Algebraic Geometry and Statistical Learnin...

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

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

Inhaltsverzeichnis

Preface; 1. Introduction; 2. Singularity theory; 3. Algebraic geometry; 4. Zeta functions and singular integral; 5. Empirical processes; 6. Singular learning theory; 7. Singular learning machines; 8. Singular information science; Bibliography; Index.

Details

Erscheinungsjahr:	2017
Genre:	Importe , Informatik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	Gebunden
ISBN-13:	9780521864671
ISBN-10:	0521864674
Sprache:	Englisch
Einband:	Gebunden
Autor:	Watanabe, Sumio
Hersteller:	Cambridge University Press
Verantwortliche Person für die EU:	Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße:	235 x 157 x 22 mm
Von/Mit:	Sumio Watanabe
Erscheinungsdatum:	21.04.2017
Gewicht:	0,637 kg