Bibliography

1

Aarts, E. & Korts, J. (1989) Simulated Annealing and Boltzmann Machines. New York: Wiley.

2

Abu-Mostafa, Y. (1990) Learning from Hints in Neural Networks. Journal of Complexity 6, 192-198.

3

Abu-Mostafa, Y. (1993) Hints and the VC Dimension. Neural Computation 5, 278-288.

4

Abu-Mostafa, Y. (1993b) A method for learning from hints. Advances in Neural Information Processing Systems 5, S. Hanson et al (eds.), 73-80, San Mateo, CA: Morgan Kauffmann.

5

Aida, T. (1999) $\quad$ Field Theoretical Analysis of On-line Learning of Probability Distributions. $\quad$ Phys. Rev. Lett. 83, 3554-3557, arXiv:cond-mat/9911474.

6

Allen, D.M. (1974) The relationship between variable selection and data augmentation and a method of prediction. Technometrics 16, 125.

7

Amari, S., Cichocki, A., & Yang, H.H.(1996) A New Learning Algorithm for Blind Signal Separation. in Advances in Neural Information Processing Systems 8, D.S. Touretzky et al (eds.), 757-763, Cambridge, MA: MIT Press.

8

Ames, W.F. (1977) Numerical Methods for Partial Differential Equations. (2nd. ed.) New York: Academic Press.

9

Balian, R. (1991) From Microphysics to Macrophysics. Vol. I. Berlin: Springer Verlag.

10

Ballard, D.H. (1997) An Introduction to Natural Computation. Cambridge, MA: MIT Press.

11

Bayes, T.R. (1763) An Essay Towards Solving a Problem in the Doctrine of Chances. Phil. Trans. Roy. Soc. London 53, 370. (Reprinted in Biometrika (1958) 45, 293)

12

Bazaraa, M.S., Sherali, H.D., & Shetty, C.M. (1993) Nonlinear Programming. (2nd ed.) New York: Wiley.

13

Beck, C. & Schlögl, F. (1993) Thermodynamics of chaotic systems. Cambridge: Cambridge University Press.

14

Bell, A.J. & Sejnowski, T.J. (1995) Neural Computation 7(6), 1129-1159.

15

Ben-Israel, A. & Greville, T.N.E. (1974) Generalized Inverses: Theory and Applications New York: Wiley.

16

Berger, J.O. (1980) Statistical Decision Theory and Bayesian Analysis. New York: Springer Verlag.

17

Berger, J.O. & Wolpert R. (1988) The Likelihood Principle. (2nd ed.) Hayward, CA: IMS Lecture Notes -- Monograph Series 9.

18

Bernado, J.M. & Smith, A.F. (1994) Bayesian Theory. New York: John Wiley.

19

Bertsekas, D.P. (1995) Nonlinear Programming. Belmont, MA: Athena Scientific.

20

Bialek, W., Callan, C.G., & Strong, S.P. (1996) Field Theories for Learning Probability Distributions. Phys. Rev. Lett. 77, 4693-4697, arXiv:cond-mat/9607180.

21

Binder, K. & Heermann, D.W. (1988) Monte Carlo simulation in statistical physics: An introduction. Berlin: Springer Verlag.

22

Bishop, C.M. (1993) Curvature-driven smoothing: A learning algorithm for feedforward networks. IEEE Transactions on Neural Networks 4(5),882-884.

23

Bishop, C.M. (1995) Training with noise is equivalent to Tikhonov regularization. Neural Computation 7 (1), 108-116.

24

Bishop, C.M. (1995) Neural Networks for Pattern Recognition. Oxford: Oxford University Press.

25

Bishop, E. & Bridges, D. (1985) Constructive Analysis. Grundlehren der Mathematischen Wissenschaften, Vol. 279. Berlin: Springer Verlag.

26

Black, M.J. & Rangarajan, A. (1996) On the Unification of Line Processes, Outlier Rejection, and Robust Statistics With Applications in Early Vision. Int'l J. Computer Vision 19 (1).

27

Blaizot, J.-P. & Ripka, G. (1986) Quantum Theory of Finite Systems. Cambridge, MA: MIT Press.

28

Blake, A. & Zisserman, A. (1987) Visual reconstruction Cambridge, MA: MIT Press.

29

Blanchard, P. & Bruening, E. (1982) Variational Methods in Mathematical Physics. Berlin: Springer Verlag.

