Algebraic geometry and statistical learning theory (Record no. 60403)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 01894 a2200229 4500 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240502b |||||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780521864671 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 006.31 WAT |
| 100 ## - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Watanabe, Sumio |
| 245 ## - TITLE STATEMENT | |
| Title | Algebraic geometry and statistical learning theory |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication, distribution, etc | Cambridge: |
| Name of publisher, distributor, etc | Cambridge University Press, |
| Date of publication, distribution, etc | 2009 |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | viii, 286p.: |
| Other physical details | hbk.: |
| Dimensions | 23cm |
| 440 ## - SERIES STATEMENT/ADDED ENTRY--TITLE | |
| Title | Cambridge Monographs on Applied and Computational Mathematics, 25 |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | 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.<br/><br/>https://www.cambridge.org/in/universitypress/subjects/computer-science/pattern-recognition-and-machine-learning/algebraic-geometry-and-statistical-learning-theory?format=HB |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Algebraic Geometry |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Algebra |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Computational Learning Theory |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Mathematics |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Computational Science |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Computer Science |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Item type | Books |
| Source of classification or shelving scheme | Dewey Decimal Classification |
| Withdrawn status | Lost status | Source of classification or shelving scheme | Damaged status | Not for loan | Collection code | Home library | Current library | Date acquired | Source of acquisition | Cost, normal purchase price | Total Checkouts | Full call number | Barcode | Date last seen | Copy number | Cost, replacement price | Koha item type |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Dewey Decimal Classification | General | IIT Gandhinagar | IIT Gandhinagar | 01/05/2024 | CBS Publishers | 7497.75 | 006.31 WAT | 034233 | 01/05/2024 | 1 | 7497.75 | Books |
