Cambridge monographs on applied and computational mathematics 25 algebraic geometry and statistical learning theory
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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 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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Taal: en
Bindwijze: E-book
Oorspronkelijke releasedatum: 13 augustus 2009
Ebook Formaat: Adobe ePub
Illustraties: Met illustraties
Hoofdauteur: Sumio Watanabe
Hoofduitgeverij: Cambridge University Press
Lees dit ebook op: Android (smartphone en tablet)
Lees dit ebook op: Kobo e-reader
Lees dit ebook op: Desktop (Mac en Windows)
Lees dit ebook op: iOS (smartphone en tablet)
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Product breedte: 159 mm
Product hoogte: 25 mm
Product lengte: 229 mm
Studieboek: Ja
EAN: 9781107713963