30

Bleistein, N. & Handelsman, N. (1986) Asymptotic Expansions of Integrals. (Originally published in 1975 by Holt, Rinehart and Winston, New York) New York: Dover.

31

Breiman, L. (1993) Hinging hyperplanes for regression, classification, and function approximation. IEEE Trans. Inform. Theory 39(3), 999-1013.

32

Breiman, L., Friedman, J.H., Olshen, R.A., & Stone, C.J. (1993) Classification and Regression Trees., New York: Chapman & Hall.

33

Bretthorst, G.L. (1988) Bayesian spectrum analysis and parameter estimation. Lecture Notes in Statistics, Vol. 48. Berlin: Springer Verlag.
(Available at http://bayes.wustl.edu/glb/book.pdf)

34

Cardy, J. (1996) Scaling and Renormalization in Statistical Physics. Cambridge: Cambridge University Press.

35

Carlin, B.P. & Louis T.A. (1996) Bayes and Empirical Bayes Methods for Data Analysis. Boca Raton: Chapman & Hall/CRC.

36

Choquet-Bruhat Y., DeWitt-Morette, C., & Dillard-Bleick, M. (1982) Analysis, Manifolds, and Physics. Part I. Amsterdam: North-Holland.

37

Collins, J. (1984) Renormalization. Cambridge: Cambridge University Press.

38

Cox, D.R. & Hinkley, D.V. (1974) Theoretical Statistics. London: Chapman & Hall.

39

Craven, P. & Wahba, G. (1979) Smoothing noisy data with spline functions: estimating the correct degree of smoothing by the method of generalized cross-validation. Numer. Math. 31, 377-403.

40

Cressie, N.A.C. (1993) Statistics for Spatial Data. New York, Wiley.

41

Creutz, M. (1983) Quarks, gluons and lattices. Cambridge: Cambridge University Press.

42

D'Agostini, G. (1999) Bayesian Reasoning in High Energy Physics. -- Principles and Applications -- CERN Yellow Report 99-03 (Available at http://www-zeus.roma1.infn.it/${}^\sim$agostini/prob+stat.html)

43

Davis, L. (ed.) (1987) Genetic Algorithms and Simulated Annealing. San Mateo, CA: Morgan Kaufmann.

44

Davis, L. (ed.) (1991) Handbook of Genetic Algorithms. New York: Van Nostrand Reinhold.

45

De Bruijn, N.G. (1981) Asymptotic Methods in Analysis. (Originally published in 1958 by the North-Holland Publishing Co., Amsterdam) New York: Dover.

46

Deco, G. & Obradovic, D. (1996) An Information-Theoretic Approach to Neural Computing. New York: Springer Verlag.

47

Devroye, L., Györfi, L., & Lugosi, G. (1996) A Probabilistic Theory of Pattern recognition. New York: Springer Verlag.

48

Di Castro, C. & Jona-Lasinio, G. (1976) The Renormalization Group Approach to Critical Phenomena. In: Domb, C. & Green M.S. (eds.) Phase Transitions and Critical Phenomena. London: Academic Press.

49

Dietrich, R., Opper, M., & Sompolinsky, H. (1999) Statistical Mechanics of Support Vector Networks. Physical Review Letters 82(14), 2975-2978.

50

Donoho, D.L. & Johnstone, I.M. (1989) Projection-based approximation and a duality with kernel methods. Ann. Statist. 17(1),58-106.

51

Doob, J.L. (1953) Stochastic Processes. (New edition 1990) New York: Wiley.

52

Dudley, R.M. (1984) A course on empirical processes. Lecture Notes in Mathematics 1097,2-142.

53

Ebeling, W., Freund, J., & Schweitzer, F. (1998) Komplexe Strukturen: Entropie und Information. Stuttgart: Teubner.

54

Efron, B. & Tibshirani R.J. (1993) An Introduction to the Bootstrap. New York: Chapman & Hall.

55

Eisenberg, J. & Greiner, W. (1972) Microscopic Theory of the Nucleus. North-Holland, Amsterdam.

56

Fernández, R., Fröhlich, J., & Sokal, A.D. (1992) Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory. Berlin: Springer Verlag.

57

Fletcher, R. (1987) Practical Methods of Optimization. New York: Wiley.

58

Fredholm I. (1903) Acta Math. 27.

59

Friedman, J.H. & Tukey, J.W. (1974) A projection pursuit algorithm for exploratory data analysis. IEEE Trans. Comput. 24, 1000-1006.

