Citation Relationships

Legends: Link to a Model Reference cited by multiple papers


Franz MO, Schölkopf B (2006) A unifying view of wiener and volterra theory and polynomial kernel regression. Neural Comput 18:3097-118 [PubMed]

References and models cited by this paper

References and models that cite this paper

Ahmed NU (1970) Closure and completeness of Wieners orthogonal set Gn in the class L2( , B,) and its application to stochastic hereditary differential systems Information And Control 17:161-174
Alper A (1965) A consideration of the discrete Volterra series IEEE Trans Autom Contr 3:322-327
Barrett JF (1963) The use of functionals in the analysis of non-linear physical systems J Electron Control 15:567-615
Boyd S, Chua LO (1985) Fading memory and the problem of approximating nonlinear operators with Volterra series IEEE Trans Circuits Syst 32:1150-1161
Brilliant MB (1958) Theory of the analysis of nonlinear systems RLE Tech Rep 345 MIT
Dodd TJ, Harrison RF (2002) A new solution to Volterra series estimation Proc 2002 IFAC World Congress
Franz MO, Kwon Y, Rasmussen CE, Scholkopf B (2004) Semi-supervised kernel regression using whitened function classes Pattern recognition Proc 26th DAGM Symposium, Rasmussen CE:Bulthoff HH:Giese MA:Scholkopf B, ed. pp.18
Franz MO, Scholkopf B (2004) Implicit estimation of Wiener series Proc IEEE Signal Process Society Workshop, Barros A:Principe J:Larsen J:Adali T:Douglas S, ed. pp.735
Franz MO, Scholkopf B (2005) Implicit Wiener series for higher-order image analysis Advances in neural information processing systems, Saul LK:Weiss Y:Bottou L, ed. pp.465
Frechet M (1910) Sur les fonctionelles continues Annales Scientifiques De LEcoleNormale Superieure 27:193-216
Gehler PV, Franz MO (2006) Implicit Wiener Series. Part II: Regularised estimation MPI Tech Rep 148, Max-Planck Institute for Biological Cybernetics Tubingen Germany
Giannakis GB, Serpedin E (2001) A bibliography on nonlinear system identification Signal Processing 81:533-580
Hille E, Phillips RS (1957) Functional analysis and semi-groups
Hyvärinen A, Hoyer P (2000) Emergence of phase- and shift-invariant features by decomposition of natural images into independent feature subspaces. Neural Comput 12:1705-20 [PubMed]
Korenberg MJ (1983) Statistical identification of parallel cascades of linear and nonlinear systems Proc IFAC Symp Identification and System Parameter Estimation :669-674
Korenberg MJ (1991) Parallel cascade identification and kernel estimation for nonlinear systems. Ann Biomed Eng 19:429-55 [PubMed]
Korenberg MJ, Bruder SB, McIlroy PJ (1988) Exact orthogonal kernel estimation from finite data records: extending Wiener's identification of nonlinear systems. Ann Biomed Eng 16:201-14 [PubMed]
Korenberg MJ, Hunter IW (1990) The identification of nonlinear biological systems: Wiener kernel approaches. Ann Biomed Eng 18:629-54 [PubMed]
Lee YW, Schetzen M (1965) Measurement of the Wiener kernels of a non-linear system by cross-correlation Int J Cont 2:237-255
Liusternik L, Sobolev V (1961) Elements of functional analysis
Mathews VJ, Sicuranza GL (2000) Polynomial signal processing
Nowak R (1998) Penalized least squares estimation of Volterra filters and higher order statistics IEEE Trans Signal Process 46:419-428
Ogura H (1972) Orthogonal functionals of the Poisson process IEEE Trans Inf Theory 18:473-481
Palm G (1978) On representation and approximation of nonlinear systems Biol Cybern 31:119-124
Palm G, Poggio T (1977) Volterra representation and Wiener expansion validity and pitfalls Siam J Appl Math 33:195-216
Palm G, Poggio T (1978) Stochastic identification methods for nonlinear Systems: An extension of Wiener theory SIAM J Appl Math 34:524-534
Papoulis A (1991) Probability, Random Variables, And Stochastic Processes
Poggio T (1975) On optimal nonlinear associative recall. Biol Cybern 19:201-9 [PubMed]
Prenter PM (1970) A Weierstrass theorem for real, separable Hilbert spaces J Approx Theory 3:341-351
Rasmussen CE, Williams CKI (2006) Gaussian processes for machine learning
Rugh WJ (1981) Nonlinear system theory: The Volterra-Wiener approach
Saunders C, Stitson M, Weston J, Bottou L, Schoelkopf B, Smola A (1998) Support vector machine-reference manual Tech. Rep. TR CSD-TR-98-03
Schetzen M (1965) A theory of nonlinear system identification Intl J Control 20:577-592
Schetzen M (1980) The Volterra and Wiener theories of nonlinear systems
Scholkopf B, Smola AJ (2001) Learning with kernels: Support vector machines, regularization, optimization, and beyond
Segall A, Kailath T (1976) Orthogonal functionals of independent-increment processes IEEE Trans Inf Theory 22:287-298
Steinwart I (2001) On the influence of the kernel on the consistency of support vector machines JMLR 2:67-93
Vapnik VN (1982) Estimation of dependencies based on empirical data
Volterra V (1887) Sopra le funzioni che dipendono de altre funzioni, Rend R, ed. pp.97
Volterra V (1930) Theory of Functionals and of Integro-Differential Equations
Wahba G (1990) Splines models for observational data
Wiener N (1958) Nonlinear Problems in Random Theory
Wray J, Green GGR (1994) Calculation of the Volterra kernels of non-linear dynamic systems using an artificial neural network Biol Cybern 71:187-195
Kovacic G, Tao L, Cai D, Shelley MJ (2008) Theoretical analysis of reverse-time correlation for idealized orientation tuning dynamics. J Comput Neurosci 25:401-38 [Journal] [PubMed]
   Reverse-time correlation analysis for idealized orientation tuning dynamics (Kovacic et al. 2008) [Model]
(44 refs)