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.

*"synopsis" may belong to another edition of this title.*

"Overall, the many insightful remarks and simple direct language make the book a pleasure to read."

Shaowei Lin, Mathematical Reviews

Sure to be influential, this book lays the foundations for the use of algebraic geometry in statistical learning theory. Many widely used statistical models are singular: mixture models, neural networks, HMMs, and Bayesian networks are major examples. The theory achieved here underpins accurate estimation techniques in the presence of singularities.

*"About this title" may belong to another edition of this title.*

£ 62.32

**Shipping:**
FREE

From United Kingdom to U.S.A.

Published by
CAMBRIDGE UNIVERSITY PRESS, United Kingdom
(2017)

ISBN 10: 0521864674
ISBN 13: 9780521864671

New
Hardcover
Quantity Available: 10

Seller:

Rating

**Book Description **CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2017. Hardback. Condition: New. Language: English. Brand new Book. 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. Seller Inventory # LHB9780521864671

Published by
Cambridge University Press
(2009)

ISBN 10: 0521864674
ISBN 13: 9780521864671

New
Quantity Available: > 20

Seller:

Rating

**Book Description **Cambridge University Press, 2009. HRD. Condition: New. New Book. Shipped from UK. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Seller Inventory # IG-9780521864671

ISBN 10: 0521864674
ISBN 13: 9780521864671

New
Quantity Available: 5

Seller:

Rating

**Book Description **Condition: New. Seller Inventory # 6165683-n

Published by
Cambridge University Press

ISBN 10: 0521864674
ISBN 13: 9780521864671

New
Hardcover
Quantity Available: 1

Seller:

Rating

**Book Description **Cambridge University Press. Hardcover. Condition: new. This item is printed on demand. Seller Inventory # 9780521864671

Published by
Cambridge

ISBN 10: 0521864674
ISBN 13: 9780521864671

New
Quantity Available: 5

Seller:

Rating

**Book Description **Cambridge. Condition: new. Algebraic Geometry and Statistical Learning Theory. Seller Inventory # 462fcc49a51a8d6f053849735e313c08

Published by
Cambridge University Press
(2009)

ISBN 10: 0521864674
ISBN 13: 9780521864671

New
Hardcover
Quantity Available: 1

Seller:

Rating

**Book Description **Cambridge University Press, 2009. Hardcover. Condition: BRAND NEW. Seller Inventory # 0521864674_abe_bn

Published by
Cambridge University Press

ISBN 10: 0521864674
ISBN 13: 9780521864671

New
Hardcover
Quantity Available: 5

Seller:

Rating

**Book Description **Cambridge University Press. Hardback. Condition: New. This item is printed on demand. New copy - Usually dispatched within 5-9 working days. Seller Inventory # C9780521864671

ISBN 10: 0521864674
ISBN 13: 9780521864671

New
Quantity Available: 5

Seller:

Rating

**Book Description **Condition: New. Seller Inventory # 6165683-n

ISBN 10: 0521864674
ISBN 13: 9780521864671

New
Hardcover
Quantity Available: 1

Seller:

Rating

**Book Description **2009. Hardback. Condition: NEW. 9780521864671 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. For all enquiries, please contact Herb Tandree Philosophy Books directly - customer service is our primary goal. Seller Inventory # HTANDREE0481185

Published by
Cambridge University Press 2009-08-13
(2009)

ISBN 10: 0521864674
ISBN 13: 9780521864671

New
Hardcover
Quantity Available: 20

Seller:

Rating

**Book Description **Cambridge University Press 2009-08-13, 2009. Hardcover. Condition: New. Seller Inventory # 6666-ING-9780521864671