Algebraic analysis for non-regular learning machines

Advances in Neural Information Processing Systems

Volumn , Issue , 2000, Pages 356-362

  Watanabe, Sumio ^a  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA;

ALGEBRAIC ANALYSIS; ALGEBRAIC GEOMETRY; HIERARCHICAL LEARNING; LEARNING MACHINES; NON-REGULAR LEARNING MACHINES; RATIONAL NUMBERS; RESOLUTION OF SINGULARITIES; STOCHASTIC COMPLEXITY;

LEARNING SYSTEMS;

EID: 0000213888     PISSN: 10495258     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (11)

1. Amari, S., Murata, N.(1993) Statistical theory of learning curves under entropie loss. Neural Computation, 5 (4) pp.140-153.
2. Atiyah, M.F. (1970) Resolution of singularities and division of distributions. Comm. Pure and Appl. Math., 13 pp. 145-150.
3. Fukurnizu, K. (1999) Generalization error of linear neural networks in unidentifiable cases. Lecture Notes in Computer Science, 1720 Springer, pp.51-62.
4. Hagiwara.K., Toda, N., Usui.S. (1993) On the problem of applying AIC to determine the structure of a layered feed-forward neural network. Proc. of IJCNN, 3 pp. 2263-2266.
5. Hironaka, H. (1964) Resolution of singularities of an algebraic variety over a field of characteristic zero, I.II. Annals of Math., 79 pp. 109-326.
6. Kashiwara, M. (1976) B-functions and holonomic systems, Invent. Math., 38 pp.33-53.
7. Oaku, T. (1997) An algorithm of computing b-funcitions. Duke Math. J., 87 pp.115-132.
8. Sato, M., Shintani.T. (1974) On zeta functions associated with prehomogeneous vector space. Annals of Math., 100, pp.131-170.
9. Watanabe, S.(1998) On the generalization error by a layered statistical model with Bayesian estimation. IEICE Trans., J81-A pp. 1442-1452.
10. English version: Elect. Comm. in Japan., to appear.
11. Watanabe, S. (1999) Algebraic analysis for singular statistical estimation. Lecture Notes in Computer Science, 1720 Springer, pp.39-50.