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Algebraic Geometry and Statistical Learning Theory (Cambridge Monographs on Applied and Computational Mathematics, Series Number 25) - Hardcover
Synopsis
Sure to be influential, Watanabe’s book lays the foundations for the use of algebraic geometry in statistical learning theory. Many models/machines are singular: mixture models, neural networks, HMMs, Bayesian networks, stochastic context-free grammars are major examples. The theory achieved here underpins accurate estimation techniques in the presence of singularities.
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About the Author
Sumio Watanabe is a Professor in the Precision and Intelligence Laboratory at the Tokyo Institute of Technology.
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Algebraic Geometry and Statistical Learning Theory
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Cambridge University Press, 2009
ISBN 10: 0521864674
ISBN 13: 9780521864671
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Algebraic Geometry and Statistical Learning Theory (Cambridge Monographs on Applied and Computational Mathematics, Series Number 25)
Published by
Cambridge University Press, 2009
ISBN 10: 0521864674
ISBN 13: 9780521864671
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Hardcover
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Algebraic Geometry and Statistical Learning Theory (Cambridge Monographs on Applied and Computational Mathematics, Series Number 25)
Published by
Cambridge University Press, 2009
ISBN 10: 0521864674
ISBN 13: 9780521864671
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Hardcover
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Algebraic Geometry and Statistical Learning Theory
Published by
Cambridge University Press, 2009
ISBN 10: 0521864674
ISBN 13: 9780521864671
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Algebraic Geometry and Statistical Learning Theory (Hardcover)
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Cambridge University Press, Cambridge, 2009
ISBN 10: 0521864674
ISBN 13: 9780521864671
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Hardcover. Condition: new. Hardcover. 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 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. 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. The theory achieved here underpins accurate estimation techniques in the presence of singularities. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9780521864671
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Algebraic Geometry and Statistical Learning Theory
Published by
Cambridge University Press, 2009
ISBN 10: 0521864674
ISBN 13: 9780521864671
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Hardcover. Condition: Brand New. 1st edition. 300 pages. 9.00x6.25x1.00 inches. In Stock. This item is printed on demand. Seller Inventory # __0521864674
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Algebraic Geometry and Statistical Learning Theory (Cambridge Monographs on Applied and Computational Mathematics, Series Number 25)
Published by
Cambridge University Press, 2009
ISBN 10: 0521864674
ISBN 13: 9780521864671
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Algebraic Geometry and Statistical Learning Theory
Published by
Cambridge University Press, 2009
ISBN 10: 0521864674
ISBN 13: 9780521864671
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Algebraic Geometry and Statistical Learning Theory
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ISBN 10: 0521864674
ISBN 13: 9780521864671
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Algebraic Geometry and Statistical Learning Theory
Published by
Cambridge University Press, 2009
ISBN 10: 0521864674
ISBN 13: 9780521864671
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Seller: GreatBookPricesUK, Woodford Green, United Kingdom
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Condition: As New. Unread book in perfect condition. Seller Inventory # 6165683
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