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" Algebraic geometry and statistical learning theory / "
Sumio Watanabe.
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BL
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| Record Number
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948566
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| Doc. No
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b702936
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| Main Entry
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Watanabe, Sumio,1959-
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| Title & Author
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Algebraic geometry and statistical learning theory /\ Sumio Watanabe.
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| Publication Statement
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Cambridge ;New York :: Cambridge University Press,, ©2009.
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| Series Statement
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Cambridge monographs on applied and computational mathematics ;; 25
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| Page. NO
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viii, 286 pages :: illustrations ;; 24 cm.
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| ISBN
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0521864674
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: 9780521864671
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Abstract
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"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 networks, and stochastic context-free grammars are major examples. Algebraic geometry and singularity theory provide the necessary tools for studying such non-smooth models. Four main formulas are established: 1. the log likelihood function can be given a common standard form using resolution of singularities, even applied to more complex models; 2. the asymptotic behaviour of the marginal likelihood or 'the evidence' is derived based on zeta function theory; 3. new methods are derived to estimate the generalization errors in Bayes and Gibbs estimations from training errors; 4. the generalization errors of maximum likelihood and a posteriori methods are clarified by empirical process theory on algebraic varieties."--Jacket.
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| Subject
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Computational learning theory-- Statistical methods.
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| Subject
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Geometry, Algebraic.
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Algebraische Geometrie
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Algebraisk geometri.
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Artificiell intelligens.
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Computational learning theory-- Statistical methods.
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Geometry, Algebraic.
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Geometry, Algebraic.
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Learning models (Stochastic processes)
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| Subject
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Mathematische Lerntheorie
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| Dewey Classification
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006.3/1
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| LC Classification
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Q325.7.W38 2009
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| NLM classification
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QH 740rvk
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SK 240rvk
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