The effect of singularities in a learning machine when the true parameters do not lie on such singularities

Advances in Neural Information Processing Systems

Volumn , Issue , 2003, Pages

  Watanabe, Sumio ^a   Amari, Shun Ichi ^b  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

^b RIKEN BRAIN SCIENCE INSTITUTE   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

FISHER INFORMATION MATRIX;

GENERALIZATION ERROR; HIDDEN VARIABLE; KULLBACK INFORMATION; LEARNING MACHINES; LEARNING THEORY; PARAMETER SPACES; TRAINING ERRORS; ZETA FUNCTION;

LEARNING SYSTEMS;

EID: 84898942349     PISSN: 10495258     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (9)

1. Amari, S., Park, H., and Ozeki, T. (2002) Geometrical singularities in the neuro-manifold of multilayer perceptrons. Advances in Neural Information Processing Systems, Vol. 14.
2. Hartigan, J. A. (1985) A Failure of likelihood asymptotics for normal mixtures. Proceedings of the Berkeley Conference in Honor of J. Neyman and J. Kiefer, Vol. 2, pp. 807-810.
3. Hironaka, H. (1964). Resolution of singularities of an algebraic variety over a field of characteristic zero. Annals of Mathematics, 79, 109-326.
4. Rusakov, D, Geiger, D. (2002) Asymptotic model selection for naive Bayesian networks. Proc. of UAI02.
5. Watanabe, S. (1999). Algebraic analysis for singular statistical estimation. Lecture Notes in Computer Science, 1720, 39-50.
6. Watanabe, S., (2001) Algebraic analysis for nonidentifiable learning machines. Neural Computation, 13, (4), pp. 899-933.
7. Watanabe, S. (2001) Algebraic information geometry for learning machines with singularities. Advances in Neural Information Processing Systems, Vol. 13, 329-336.
8. Watanabe, S. (2001) Algebraic geometrical methods for hierarchical learning machines. International Journal of Neural Networks, Vol. 14, No. 8, 1049-1060.
9. Watanabe, S., & Amari, S.-I. (2003) Learning coefficients of layered models when the true distriburion mismatches the singularities. Neural Computation, to appear. Technology