Iterative solution to approximation in reproducing kernel hilbert spaces

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 15, Issue 1, 2002, Pages 103-108

  Dodd, Tony J ^a   Harrison, Robert F ^a  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

Author keywords

Function approximation; Gaussian processes; Hubert spaces; Iterative methods; Least squares approximation; Regularisation; System identification

Indexed keywords

AUTOMATION; IDENTIFICATION (CONTROL SYSTEMS); ITERATIVE METHODS;

COMPUTATIONAL BURDEN; FUNCTION APPROXIMATION; GAUSSIAN PROCESSES; HUBERT SPACE; ITERATIVE SOLUTIONS; REGULARISATION; REPRODUCING KERNEL HILBERT SPACES; REPRODUCING KERNEL HUBERT SPACES;

LEAST SQUARES APPROXIMATIONS;

EID: 84945543219     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20020721-6-es-1901.00428     Document Type: Conference Paper

References (15)

1. Aizerman, M.A., E.M. Braverman and L.I. Rozonoer (1964). Theoretical foundations of the potential function method in pattern recognition learning. Automatika i Telemekhanika 25(6), 821-837.
2. Akhiezer, N.I. and I.M. Glazman (1981). Theory of Linear Operators in Hubert Space. Vol. I. Pitman.
3. Aronszajin, N. (1950). Theory of reproducing kernels. Transactions of the American Mathematical Society 68, 337-404.
4. Bertero, M., C. De Mol and E.R. Pike (1985). Linear inverse problems with discrete data. I: General formulation and singular system analysis. Inverse Problems 1, 301-330.
5. Bertero, M., C. De Mol and E.R. Pike (1988). Linear inverse problems with discrete data. II: Stability and regularisation. Inverse Problems 4, 573-594.
6. Billings, S.A. and W.S.F. Voon (1986). Correlation-based model validity tests for non-linear models. Internationaljournal of Control 44, 235-244.
7. Chen, S. and S.A. Billings (1992). Neural networks for nonlinear dynamic system modeling and identification. International Journal of Control 56(2), 319-346.
8. Freiß, T.T. and R.F. Harrison (1999). A kernel-based adaline for function approximation. Journal of Intelligent Data Analysis 3, 307-313.
9. Fu, K.S. (1968). Sequential Methods in Pattern Recognition and Machine Learning. Vol. 52 of Mathematics in Science and Engineering. Academic Press.
10. Kailath, T. (1971). RKHS approach to detection and estimation problems - Part I: Deterministic signals in Gaussian noise. IEEE Transactions on Information Theory IT-17(5), 530-549.
11. Parzen, E. (1961). An approach to time series analysis. Annals of Mathematical Statistics 32, 951-989.
12. Vapnik, V.N. (1998). Statistical Learning Theory. Adaptive and Learning Systems for Signal Processing, Communications and Control. John Wiley & Sons.
13. Wahba, G. (1990). Spline Models for Observational Data. Vol. 50 of Series in Applied Mathematics. SIAM. Philadelphia.
14. Weiner, H.J. (1965). The gradient iteration in time series analysis. Journal of the Society for Industrial and Applied Mathematics 13(4), 1096-1101.
15. Williams, C.K.I. (1999). Prediction with Gaussian processes: From linear regression to linear prediction and beyond. In: Learning in Graphical Models (M.I. Jordan, Ed.). The MIT Press. pp. 599-621.