Algebraic Geometry and Statistical Learning Theory

Name: Algebraic Geometry and Statistical Learning Theory
Brand: Cambridge University Press
SKU: 9780521864671
Price: 108.37 EUR
Availability: InStock

Автор: Sumio Watanabe

Език:

Корици: С твърди корици

Издател: Cambridge University Press

Наличност: Външен склад

Изпращаме след 9-15 дни

108.37 € 211.96 лв

Sure to be influential, this book lays the foundations for the use of algebraic geometry in statisti...

Информация за книгата

Автор

Sumio Watanabe

Език

Английски език

Корици

Книга - С твърди корици

Издадена

2009

страници

300

EAN

9780521864671

ISBN

0521864674

Enbook ID

04378995

Издател

Cambridge University Press

Теглоt

590

Размери

159 x 237 x 21

Пълно описание

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.

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Algebraic Geometry and Statistical Learning Theory

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