An Introduction To Algebraic Statistics With Tensors

Author : Cristiano Bocci,Luca Chiantini
Publisher : Springer Nature
Page : 235 pages
File Size : 43,5 Mb
Release : 2019-09-11
Category : Mathematics
ISBN : 9783030246242

Get Book

An Introduction to Algebraic Statistics with Tensors by Cristiano Bocci,Luca Chiantini Pdf

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.

Author : Seth Sullivant
Publisher : American Mathematical Society
Page : 506 pages
File Size : 44,9 Mb
Release : 2023-11-17
Category : Mathematics
ISBN : 9781470475109

Get Book

Algebraic Statistics by Seth Sullivant Pdf

Algebraic statistics uses tools from algebraic geometry, commutative algebra, combinatorics, and their computational sides to address problems in statistics and its applications. The starting point for this connection is the observation that many statistical models are semialgebraic sets. The algebra/statistics connection is now over twenty years old, and this book presents the first broad introductory treatment of the subject. Along with background material in probability, algebra, and statistics, this book covers a range of topics in algebraic statistics including algebraic exponential families, likelihood inference, Fisher's exact test, bounds on entries of contingency tables, design of experiments, identifiability of hidden variable models, phylogenetic models, and model selection. With numerous examples, references, and over 150 exercises, this book is suitable for both classroom use and independent study.

Author : Giovanni Pistone,Eva Riccomagno,Henry P. Wynn
Publisher : CRC Press
Page : 180 pages
File Size : 51,8 Mb
Release : 2000-12-21
Category : Mathematics
ISBN : 9781420035766

Get Book

Algebraic Statistics by Giovanni Pistone,Eva Riccomagno,Henry P. Wynn Pdf

Written by pioneers in this exciting new field, Algebraic Statistics introduces the application of polynomial algebra to experimental design, discrete probability, and statistics. It begins with an introduction to Grobner bases and a thorough description of their applications to experimental design. A special chapter covers the binary case

Author : J. M. Landsberg
Publisher : American Mathematical Soc.
Page : 464 pages
File Size : 52,6 Mb
Release : 2011-12-14
Category : Mathematics
ISBN : 9780821869079

Get Book

Tensors: Geometry and Applications by J. M. Landsberg Pdf

Tensors are ubiquitous in the sciences. The geometry of tensors is both a powerful tool for extracting information from data sets, and a beautiful subject in its own right. This book has three intended uses: a classroom textbook, a reference work for researchers in the sciences, and an account of classical and modern results in (aspects of) the theory that will be of interest to researchers in geometry. For classroom use, there is a modern introduction to multilinear algebra and to the geometry and representation theory needed to study tensors, including a large number of exercises. For researchers in the sciences, there is information on tensors in table format for easy reference and a summary of the state of the art in elementary language. This is the first book containing many classical results regarding tensors. Particular applications treated in the book include the complexity of matrix multiplication, P versus NP, signal processing, phylogenetics, and algebraic statistics. For geometers, there is material on secant varieties, G-varieties, spaces with finitely many orbits and how these objects arise in applications, discussions of numerous open questions in geometry arising in applications, and expositions of advanced topics such as the proof of the Alexander-Hirschowitz theorem and of the Weyman-Kempf method for computing syzygies.

Author : Toshio Sakata,Toshio Sumi,Mitsuhiro Miyazaki
Publisher : Springer
Page : 108 pages
File Size : 52,5 Mb
Release : 2016-03-18
Category : Mathematics
ISBN : 9784431554592

Get Book

Algebraic and Computational Aspects of Real Tensor Ranks by Toshio Sakata,Toshio Sumi,Mitsuhiro Miyazaki Pdf

This book provides comprehensive summaries of theoretical (algebraic) and computational aspects of tensor ranks, maximal ranks, and typical ranks, over the real number field. Although tensor ranks have been often argued in the complex number field, it should be emphasized that this book treats real tensor ranks, which have direct applications in statistics. The book provides several interesting ideas, including determinant polynomials, determinantal ideals, absolutely nonsingular tensors, absolutely full column rank tensors, and their connection to bilinear maps and Hurwitz-Radon numbers. In addition to reviews of methods to determine real tensor ranks in details, global theories such as the Jacobian method are also reviewed in details. The book includes as well an accessible and comprehensive introduction of mathematical backgrounds, with basics of positive polynomials and calculations by using the Groebner basis. Furthermore, this book provides insights into numerical methods of finding tensor ranks through simultaneous singular value decompositions.

Author : Can Chen
Publisher : Springer Nature
Page : 115 pages
File Size : 42,9 Mb
Release : 2024-06-23
Category : Electronic
ISBN : 9783031545054

Get Book

Tensor-Based Dynamical Systems by Can Chen Pdf

Author : Peter McCullagh
Publisher : Courier Dover Publications
Page : 308 pages
File Size : 46,7 Mb
Release : 2018-07-18
Category : Mathematics
ISBN : 9780486832692

Get Book

Tensor Methods in Statistics by Peter McCullagh Pdf

A pioneering monograph on tensor methods applied to distributional problems arising in statistics, this work begins with the study of multivariate moments and cumulants. An invaluable reference for graduate students and professional statisticians. 1987 edition.