60

Friedman, J.H. & Stuetzle, W. (1981) Projection pursuit regression. J. Am. Statist. Assoc. 76(376), 817-823.

61

Fukunaga, K. (1990) Statistical Pattern Recognition. Boston: Academic Press.

62

Gardiner, C.W. (1990) Handbook of Stochastic Methods. (2nd ed.) Berlin: Springer Verlag.

63

Gardner, E. (1987) Maximum Storage Capacity in Neural Networks. Europhysics Letters 4 481-485.

64

Gardner, E. (1988) The Space of Interactions in Neural Network Models. Journal of Physics A 21 257-270.

65

Gardner, E. & Derrida B. (1988) Optimal Storage Properties of Neural Network Models. Journal of Physics A 21 271-284.

66

Geiger, D. & Girosi, F. (1991) Parallel and Deterministic Algortihms for MRFs: Surface Reconstruction. IEEE Trans. on Pattern Analysis and Machine Intelligence 13 (5), 401-412.

67

Geiger, D. & Yuille, A.L. (1991) A Common Framework for Image Segmentation. Int'l J. Computer Vision 6 (3), 227-243.

68

Gelfand, S.B. & Mitter, S.K. (1993) On Sampling Methods and Annealing Algorithms. Markov Random Fields - Theory and Applications. New York: Academic Press.

69

Gelman, A., Carlin, J.B., Stern, H.S., & Rubin, D.B. (1995) Bayesian Data Analysis. New York: Chapman & Hall.

70

Geman, S. & Geman, D. (1984) Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Trans. on Pattern Analysis and Machine Intelligence 6, 721-741. Reprinted in Shafer & Pearl (eds.) (1990) Readings in Uncertainty Reasoning. San Mateo, CA: Morgan Kaufmann.

71

Geman, D. & Reynoids, G. (1992) Constraint restoration and the Recover of Discontinuities. IEEE Trans. on Pattern Analysis and Machine Intelligence. 14, 367-383.

72

Giraud, B.G., Lapedes, A., Liu, L.C., & Lemm, J.C. (1995) Lorentzian Neural Nets. Neural Networks 8 (5), 757-767.

73

Girosi, F. (1991) Models of noise and robust estimates. A.I.Memo 1287, Artificial Intelligence Laboratory, Massachusetts Institute of Technology.

74

Girosi, F. (1997) An equivalence between sparse approximation and support vector machines. A.I. Memo No.1606, Artificial Intelligence Laboratory, Massachusetts Institute of Technology.

75

Girosi, F., Poggio, T., & Caprile, B. (1991) Extensions of a theory of networks for approximations and learning: Outliers and negative examples. In Lippmann, R., Moody, J., & Touretzky, D. (eds.) Advances in Neural Information Processing Systems 3, San Mateo, CA: Morgan Kaufmann.

76

Girosi, F., Jones, M., & Poggio, T. (1995) Regularization Theory and Neural Networks Architectures. Neural Computation 7 (2), 219-269.

77

Glimm, J. & Jaffe, A. (1987) Quantum Physics. A Functional Integral Point of View. New York: Springer Verlag.

78

Goeke, K., Cusson, R.Y., Gruemmer, F., Reinhard, P.-G., Reinhardt, H., (1983) Time-Dependent Hartree-Fock and Beyond: A Review. Prog. Theor. Physics [Suppl.] 74 & 75, 33.

79

Goldberg, D.E. (1989) Genetic Algorithms in Search, Optimization, and Machine Learning. Redwood City, CA: Addison-Wesley.

80

Golden, R.M. (1996) Mathematical Methods for Neural Network Analysis and Design. Cambridge, MA: MIT Press.

81

Golup, G., Heath, M., & Wahba, G.(1979) Generalized cross validation as a method for choosing a good ridge parameter. Technometrics 21, 215-224.

82

Good, I.J. & Gaskins, R.A. (1971) Nonparametric roughness penalties for probability densities. Biometrika 58, 255-277.

83

Green, P.J. & Silverman, B.W. (1994) Nonparametric Regression and Generalized Linear Models. London: Chapman & Hall.

84

Großman, Ch. & Roos H.-G. (1994) Numerik partieller Differentialgleichungen. Stuttgart: Teubner.

85

Gull, S.F. (1988) Bayesian data analysis - straight line fitting. In Skilling, J., (ed.) Maximum Entropy and Bayesian Methods. Cambridge, 511 -518, Dordrecht: Kluwer.

