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Algebraic geometry and statistical l...

Watanabe, Sumio, (1959-)

Algebraic geometry and statistical learning theory /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Algebraic geometry and statistical learning theory // Sumio Watanabe.
Author:	Watanabe, Sumio,
Published:	Cambridge ;Cambridge University Press, : c2009.,
Description:	viii, 286 p. :ill. ; : 24 cm.;
Subject:	Computational learning theory - Statistical methods. -
ISBN:	9780521864671 (hbk.) :

Algebraic geometry and statistical learning theory /
Watanabe, Sumio,1959-

Algebraic geometry and statistical learning theory /Sumio Watanabe. - Cambridge ;Cambridge University Press,c2009. - viii, 286 p. :ill. ;24 cm. - Cambridge monographs on applied and computational mathematics ;25. - Cambridge monographs on applied and computational mathematics ;16..

Includes bibliographical references and index.

"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."--Jacket.

ISBN: 9780521864671 (hbk.) :NT4808

LCCN: 2009011366

Nat. Bib. No.: GBA954183bnbSubjects--Topical Terms:

984780
Computational learning theory
--Statistical methods.

LC Class. No.: Q325.7 / .W38 2009

Dewey Class. No.: 006.3/1

Algebraic geometry and statistical learning theory /
LDR:01864cam a2200241 a 4500 001 788838
003 OCoLC
005 20140924054913.0
008 141013s2009 enka 001 0 eng
010 $a 2009011366
015 $2 bnb $a GBA954183
020 $a 9780521864671 (hbk.) : $c NT4808
020 $a 0521864674 (hbk.)
035 $a (OCoLC)299942247
035 $a ocn299942247
040 $a DLC $b eng $c DLC $d YDXCP $d BTCTA $d UKM $d BWKUK $d BWK $d SNK $d DEBBG $d OCL $d CDX $d OCL $d MIX $d OCLCQ $d OCLCO $d OCLCQ $d NFU
050 0 0 $a Q325.7 $b .W38 2009
082 0 0 $2 22 $a 006.3/1
100 1 $a Watanabe, Sumio, $d 1959- $3 984779
245 1 0 $a Algebraic geometry and statistical learning theory / $c Sumio Watanabe.
260 # $a Cambridge ; $a New York : $c c2009. $b Cambridge University Press,
300 $a viii, 286 p. : $b ill. ; $c 24 cm.
490 1 $a Cambridge monographs on applied and computational mathematics ; $v 25
504 $a Includes bibliographical references and index.
520 1 $a "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."--Jacket.
650 # 0 $a Computational learning theory $x Statistical methods. $3 984780
650 # 0 $a Geometry, Algebraic. $3 580393
830 0 $a Cambridge monographs on applied and computational mathematics ; $v 16. $3 746415