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Sure to be influential, this book lays the foundations for the use of algebraic geometry in statistical learning theory.Many widely used statistical models are singular: mixture models, neural networks, HMMs, and Bayesian networks are major examples. Algebraic geometry and singularity theory provide the mathematical foundation on which a new statistical learning theory is constructed. For example, resolution of singularities is a powerful method which makes the log likelihood function be a common standard form. Algebraic geometry 2 Algebraic Description of Graphical Models Review of GM De ninitions Algebraic and semialgebraic descriptions Restricted Boltzmann machines 3 Identi ability, singular learning theory, other perspectives Identi ability Singular Learning Theory Jason Morton (Penn State) Algebraic Deep Learning 7/19/2012 3 / 103 Algebraic Geometry and Statistical Learning Theory, Cambridge University Press 2009. Paolo Gibilisco, Eva Riccomagno, Maria-Piera Rogantin, Henry P. Wynn . Algebraic and Geometric Methods in Statistics , Cambridge 2009.

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Q325.7.W38 2009 006.3 1 – dc22 2009011366 ISBN 978-0-521-86467-1 hardback ‎Sure to be influential, this book lays the foundations for the use of algebraic geometry in statistical learning theory. Many widely used statistical models and learning machines applied to information science have a parameter space that is singular: mixture models, neural networks, HMMs, Bayesian n… Algebraic Geometry and Statistical Learning Theory 作者 : Sumio Watanabe 出版社: Cambridge University Press 出版年: 2009-8-13 页数: 300 定价: GBP 57.00 装帧: Hardcover ISBN: 9780521864671 Application of algebraic geometry to statistical learning theory Algebraic geometry has also recently found applications to statistical learning theory, including a generalization of the Akaike information criterion to singular statistical models. Statistical learning theory is now a well-established subject, and has found practical use in artificial intelligence as well as a framework for studying computational learning theory.

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Many widely used statistical models and learning machines applied to information science have a parameter space that is singular: mixture models, neural networks, HMMs, Bayesian networks, and stochastic context-free grammars are major examples. Algebraic geometry and DOI: 10.1017/CBO9780511800474 Corpus ID: 53813935.

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