86

Gull, S.F. (1989) Developments in maximum entropy data analysis. In Skilling, J, (ed.) Maximum Entropy and Bayesian Methods. Cambridge 1988, 53 - 71, Dordrecht: Kluwer.

87

Hackbusch, W. (1985) Multi-grid Methods and Applications. New York: Springer Verlag.

88

Hackbusch, W. (1989) Integralgleichungen. Teubner Studienbücher. Stuttgart: Teubner.

89

Hackbusch, W. (1993) Iterative Lösung großer schwachbesetzter Gleichungssysteme. Teubner Studienbücher. Stuttgart: Teubner.

90

Härdle, W. (1990) Applied nonparametric regression. Cambridge: Cambridge University Press.

91

Hammersley, J.M. & Handscomb, D.C. (1964) Monte Carlo Methods. London: Chapman & Hall.

92

Hastie, T.J. & Tibshirani, R.J. (1986) Generalized Additive Models. Statist. Sci. 1, 297-318.

93

Hastie, T.J. & Tibshirani, R.J. (1987) Generalized Additive Models: Some applications. J. Am. Statist. Assoc. 82,371-386.

94

Hastie, T.J. & Tibshirani, R.J. (1990) Generalized Additive Models. London: Chapman & Hall.

95

Hastings, W.K. (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 97-109.

96

Hertz, J., Krogh, A. & Palmer, R.G. (1991) Introduction to the Theory of Neural Computation. Santa Fe Institute, Lecture Notes Volume I, Addison-Wesley.

97

Hilbert, D. & Courant, R. (1989) Methods of Mathematical Physics. Vol.1&2,(1st German editions 1924,1937, Springer Verlag) New York: Wiley.

98

Holland, J.H. (1975) Adaption in Natural and Artificial Systems. University of Michigan Press. (2nd ed. MIT Press, 1992.)

99

Horst, R., Pardalos, M., & Thoai, N.V. (1995) Introduction to Global Optimization. Dordrecht: Kluwer.

100

Huber, P.J. (1979) Robust Smoothing. In Launer, E. & Wilkinson G. (eds.) Robustness in Statistics New York: Academic Press.

101

Huber, P.J. (1981) Robust Statistics. New York: Wiley.

102

Huber, P.J. (1985) Projection Pursuit. Ann. Statist. 13(2),435-475.

103

Itzkyson, C. & Drouffe, J.-M. (1989) Statistical Field Theory. (Vols. 1 and 2) Cambridge: Cambridge University Press.

104

Jaynes, E.T. (in preparation) Probability Theory: The Logic Of Science. (Available at http://bayes.wustl.edu/etj/prob.html)

105

Jeffrey, R. (1999). Probabilistic Thinking.
(Available at http://www.princeton.edu/${}^\sim$bayesway/)

106

Jeggle, H. (1979) Nichtlineare Funktionalanalysis. Stuttgart: Teubner.

107

Jensen, F.V. (1996) An Introduction to Bayesian Networks. New York: Springer Verlag.

108

Jones, M.C. & Sibson, R. (1987) What is Projection Pursuit? J. Roy. Statist. Soc. A 150, 1-36.

109

Kaku, M. (1993) Quantum Field Theory. Oxford: Oxford University Press.

110

van Kampen, N.G. (1992) Stochastic Processes in Physics and Chemistry. Amsterdam: North-Holland.

111

Kant, I. (1911) Kritik der reinen Vernunft.(2nd ed.) Werke, Vol.3 Berlin: Königliche Akademie der Wissenschaften.

112

Kimmeldorf, G.S. & Wahba, G. (1970) A correspondence between Bayesian estimation on stochastic processes and smoothing splines. Ann. Math. Stat. 41, 495-502.

113

Kimmeldorf, G.S. & Wahba, G. (1970) Spline functions and stochastic processes. Sankhya Ser. A 32, Part 2, 173-180.

114

Kirkpatrick, S., Gelatt Jr., C.D., & Vecchi, M.P. (1983) Optimization by Simulated Annealing. Science 220, 671-680.

115

Kirsch, A. (1996) An Introduction to the Mathematical Theory of Inverse Problems. New York: Springer Verlag.

116

Kitagawa, G., Gersch, W. (1996) Smoothness Priors Analysis of Time Series New York: Springer Verlag.

