe |
| Publisher | : CRC Press |
| Total Pages | : 229 |
| Release | : 2018-04-27 |
| Genre | : Mathematics |
| ISBN | : 1315355698 |
Download Mathematical Theory of Bayesian Statistics Book in PDF, ePub and Kindle
Mathematical Theory of Bayesian Statistics introduces the mathematical foundation of Bayesian inference which is well-known to be more accurate in many real-world problems than the maximum likelihood method. Recent research has uncovered several mathematical laws in Bayesian statistics, by which both the generalization loss and the marginal likelihood are estimated even if the posterior distribution cannot be approximated by any normal distribution. Features Explains Bayesian inference not subjectively but objectively. Provides a mathematical framework for conventional Bayesian theorems. Introduces and proves new theorems. Cross validation and information criteria of Bayesian statistics are studied from the mathematical point of view. Illustrates applications to several statistical problems, for example, model selection, hyperparameter optimization, and hypothesis tests. This book provides basic introductions for students, researchers, and users of Bayesian statistics, as well as applied mathematicians. Author Sumio Watanabe is a professor of Department of Mathematical and Computing Science at Tokyo Institute of Technology. He studies the relationship between algebraic geometry and mathematical statistics.
| Author | : Shun-ichi Amari |
| Publisher | : Springer |
| Total Pages | : 378 |
| Release | : 2016-02-02 |
| Genre | : Mathematics |
| ISBN | : 4431559787 |
Download Information Geometry and Its Applications Book in PDF, ePub and Kindle
This is the first comprehensive book on information geometry, written by the founder of the field. It begins with an elementary introduction to dualistic geometry and proceeds to a wide range of applications, covering information science, engineering, and neuroscience. It consists of four parts, which on the whole can be read independently. A manifold with a divergence function is first introduced, leading directly to dualistic structure, the heart of information geometry. This part (Part I) can be apprehended without any knowledge of differential geometry. An intuitive explanation of modern differential geometry then follows in Part II, although the book is for the most part understandable without modern differential geometry. Information geometry of statistical inference, including time series analysis and semiparametric estimation (the Neyman–Scott problem), is demonstrated concisely in Part III. Applications addressed in Part IV include hot current topics in machine learning, signal processing, optimization, and neural networks. The book is interdisciplinary, connecting mathematics, information sciences, physics, and neurosciences, inviting readers to a new world of information and geometry. This book is highly recommended to graduate students and researchers who seek new mathematical methods and tools useful in their own fields.
| Author | : Frédéric Barbaresco |
| Publisher | : Springer Nature |
| Total Pages | : 466 |
| Release | : 2021-06-27 |
| Genre | : Mathematics |
| ISBN | : 3030779572 |
Download Geometric Structures of Statistical Physics, Information Geometry, and Learning Book in PDF, ePub and Kindle
Machine learning and artificial intelligence increasingly use methodological tools rooted in statistical physics. Conversely, limitations and pitfalls encountered in AI question the very foundations of statistical physics. This interplay between AI and statistical physics has been attested since the birth of AI, and principles underpinning statistical physics can shed new light on the conceptual basis of AI. During the last fifty years, statistical physics has been investigated through new geometric structures allowing covariant formalization of the thermodynamics. Inference methods in machine learning have begun to adapt these new geometric structures to process data in more abstract representation spaces. This volume collects selected contributions on the interplay of statistical physics and artificial intelligence. The aim is to provide a constructive dialogue around a common foundation to allow the establishment of new principles and laws governing these two disciplines in a unified manner. The contributions were presented at the workshop on the Joint Structures and Common Foundation of Statistical Physics, Information Geometry and Inference for Learning which was held in Les Houches in July 2020. The various theoretical approaches are discussed in the context of potential applications in cognitive systems, machine learning, signal processing.
| Author | : Olivier Catoni |
| Publisher | : Springer |
| Total Pages | : 278 |
| Release | : 2004-08-30 |
| Genre | : Mathematics |
| ISBN | : 3540445072 |
Download Statistical Learning Theory and Stochastic Optimization Book in PDF, ePub and Kindle
Statistical learning theory is aimed at analyzing complex data with necessarily approximate models. This book is intended for an audience with a graduate background in probability theory and statistics. It will be useful to any reader wondering why it may be a good idea, to use as is often done in practice a notoriously "wrong'' (i.e. over-simplified) model to predict, estimate or classify. This point of view takes its roots in three fields: information theory, statistical mechanics, and PAC-Bayesian theorems. Results on the large deviations of trajectories of Markov chains with rare transitions are also included. They are meant to provide a better understanding of stochastic optimization algorithms of common use in computing estimators. The author focuses on non-asymptotic bounds of the statistical risk, allowing one to choose adaptively between rich and structured families of models and corresponding estimators. Two mathematical objects pervade the book: entropy and Gibbs measures. The goal is to show how to turn them into versatile and efficient technical tools, that will stimulate further studies and results.
| Author | : Joe Suzuki |
| Publisher | : Springer Nature |
| Total Pages | : 241 |
| Release | : 2023-11-25 |
| Genre | : Computers |
| ISBN | : 9819938384 |
Download WAIC and WBIC with R Stan Book in PDF, ePub and Kindle
Master the art of machine learning and data science by diving into the essence of mathematical logic with this comprehensive textbook. This book focuses on the widely applicable information criterion (WAIC), also described as the Watanabe-Akaike information criterion, and the widely applicable Bayesian information criterion (WBIC), also described as the Watanabe Bayesian information criterion. This book expertly guides you through relevant mathematical problems while also providing hands-on experience with programming in R and Stan. Whether you’re a data scientist looking to refine your model selection process or a researcher who wants to explore the latest developments in Bayesian statistics, this accessible guide will give you a firm grasp of Watanabe Bayesian Theory. The key features of this indispensable book include: A clear and self-contained writing style, ensuring ease of understanding for readers at various levels of expertise. 100 carefully selected exercises accompanied by solutions in the main text, enabling readers to effectively gauge their progress and comprehension. A comprehensive guide to Sumio Watanabe’s groundbreaking Bayes theory, demystifying a subject once considered too challenging even for seasoned statisticians. Detailed source programs and Stan codes that will enhance readers’ grasp of the mathematical concepts presented. A streamlined approach to algebraic geometry topics in Chapter 6, making Bayes theory more accessible and less daunting. Embark on your machine learning and data science journey with this essential textbook and unlock the full potential of WAIC and WBIC today!
