Asymptotic Properties of the Fisher Kernel

Neural Computation

Volumn 16, Issue 1, 2004, Pages 115-137

  Tsuda, Koji ^a,b   Akaho, Shotaro ^b   Kawanabe, Motoaki ^c   Müller, Klaus Robert ^c,d  

^a MAX PLANCK INSTITUTE FOR BIOLOGICAL CYBERNETICS   (Germany)

^b NATIONAL INSTITUTE OF ADVANCED INDUSTRIAL SCIENCE AND TECHNOLOGY AIST   (Japan)

^c FRAUNHOFER FIRST   (Germany)

^d UNIVERSITY OF POTSDAM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; ARTIFICIAL NEURAL NETWORK; REPRODUCIBILITY; STATISTICAL MODEL;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; MODELS, STATISTICAL; NEURAL NETWORKS (COMPUTER); REPRODUCIBILITY OF RESULTS; SUPPORT, NON-U.S. GOV'T;

EID: 0346895562     PISSN: 08997667     EISSN: None     Source Type: Journal    
DOI: 10.1162/08997660460734029     Document Type: Article

References (36)

1. Albert, A. (1972). Regression and the Moore-Penrose pseudoinverse. Orlando, FL: Academic Press.
2. Amari, S., & Murata, N. (1993). Statistical theory of learning curves under entropic loss criterion. Neural Computation, 5, 140-153.
3. Amari, S. & Nagaoka, H. (2001). Methods of information geometry. Providence, RI: American Mathematical Society.
4. Barndorff-Nielsen, O., & Cox, D. (1989). Asymptotic techniques for use in statistics. London: Chapman and Hall.
5. Baum, E., & Haussler, D. (1989). What size net gives valid generalization? Neural Computation, 1, 151-160.
6. Campbell, S., & Meyer, C. (1979). Generalized inverse of linear transformations. New York: Pitman Publishing.
7. Cox, D., & Hinkley, D. (1974). Theoretical statistics. London: Chapman & Hall.
8. Cristianini, N., & Shawe-Taylor, J. (2000). An introduction to support vector machines. Cambridge: Cambridge University Press.
9. Devroye, L., Györfi, L., & Lugosi, G. (1996). A probabilistic theory of pattern recognition. New York: Springer-Verlag.
10. Eguchi, S., & Copas, J. (2001). Information geometry on discriminant analysis and recent development. Journal of the Korean Statistical Society, 27, 101-117.
11. Gelfand, I., & Fomin, S. (1963). Calculus of variations. Englewood Cliffs, NJ: Prentice-Hall.
12. Gotoh, O. (1982). An improved algorithm for matching biological sequences. Journal of Molecular Biology, 162, 705-708.
13. Haussler, D., Kearns, M., Seung, H., & Tishby, N. (1996). Rigorous learning curve bounds from statistical mechanics. Machine Learning, 25, 195-236.
14. Jaakkola, T., & Haussler, D. (1999). Exploiting generative models in discriminative classifiers. In M. Kearns, S. Solla, & D. Conn (Eds.), Advances in neural information processing systems, 11 (pp. 487-493). Cambridge, MA: MIT Press.
15. Jaakkola, T., Meila, M., & Jebara, T. (1999). Maximum entropy discrimination (Tech. Rep. No. AITR-1668). Cambridge, MA: MIT Press.
16. Kawanabe, M., & Amari, S. (1994). Estimation of network parameters in semiparametric stochastic perceptron. Neural Computation, 6, 1244-1261.
17. Malzahn, D., & Opper, M. (2002). A variational approach to learning curves. In T. G. Dietterich, S. Becker, & Z. Ghahramani (Eds.), Advances in neural information processing systems, 14 (pp. 463-469). Cambridge, MA: MIT Press.
18. Müller, K.-R., Finke, M., Schulten, K., Murata, N., & Amari, S. (1996). A numerical study on learning curves in stochastic multi-layer feed-forward networks. Neural Computation, 8, 1085-1106.
19. Müller, K.-R., Mika, S., Rätsch, G., Tsuda, K., & Schölkopf, B. (2001). An introduction to kernel-based learning algorithms. IEEE Trans. Neural Networks, 12, 181-201.
20. Schölkopf, B., & Smola, A. (2002). Learning with kernels. Cambridge, MA: MIT Press.
21. Seeger, M. (2001). Learning with labeled and unlabeled data (Tech. Rep.). Edinburgh: Institute for Adaptive and Neural Computation, University of Edinburgh. Available on-line: http://www.dai.ed.ac.uk/homes/seeger/ papers/review.ps.gz.
22. Seeger, M. (2002). Covariance kernels from Bayesian generative models. In T. G. Dietterich, S. Becker, & Z. Ghahramani (Eds.), Advances in neural information processing systems, 14, (pp. 905-912). Cambridge, MA: MIT Press.
23. Seung, S., Sompolinsky, H., & Tishby, N. (1992). Statistical mechanics of learning from examples. Physical Review A, 45, 6056.
24. Smith, N. & Gales, M. (2002). Speech recognition using SVMs. In T. G. Dietterich, S. Becker, & Z. Ghahramani (Eds.), Advances in neural information processing systems, 14, (pp. 1197-1204). Cambridge, MA: MIT Press.
25. Sonnenburg, S., Rätsch, G., Jagota, A., & Müller, K.-R. (2002). New methods for splice site recognition. In J. Dorronsoro (Ed.), Artificial neural networks - ICANN 2002 (pp. 329-336). New York: Springer-Verlag.
26. Sugiyama, M. (2001). A theory of model selection and active learning for supervised learning. Unpublished doctoral dissertation, Tokyo Institute of Technology.
27. Tsuda, K., & Kawanabe, M. (2002). The leave-one-out kernel. In J. Dorronsoro (Ed.), Artificial neural networks - ICANN 2002 (pp. 727-732). New York: Springer-Verlag.
28. Tsuda, K., Kawanabe, M., & Müller, K.-R. (in press). Clustering with the Fisher score. In S. Becker, S. Thrun, & K. Obermayer (Eds.), Advances in neural information processing systems, 15. Cambridge, MA: MIT Press.
29. Tsuda, K., Kawanabe, M., Rätsch, G., Sonnenburg, S., & Müller, K.-R. (2002). A new discriminative kernel from probabilistic models. Neural Computation, 14, 2397-2414.
30. van der Vaart, A. (1998). Asymptotic statistics. Cambridge: Cambridge University Press.
31. Vapnik, V. (1998). Statistical learning theory. New York: Wiley.
32. Vinokourov, A., & Girolami, M. (2002). A probabilistic framework for the hierarchic organization and classification of document collections. Journal of Intelligent Information Systems, 18, 153-172.
33. Watanabe, S. (2001). Algebraic analysis for non-identifiable learning machines. Neural Computation, 13, 899-933.
34. Watkin, T., Rau, A., & Biehl, M. (1993). The statistical mechanics of learning a rule. Reviews of Modern Physics, 65, 499.
35. Zhang, T., & Oles, F. (2000). The value of unlabeled data for classification problems. In P. Langley (Ed.), Proceedings of the Seventeenth International Conference on Machine Learning (pp. 1191-1198). San Mateo, CA: Morgan Kaufmann.
36. Zien, A., Rätsch, G., Mika, S., Schölkopf, B., Lengauer, T., & Müller, K.-R. (2000). Engineering support vector machine kernels that recognize translation initiation sites. Bioinformatics, 16, 799-807.