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Algebraic Geometry and Statistical Learning Theory

ISBN-10: 0521864674

ISBN-13: 9780521864671

Edition: 2009

Authors: Sumio Watanabe

List price: $150.00
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Book details

List price: $150.00
Copyright year: 2009
Publisher: Cambridge University Press
Publication date: 8/13/2009
Binding: Hardcover
Pages: 300
Size: 6.25" wide x 9.00" long x 1.00" tall
Weight: 1.232
Language: English

Sumio Watanabe is a Professor in the Precision and Intelligence Laboratory at the Tokyo Institute of Technology.

Preface
Introduction
Basic concepts in statistical learning
Statistical models and learning machines
Statistical estimation methods
Four main formulas
Overview of this book
Probability theory
Singularity theory
Polynomials and analytic functions
Algebraic set and analytic set
Singularity
Resolution of singularities
Normal crossing singularities
Manifold
Algebraic geometry
Ring and ideal
Real algebraic set
Singularities and dimension
Real projective space
Blow-up
Examples
Zeta function and singular integral
Schwartz distribution
State density function
Mellin transform
Evaluation of singular integral
Asymptotic expansion and b-function
Empirical processes
Convergence in law
Function-valued analytic functions
Empirical process
Fluctuation of Gaussian processes
Singular learning theory
Standard form of likelihood ratio function
Evidence and stochastic complexity
Bayes and Gibbs estimation
Maximum likelihood and a posteriori
Singular learning machines
Learning coefficient
Three-layered neural networks
Mixture models
Bayesian network
Hidden Markov model
Singular learning process
Bias and variance
Non-analytic learning machines
Singular statistics
Universally optimal learning
Generalized Bayes information criterion
Widely applicable information criteria
Singular hypothesis test
Realization of a posteriori distribution
From regular to singular
Bibliography
Index