Stochastic complexities of reduced rank regression in Bayesian estimation

Neural Networks

Volumn 18, Issue 7, 2005, Pages 924-933

  Aoyagi, Miki ^a   Watanabe, Sumio ^b  

^a SOPHIA UNIVERSITY   (Japan)

^b TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

Bayesian estimate; Generalization error; Kullback information; Non regular learning machines; Reduced rank regression models; Resolution of singularities; Stochastic complexity; Zeta function

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; ERROR ANALYSIS; LEARNING SYSTEMS; MATHEMATICAL MODELS; MATRIX ALGEBRA; RANDOM PROCESSES; REGRESSION ANALYSIS;

BAYESIAN ESTIMATE; GENERALIZATION ERRORS; KULLBACK INFORMATION; NON-REGULAR LEARNING MACHINES; REDUCED RANK REGRESSION MODELS; RESOLUTION OF SINGULARITIES; STOCHASTIC COMPLEXITY; ZETA FUNCTION;

NEURAL NETWORKS;

ARTICLE; ARTIFICIAL NEURAL NETWORK; BAYES THEOREM; LEARNING; MATHEMATICAL ANALYSIS; PRIORITY JOURNAL; STATISTICAL ANALYSIS; STOCHASTIC MODEL; THEORETICAL STUDY;

ARTIFICIAL INTELLIGENCE; BAYES THEOREM; NEURAL NETWORKS (COMPUTER); REGRESSION ANALYSIS; STOCHASTIC PROCESSES;

EID: 24344502351     PISSN: 08936080     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neunet.2005.03.014     Document Type: Article

References (16)

1. H. Akaike A new look at the statistical model identification IEEE Transactions on Automatic Control 19 1974 716 723
2. M.F. Atiyah Resolution of singularities and division of distributions Communications on Pure and Applied Mathematics 13 1970 145 150
3. P. Baldi, and K. Hornik Learning in linear networks: A survey IEEE Transactions on Neural Networks 6 4 1995 837 858
4. I.N. Bernstein The analytic continuation of generalized functions with respect to a parameter Functional Analysis Applications 6 1972 26 40
5. E.J. Hannan, and B.G. Quinn The determination of the order of an autoregression Journal of Royal Statistical Society, Series B 41 1979 190 195
6. H. Hironaka Resolution of singularities of an algebraic variety over a field of characteristic zero Annals of Mathematics 79 1964 109 326
7. N.J. Murata, S.G. Yoshizawa, and S. Amari Network information criterion - Determining the number of hidden units for an artificial neural network model IEEE Transactions on Neural Networks 5 6 1994 865 872
8. J. Rissanen Universal coding, information, prediction, and estimation IEEE Transactions on Information Theory 30 4 1984 629 636
9. M. Sato, and T. Shintani On zeta functions associated with prehomogeneous vector space Annals of Mathematics 100 1974 131 170
10. G. Schwarz Estimating the dimension of a model Annals of Statistics 6 2 1978 461 464
11. K. Takeuchi Distribution of an information statistic and the criterion for the optimal model Mathematical Science 153 1976 12 18 In Japanese
12. S. Watanabe Algebraic analysis for singular statistical estimation Lecture Notes on Computer Science 1720 1999 39 50
13. S. Watanabe Algebraic analysis for nonidentifiable learning machines Neural Computation 13 4 2001 899 933
14. S. Watanabe Algebraic geometrical methods for hierarchical learning machines Neural Networks 14 8 2001 1049 1060
15. S. Watanabe Algebraic geometry of learning machines with singularities and their prior distributions Journal of Japanese Society of Artificial Intelligence 16 2 2001 308 315
16. K. Watanabe, and S. Watanabe Upper bounds of bayesian generalization errors in reduced rank regression IEICE Transactions J86-A 3 2003 278 287 (in Japanese)