Algebraic Geometry and Statistical Learning Theory Cambridge Monographs on Applied and Computational Mathematics, Series Number 25 1st Edition
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Algebraic Geometry and Statistical Learning Theory Cambridge Monographs on Applied and Computational Mathematics, Series Number 25 1st Edition
Watanabe’s book lays the foundations for the use of algebraic geometry in statistical learning theory.
Algebraic Geometry and Statistical Learning Theory Cambridge Monographs on Applied and Computational Mathematics, Series Number 25 1st Edition
Artikelnr.: 58626472

Algebraic Geometry and Statistical Learning Theory Cambridge Monographs on Applied and Computational Mathematics, Series Number 25 1st Edition

Artikelnr.: 58626472

ANG 195

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Watanabe’s book lays the foundations for the use of algebraic geometry in statistical learning theory.
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Wat opvalt

Interdisciplinary Approach
Combines algebraic geometry and statistical learning theory, offering a unique perspective that bridges mathematics and statistics for advanced learners and researchers.
Comprehensive Coverage
Provides in-depth theoretical insights and practical applications, making complex concepts accessible for graduate students and professionals in applied mathematics.
Renowned Authors
Authored by leading experts in the field, ensuring high-quality content that reflects current trends and research in applied and computational mathematics.

Productdetails

Shop Algebraic Geometry and Statistical Learning Theory Cambridge Monographs on Applied and Computational Mathematics, Series Number 25 1st Edition online at a best price in curacao. 0521864674
  • Foundational book by Watanabe integrating algebraic geometry into statistical learning theory
  • Addresses singular models/machines such as mixture models, neural networks, HMMs, Bayesian networks, and stochastic context-free grammars
  • Provides theoretical basis for accurate estimation techniques in the presence of singularities
  • Part of the Cambridge Monographs on Applied and Computational Mathematics series
  • Sure to have a significant impact in the field of statistical learning theory
  • First edition of the book
Publisher Cambridge University Press
Publication date September 28, 2009
Edition 1st
Language English
Print length 300 pages
ISBN-10 0521864674
ISBN-13 978-0521864671
Item Weight 1.25 pounds (570 grams)
Dimensions 6.25 x 1 x 9 inches (15.9 x 2.5 x 22.9 cm)

Voor wie is dit geschikt?

Suitable For
  • Graduate Students

    Ideal for advanced graduate students focusing on the intersection of algebraic geometry and statistical learning theory.

  • Research Professionals

    Useful for researchers seeking to apply algebraic geometry concepts in statistical learning frameworks and computational mathematics.

  • Mathematical Statisticians

    Perfect for statisticians interested in theoretical foundations and mathematical underpinnings of statistical learning algorithms.

Not Suitable For
  • Casual Readers

    Not suitable for casual readers; the content is complex and requires foundational knowledge in mathematics.

  • Undergraduate Students

    Undergraduates may find the material too advanced without prior exposure to algebraic geometry or statistical theory.

  • Practitioners Only

    This book is theoretical and may not cater to practitioners seeking practical applications without mathematical rigor.

PRODUCTBESCHRIJVING

Algebraic Geometry and Statistical Learning Theory Cambridge Monographs on Applied and Computational Mathematics, Series Number 25 1st Edition

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Vragen & Antwoorden van klanten

  • vraag: What is the focus of Watanabe's book?

    antwoord: The book lays the foundations for the use of algebraic geometry in statistical learning theory.
  • vraag: What are some examples of singular models/machines?

    antwoord: Mixture models, neural networks, HMMs, Bayesian networks, stochastic context-free grammars are some of the major examples.
  • vraag: What is the usefulness of this book?

    antwoord: The theory achieved in the book will help in accurate estimation techniques in the presence of singularities.

Computer Vision & Pattern Recognition Editorial Review

The editorial review of the book "Algebraic Geometry and Statistical Learning Theory" acknowledges its potential to provide an approachable understanding of a complex theoretical topic important for practitioners in the field of machine learning and data science. The reviewer praises the content but criticizes the clarity of the author's transitions between definitions, statements, remarks, and theorems, as well as pointing out issues with the English and typographical errors. They note that parsing through the book can be frustrating, requiring the reader to repeatedly verify each step due to these issues. The reviewer recommends a second edition and suggests that readers with a strong background in measure theory, differential geometry, and abstract algebra, and the right motivation, could benefit from the book. Another review commends the clarity of the book, highlighting its relevance for those interested in the application of algebraic geometry in statistical learning theory. The author's use of real algebraic geometry over algebraically closed fields is Considered advantageous, as it reduces the need for heavy machinery associated with contemporary texts on the subject. The book is said to require readers to have preparation in real and functional analysis and a good background in algebraic geometry, although not necessarily at the level of modern approaches to the subject. The reviewer points out that the book covers important concepts from statistical learning theory and the use of Kullback-Leibler distance, and emphasizes the need for "singular" statistical learning theory in dealing with parameter spaces where the Fisher information matrix is not positive definite. The review also mentions the author's generalization of standard statistical learning Constructions to the case of singular theories, such as the Akaike information criterion and Bayes information criterion. The book's treatment of notions like stochastic complexity and its methods for calculating it are noted, as well as the author's strategies for dealing with the divergence of the maximum likelihood estimator and the failure of asymptotic normality in singular theories.

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  • Provides an approachable understanding of a complex theoretical topic.
  • Relevant for those interested in the application of algebraic geometry in statistical learning theory.
  • Covers important concepts from statistical learning theory.
  • Generalizes standard statistical learning Constructions to the case of singular theories.
  • Treatment of notions like stochastic complexity and its methods for calculating it.

Nadelen

  • Lack of clarity in the author's transitions between definitions, statements, remarks, and theorems.

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Kenmerken en voordelen

  • Algebraic geometry can now be used in statistical learning theory
  • The book focuses on singular models/machines
  • Major examples of such models include mixture models, neural networks, HMMs, Bayesian networks etc.
  • The theory lays the groundwork for accurate estimation in the presence of singularities.

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