117

Kleinert, H.(1993) Pfadintegrale. Mannheim: Wissenschaftsverlag.

118

Klir, G.J. & Yuan, B. (1995) Fuzzy Sets and Fuzzy Logic. Prentice Hall.

119

Klir, G.J. & Yuan, B. (eds.) (1996) Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems. World Scientific.

120

Koecher, M. (1985) Lineare Algebra und analytische Geometrie. Berlin: Springer Verlag.

121

Koza, J.R. (1992) Genetic Programming Cambridge, MA: MIT Press.

122

Kullback, S. & Leibler R.A. (1951) On Information and Sufficiency. Ann.Math.Statist. 22, 79-86.

123

Kullback, S. (1951) Information Theory and Statistics. New York: Wiley.

124

Lapedes, A. & Farber, R. (1988) How neural nets work. in Neural Information Processing Systems, D.Z.Anderson, (ed.),442-456. New York: American Institute of Physics.

125

Lauritzen, S.L. (1996) Graphical Models. Oxford: Clarendon Press.

126

Lawson, C. & Hanson, R. (1974) Solving Least Squares Problems. Englewood Cliffs, NJ: Prentice-Hall.

127

Le Bellac, M. (1991) Quantum and Statistical Field Theory. Oxford Science Publications, Oxford: Clarendon Press.

128

Le Cam, L. (1986) Asymptotic Methods in Statistical Decision Theory. New York: Springer Verlag.

129

Leen, T.K. (1995) From Data Distributions to Regularization in Invariant Learning. Neural Computation 7, 974-981.

130

Lemm, J.C. (1995) Inhomogeneous Random Phase Approximation for Nuclear and Atomic Reactions. Annals of Physics 244 (1), 136-200, 1995.

131

Lemm, J.C. (1995) Inhomogeneous Random Phase Approximation: A Solvable Model. Annals of Physics 244 (1), 201-238, 1995.

132

Lemm, J.C. (1996) Prior Information and Generalized Questions. A.I.Memo No. 1598, C.B.C.L. Paper No. 141, Massachusetts Institute of Technology. (Available at http://pauli.uni-muenster.de/${}^\sim$lemm)

133

Lemm, J.C. (1998) How to Implement A Priori Information: A Statistical Mechanics Approach. Technical Report MS-TP1-98-12, Münster University, arXiv:cond-mat/9808039.

134

Lemm, J.C. (1998) Fuzzy Interface with Prior Concepts and Non-Convex Regularization. In Wilfried Brauer (Ed.), Proceedings of the 5. International Workshop "Fuzzy-Neuro Systems '98" (FNS '98), March 19-20, 1998, Munich, Germany, Sankt Augustin: Infix.

135

Lemm, J.C. (1998) Quadratic Concepts. In Niklasson L., Bodén, M., & Ziemke, T. (eds.) Proceedings of the 8th International Conference on Artificial Neural Networks. (ICANN98) New York: Springer Verlag.

136

Lemm, J.C. (1998) Fuzzy Rules and Regularization Theory. In ELITE European Laboratory for Intelligent Techniques Engineering (ed.): Proceedings of the 6th European Congress on Intelligent Techniques and Soft Computing (EUFIT '98), Aachen, Germany, September 7-10, 1998, Mainz, Aachen.

137

Lemm, J.C. (1999) Mixtures of Gaussian Process Priors. In Proceedings of the Ninth International Conference on Artificial Neural Networks (ICANN99), IEEE Conference Publication No. 470. London: Institution of Electrical Engineers.

138

Lemm, J.C. (2000) Inverse Time-dependent Quantum Mechanics. Technical Report, MS-TP1-00-1, Münster University, arXiv:quant-ph/0002010.

139

Lemm, J.C., Beiu, V., & Taylor, J.G. (1995) Density Estimation as a Preprocessing Step for Constructive Algorithms. In Kappen B., Gielen, S. (eds.): Proceedings of the 3rd SNN Neural Network Symposium. The Netherlands, Nijmegen, 14-15 September 1995, Berlin, Springer Verlag.

140

Lemm, J.C., Giraud, B.G., & Weiguny, A. (1990) Mean field approximation versus exact treatment of collisions in few-body systems. Z. Phys. A - Atomic Nuclei 336, 179-188.

141

Lemm, J.C., Giraud, B.G., & Weiguny, A. (1994) Beyond the time independent mean field theory for nuclear and atomic reactions: Inclusion of particle-hole correlations in a generalized random phase approximation. Phys. Rev. Lett. 73, 420, arXiv:nucl-th/9911056.