Author : Robert C. Wrede
Publisher : Courier Corporation
Page : 436 pages
File Size : 50,7 Mb
Release : 1972-06-01
Category : Mathematics
ISBN : 9780486618791

Get Book

Introduction to Vector and Tensor Analysis by Robert C. Wrede Pdf

Text for advanced undergraduate and graduate students covers the algebra, differentiation, and integration of vectors, and the algebra and analysis of tensors, with emphasis on transformation theory

Author : Thomas Dedieu,Flaminio Flamini,Claudio Fontanari,Concettina Galati,Rita Pardini
Publisher : Springer Nature
Page : 421 pages
File Size : 41,9 Mb
Release : 2023-04-14
Category : Mathematics
ISBN : 9783031119385

Get Book

The Art of Doing Algebraic Geometry by Thomas Dedieu,Flaminio Flamini,Claudio Fontanari,Concettina Galati,Rita Pardini Pdf

This volume is dedicated to Ciro Ciliberto on the occasion of his 70th birthday and contains refereed papers, offering an overview of important parts of current research in algebraic geometry and related research in the history of mathematics. It presents original research as well as surveys, both providing a valuable overview of the current state of the art of the covered topics and reflecting the versatility of the scientific interests of Ciro Ciliberto.

Author : M. A. Akivis
Publisher : Unknown
Page : 167 pages
File Size : 52,5 Mb
Release : 1977
Category : Electronic
ISBN : OCLC:859814456

Get Book

An Introduction to Linear Algebra and Tensors by M. A. Akivis Pdf

Author : Satoshi Aoki,Hisayuki Hara,Akimichi Takemura
Publisher : Springer Science & Business Media
Page : 294 pages
File Size : 46,6 Mb
Release : 2012-07-25
Category : Mathematics
ISBN : 9781461437192

Get Book

Markov Bases in Algebraic Statistics by Satoshi Aoki,Hisayuki Hara,Akimichi Takemura Pdf

Algebraic statistics is a rapidly developing field, where ideas from statistics and algebra meet and stimulate new research directions. One of the origins of algebraic statistics is the work by Diaconis and Sturmfels in 1998 on the use of Gröbner bases for constructing a connected Markov chain for performing conditional tests of a discrete exponential family. In this book we take up this topic and present a detailed summary of developments following the seminal work of Diaconis and Sturmfels. This book is intended for statisticians with minimal backgrounds in algebra. As we ourselves learned algebraic notions through working on statistical problems and collaborating with notable algebraists, we hope that this book with many practical statistical problems is useful for statisticians to start working on the field.

Author : Cristiano Bocci
Publisher : Springer Nature
Page : 252 pages
File Size : 41,5 Mb
Release : 2024-06-23
Category : Electronic
ISBN : 9783031542633

Get Book

Hadamard Products of Projective Varieties by Cristiano Bocci Pdf

Author : Takeo Yokonuma
Publisher : American Mathematical Soc.
Page : 148 pages
File Size : 50,5 Mb
Release : 1992
Category : Mathematics
ISBN : 0821827960

Get Book

Tensor Spaces and Exterior Algebra by Takeo Yokonuma Pdf

This book explains, as clearly as possible, tensors and such related topics as tensor products of vector spaces, tensor algebras, and exterior algebras. You will appreciate Yokonuma's lucid and methodical treatment of the subject. This book is useful in undergraduate and graduate courses in multilinear algebra. Tensor Spaces and Exterior Algebra begins with basic notions associated with tensors. to facilitate understanding of the definitions, Yokonuma often presents two or more different ways of describing one object. Next, the properties and applications of tensors are developed, including the classical definition of tensors and the description of relative tensors. Also discussed are the algebraic foundations of tensor calculus and applications of exterior algebra to determinants and to geometry. This book closes with an examination of algebraic systems with bilinear multiplication. in particular, Yokonuma discusses the theory of replicas of Chevalley and several properties of Lie algebras deduced from them.

Author : Maks Aĭzikovich Akivis
Publisher : Unknown
Page : 167 pages
File Size : 45,7 Mb
Release : 1972
Category : Algebras, Linear
ISBN : OCLC:1035690191

Get Book

An Introduction to Linear Algebra and Tensors by Maks Aĭzikovich Akivis Pdf

Author : L. Pachter,B. Sturmfels
Publisher : Cambridge University Press
Page : 440 pages
File Size : 42,8 Mb
Release : 2005-08-22
Category : Mathematics
ISBN : 0521857007

Get Book

Algebraic Statistics for Computational Biology by L. Pachter,B. Sturmfels Pdf

This book, first published in 2005, offers an introduction to the application of algebraic statistics to computational biology.