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 | : 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 | : 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 | : Masashi Sugiyama |
Publisher | : Morgan Kaufmann |
Total Pages | : 535 |
Release | : 2015-10-31 |
Genre | : Mathematics |
ISBN | : 0128023503 |
Download Introduction to Statistical Machine Learning Book in PDF, ePub and Kindle
Machine learning allows computers to learn and discern patterns without actually being programmed. When Statistical techniques and machine learning are combined together they are a powerful tool for analysing various kinds of data in many computer science/engineering areas including, image processing, speech processing, natural language processing, robot control, as well as in fundamental sciences such as biology, medicine, astronomy, physics, and materials. Introduction to Statistical Machine Learning provides a general introduction to machine learning that covers a wide range of topics concisely and will help you bridge the gap between theory and practice. Part I discusses the fundamental concepts of statistics and probability that are used in describing machine learning algorithms. Part II and Part III explain the two major approaches of machine learning techniques; generative methods and discriminative methods. While Part III provides an in-depth look at advanced topics that play essential roles in making machine learning algorithms more useful in practice. The accompanying MATLAB/Octave programs provide you with the necessary practical skills needed to accomplish a wide range of data analysis tasks. Provides the necessary background material to understand machine learning such as statistics, probability, linear algebra, and calculus Complete coverage of the generative approach to statistical pattern recognition and the discriminative approach to statistical machine learning Includes MATLAB/Octave programs so that readers can test the algorithms numerically and acquire both mathematical and practical skills in a wide range of data analysis tasks Discusses a wide range of applications in machine learning and statistics and provides examples drawn from image processing, speech processing, natural language processing, robot control, as well as biology, medicine, astronomy, physics, and materials
Author | : M.K. Murray |
Publisher | : Routledge |
Total Pages | : 292 |
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 | : 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 | : Serge Lang |
Publisher | : Springer Science & Business Media |
Total Pages | : 591 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461208971 |
Download Real and Functional Analysis Book in PDF, ePub and Kindle
This book is meant as a text for a first-year graduate course in analysis. In a sense, it covers the same topics as elementary calculus but treats them in a manner suitable for people who will be using it in further mathematical investigations. The organization avoids long chains of logical interdependence, so that chapters are mostly independent. This allows a course to omit material from some chapters without compromising the exposition of material from later chapters.
Author | : Michel Talagrand |
Publisher | : Springer Science & Business Media |
Total Pages | : 227 |
Release | : 2005-12-08 |
Genre | : Mathematics |
ISBN | : 3540274995 |
Download The Generic Chaining Book in PDF, ePub and Kindle
The fundamental question of characterizing continuity and boundedness of Gaussian processes goes back to Kolmogorov. After contributions by R. Dudley and X. Fernique, it was solved by the author. This book provides an overview of "generic chaining", a completely natural variation on the ideas of Kolmogorov. It takes the reader from the first principles to the edge of current knowledge and to the open problems that remain in this domain.