Algebraic Geometry and Statistical Learning Theory (Hardcover)

Sumio Watanabe

ISBN 10: 0521864674 / ISBN 13: 9780521864671

Verlag: Cambridge University Press, Cambridge, 2009

Beschreibung

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 our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. Bestandsnummer des Verkäufers 9780521864671

Bibliografische Details

Titel: Algebraic Geometry and Statistical Learning ...

Verlag: Cambridge University Press, Cambridge

Erscheinungsdatum: 2009

Einband: Hardcover

Zustand: new

Über diesen Titel

Inhaltsangabe:

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.

Críticas:

"Overall, the many insightful remarks and simple direct language make the book a pleasure to read."
Shaowei Lin, Mathematical Reviews