142

Lemm, J.C. & Uhlig, J. (1999) Hartree-Fock Approximation for Inverse Many-Body Problems. Technical Report, MS-TP1-99-10, Münster University, arXiv:nucl-th/9908056.

143

Lemm, J.C., Uhlig J., & Weiguny, A. (2000) Bayesian Approach to Inverse Quantum Statistics. Phys. Rev. Lett. 84, 2068. arXiv:cond-mat/9907013.

144

Lifshits, M.A. (1995) Gaussian Random Functions. Dordrecht: Kluwer.

145

Loredo T. (1990) From Laplace to Supernova SN 1987A: Bayesian Inference in Astrophysics. In Fougère, P.F. (ed.) Maximum-Entropy and Bayesian Methods, Dartmouth, 1989, 81-142. Dordrecht: Kluwer.
(Available at http://bayes.wustl.edu/gregory/gregory.html)

146

Louis, A.K. (1989) Inverse und schlecht gestellte Probleme. Stuttgart: Teubner.

147

MacKay, D.J.C. (1992) The evidence framework applied to classification networks. Neural Computation 4 (5), 720-736.

148

MacKay, D.J.C. (1992) A practical Bayesian framework for backpropagation networks. Neural Computation 4 (3), 448-472.

149

MacKay, D.J.C. (1994) Hyperparameters: optimise or integrate out? In Heidbreder, G. (ed.) Maximum Entropy and Bayesian Methods, Santa Barbara 1993. Dordrecht: Kluwer.

150

MacKay, D.J.C. (1998) Introduction to Gaussian processes. In Bishop, C., (ed.) Neural Networks and Machine Learning. NATO Asi Series. Series F, Computer and Systems Sciences, Vol. 168.

151

Marquardt, D.W. (1970) Generalized Inverses, Ridge Regression, Biased Linear Estimation, and Nonlinear Regression. Technometrics 12, 591-613.

152

Marquardt, D.W. & Snee R.D. (1975) Ridge Regression in Practice The American Statistician 29, 3-20.

153

Marroquin, J.L., Mitter, S., & Poggio, T. (1987) Probabilistic solution of ill-posed problems in computational vision. J. Am. Stat. Assoc. 82, 76-89.

154

McCullagh, P. & Nelder, J.A. (1989) Generalized Linear Models London: Chapman & Hall.

155

Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., & Teller, E. (1953) Equation of state calculations by fast computing machines. Journal of Chemical Physics 21, 1087-1092.

156

Mezard, M., Parisi, G., & Virasoro, M.A. (1987) Spin Glass Theory and Beyond. Singapore: World Scientific.

157

Michalewicz, Z. (1992) Genetic Algorithms + Data Structures = Evolution Programs. Berlin: Springer Verlag.

158

Michie, D., Spiegelhalter, D.J., & Taylor, C.C. (Eds.) (1994) Machine Learning, Neural and Statistical Classification. New York: Ellis Horwood.

159

Minski, M.L. & Papert, S.A. (1990) Perceptrons. (Expanded Edition, Original edition, 1969) Cambridge, MA: MIT Press.

160

Mitchell, M. (1996) An Introduction to Genetic Algorithms. Cambridge, MA: MIT Press.

161

Mitchell, A.R. & Griffiths, D.F. (1980) The Finite Difference Method in Partial Differential Equations. New York: Wiley.

162

Molgedey, L. & Schuster, H.G. (1994) Separation of a mixture of independent signals using time delayed correlations. Phys. Rev. Lett. 72(23), 3634-3637.

163

Montvay, I. & Münster, G. (1994) Quantum Fields on a Lattice. Cambridge: Cambridge University Press.

164

On the Reciprocal of the General Algebraic Matrix. Moore, E.H. (1920) Bull.Amer.Math.Soc. 26, 394-395.

165

Morozov, V.A. (1984) Methods for Solving Incorrectly Posed problems. New York: Springer Verlag.

166

Mosteller, F. & Wallace, D. (1963) Inference in an authorship problem. A comparative study of discrimination methods applied to authorships of the disputed Federalist papers. J. Amer. Statist. Assoc. 58, 275-309.

167

Müller, B. & Reinhardt, J. (1991) Neural Networks. (2nd printing) Berlin, Springer Verlag.

