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Algebraic and Geometric Methods in Statistics

2010 Mathematics
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Release : 2010
Genre : Mathematics
Kind : eBook
Book Rating : 193/5 ( reviews)

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Book Synopsis Algebraic and Geometric Methods in Statistics by : Paolo Gibilisco

Download or read book Algebraic and Geometric Methods in Statistics written by Paolo Gibilisco. This book was released on 2010. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date account of algebraic statistics and information geometry, which also explores the emerging connections between these two disciplines.

Polyhedral and Algebraic Methods in Computational Geometry

2013-01-04 Mathematics
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Release : 2013-01-04
Genre : Mathematics
Kind : eBook
Book Rating : 177/5 ( reviews)

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Book Synopsis Polyhedral and Algebraic Methods in Computational Geometry by : Michael Joswig

Download or read book Polyhedral and Algebraic Methods in Computational Geometry written by Michael Joswig. This book was released on 2013-01-04. Available in PDF, EPUB and Kindle. Book excerpt: Polyhedral and Algebraic Methods in Computational Geometry provides a thorough introduction into algorithmic geometry and its applications. It presents its primary topics from the viewpoints of discrete, convex and elementary algebraic geometry. The first part of the book studies classical problems and techniques that refer to polyhedral structures. The authors include a study on algorithms for computing convex hulls as well as the construction of Voronoi diagrams and Delone triangulations. The second part of the book develops the primary concepts of (non-linear) computational algebraic geometry. Here, the book looks at Gröbner bases and solving systems of polynomial equations. The theory is illustrated by applications in computer graphics, curve reconstruction and robotics. Throughout the book, interconnections between computational geometry and other disciplines (such as algebraic geometry, optimization and numerical mathematics) are established. Polyhedral and Algebraic Methods in Computational Geometry is directed towards advanced undergraduates in mathematics and computer science, as well as towards engineering students who are interested in the applications of computational geometry.

Algebraic Geometry and Statistical Learning Theory

2009-08-13 Computers
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Release : 2009-08-13
Genre : Computers
Kind : eBook
Book Rating : 674/5 ( reviews)

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Book Synopsis Algebraic Geometry and Statistical Learning Theory by : Sumio Watanabe

Download or read book Algebraic Geometry and Statistical Learning Theory written by Sumio Watanabe. This book was released on 2009-08-13. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to Algebraic Statistics with Tensors

2019-09-11 Mathematics
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Release : 2019-09-11
Genre : Mathematics
Kind : eBook
Book Rating : 248/5 ( reviews)

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Book Synopsis An Introduction to Algebraic Statistics with Tensors by : Cristiano Bocci

Download or read book An Introduction to Algebraic Statistics with Tensors written by Cristiano Bocci. This book was released on 2019-09-11. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to various aspects of Algebraic Statistics with the principal aim of supporting Master’s and PhD students who wish to explore the algebraic point of view regarding recent developments in Statistics. The focus is on the background needed to explore the connections among discrete random variables. The main objects that encode these relations are multilinear matrices, i.e., tensors. The book aims to settle the basis of the correspondence between properties of tensors and their translation in Algebraic Geometry. It is divided into three parts, on Algebraic Statistics, Multilinear Algebra, and Algebraic Geometry. The primary purpose is to describe a bridge between the three theories, so that results and problems in one theory find a natural translation to the others. This task requires, from the statistical point of view, a rather unusual, but algebraically natural, presentation of random variables and their main classical features. The third part of the book can be considered as a short, almost self-contained, introduction to the basic concepts of algebraic varieties, which are part of the fundamental background for all who work in Algebraic Statistics.

Algebraic and Geometric Methods in Discrete Mathematics

2017-03-16 Mathematics
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Release : 2017-03-16
Genre : Mathematics
Kind : eBook
Book Rating : 219/5 ( reviews)

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Book Synopsis Algebraic and Geometric Methods in Discrete Mathematics by : Heather A. Harrington

Download or read book Algebraic and Geometric Methods in Discrete Mathematics written by Heather A. Harrington. This book was released on 2017-03-16. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Algebraic and Geometric Methods in Applied Discrete Mathematics, held on January 11, 2015, in San Antonio, Texas. The papers present connections between techniques from “pure” mathematics and various applications amenable to the analysis of discrete models, encompassing applications of combinatorics, topology, algebra, geometry, optimization, and representation theory. Papers not only present novel results, but also survey the current state of knowledge of important topics in applied discrete mathematics. Particular highlights include: a new computational framework, based on geometric combinatorics, for structure prediction from RNA sequences; a new method for approximating the optimal solution of a sum of squares problem; a survey of recent Helly-type geometric theorems; applications of representation theory to voting theory and game theory; a study of fixed points of tensors; and exponential random graph models from the perspective of algebraic statistics with applications to networks. This volume was written for those trained in areas such as algebra, topology, geometry, and combinatorics who are interested in tackling problems in fields such as biology, the social sciences, data analysis, and optimization. It may be useful not only for experts, but also for students who wish to gain an applied or interdisciplinary perspective.

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