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Item #:
58626472
Algebraic Geometry and Statistical Learning Theory Cambridge Monographs on Applied and Computational Mathematics, Series Number 25 1st Edition
Item #:
58626472
CAD 160
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Watanabe’s book lays the foundations for the use of algebraic geometry in statistical learning theory.
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What Stands Out
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.
Product Details
- Foundations for using algebraic geometry in statistical learning theory
- Addresses singular models/machines such as mixture models, neural networks, HMMs, Bayesian networks, stochastic context-free grammars
- Theory provides accurate estimation techniques in the presence of singularities
- Authored by Watanabe, the book is expected to have a significant influence
| 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) |
Who Should Buy?
-
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.
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Mathematical Statisticians
Perfect for statisticians interested in theoretical foundations and mathematical underpinnings of statistical learning algorithms.
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Casual Readers
Not suitable for casual readers; the content is complex and requires foundational knowledge in mathematics.
Product Description
Algebraic Geometry and Statistical Learning Theory Cambridge Monographs on Applied and Computational Mathematics, Series Number 25 1st Edition
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Customer Questions & Answers
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Question:
What is the focus of Watanabe's book?
Answer: The book lays the foundations for the use of algebraic geometry in statistical learning theory. -
Question:
What are some examples of singular models/machines?
Answer: Mixture models, neural networks, HMMs, Bayesian networks, stochastic context-free grammars are some of the major examples. -
Question:
What is the usefulness of this book?
Answer: 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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Pros
- 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.
Cons
- Lack of clarity in the author's transitions between definitions, statements, remarks, and theorems.
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Features & Benefits
- 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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