Algebraic Geometry and Statistical Learning Theory (Cambridge Monographs on

Description: 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.

Price: 81.56 USD

Location: Matraville, NSW

End Time: 2025-01-02T11:29:58.000Z

Shipping Cost: 0 USD

Product Images

Item Specifics

Return shipping will be paid by: Buyer

All returns accepted: Returns Accepted

Item must be returned within: 60 Days

Refund will be given as: Money Back

Return policy details:

EAN: 9780521864671

UPC: 9780521864671

ISBN: 9780521864671

MPN: N/A

Number of Pages: 300 Pages

Publication Name: Algebraic Geometry and Statistical Learning Theory

Language: English

Publisher: Cambridge University Press

Publication Year: 2009

Subject: Geometry / Algebraic, Computer Vision & Pattern Recognition

Item Height: 0.8 in

Item Weight: 19.7 Oz

Type: Textbook

Item Length: 9.2 in

Author: Sumio Watanabe

Subject Area: Mathematics, Computers

Item Width: 6.1 in

Series: Cambridge Monographs on Applied and Computational Mathematics Ser.

Format: Hardcover