168

Mumford, D. & Shah, J. (1989) Optimal Approximations by Piecewise Smooth Functions and Associated Variational Problems. Comm. Pure Applied Math. 42, 577-684.

169

Nadaraya, E.A. (1965) On nonparametric estimates of density functions and regression curves. Theor.Prob.Appl. 10,186-190.

170

Neal, R.M. (1996) Bayesian Learning for Neural Networks. New York: Springer Verlag.

171

Neal, R.M. (1997) Monte Carlo Implementation of Gaussian Process Models for Bayesian Regression and Classification. Technical Report No. 9702, Dept. of Statistics, Univ. of Toronto, Canada.

172

Negele, J.W. & Orland, H. (1988) Quantum Many-Particle Systems. Frontiers In Physics Series (Vol. 68), Redwood City, CA: Addison-Wesley.

173

Nitzberg, M. & Shiota T. (1992) Nonlinear Image Filtering With Edge and Corner Enhancement. IEEE Trans. on Pattern Analysis and Machine Intelligence. 14, (8) 862-833.

174

O'Hagen, A. (1994) Kendall's advanced theory of statistics, Vol. 2B: Bayesian inference. London: Edward Arnold.

175

Olshausen, B.A. & Field, D.J. (1995) Natural Image Statistics and Efficient Coding. Workshop on Information Theory and the Brain, Sept. 4-5, 1995, University of Stirling. Proceedings published in Network 7, 333-339.

176

Olshausen, B.A. & Field, D.J. (1996) Emergence of simple-cell receptive field properties by learning a spares code for natural images. Nature 381, 607-609.

177

Opper, M. (1999) Gaussian Processes for Classification: Mean Field Algorithms. Tech Report NCRG/1999/030, Neural Computing Research Group at Aston University, UK.

178

Opper, M. & Kinzel, W. (1996) Statistical Mechanics of Generalization. In Domany, E., van Hemmen, J.L., & Schulten, K. (eds.) Models of Neural Networks III. New York: Springer Verlag.

179

Opper, M., & Winther, O. (1999) Mean field methods for classification with Gaussian processes. In Kearns, M.S., Solla, S.S., & Cohn D.A. (eds.) Advances in Neural Information Processing Systems 11, 309-315, Cambridge, MA: MIT Press.

180

Ó Ruanaidh, J.J.K. & Fitzgerald W.J. (1996) Numerical Bayesian Methods Applied to Signal Processing. New York: Springer Verlag.

181

Parzen, E. (1962) An approach to time series analysis.
Ann.Math.Statist. 32, 951-989.

182

Parzen, E. (1962) On the estimation of a probability function and mode. Ann.Math.Statist. 33(3).

183

Parzen, E. (1963) Probability density functionals and reproducing kernel Hilbert spaces. In Rosenblatt, M.(ed.) Proc. Symposium on Time Series Analysis, 155-169, New York: Wiley.

184

Parzen, E. (1970) Statistical inference on time series by rkhs methods. In Pyke, R.(ed.) Proc. 12th Biennal Seminar, 1-37, Montreal, Canada: Canadian Mathematical Congress.

185

Pearl, J. (1988) Probabilistic Reasoning in Intelligent Systems. San Mateo, CA: Morgan Kauffmann.

186

Penrose, R., (1955) A generalized inverse for matrices. Proc. Cambridge Philos. Soc. 51, 406-413.

187

Penrose, R., (1956) On Best Approximate Solutions of Linear Matrix Equations. Proc. Cambridge Philos. Soc. 52, 17-19.

188

Perona, P. & Malik J. (1990) Scale-Space and Edge Detection Using Anisotropic Diffusion. IEEE Trans. on Pattern Analysis and Machine Intelligence. 12(7), 629-639.

189

Perskin, M.E. & Schroeder, D.V. (1995) An Introduction to Quantum Field Theory. Reading, MA, Addison-Wesley.

190

Pierre, D.A. (1986) Optimization Theory with Applications. New York: Dover. (Original edition Wiley, 1969).

191

Poggio, T. & Girosi, F. (1990) Networks for Approximation and Learning. Proceedings of the IEEE, Vol 78, No. 9.

192

Poggio, T., Torre, V., & Koch, C. (1985) Computational vision and regularization theory. Nature 317, 314-319.

193

Polak, E. (1997) Optimization. New York: Springer Verlag.

194

Pollard, D. (1984) Convergence of Stochastic Processes. New York: Springer Verlag.

195

Pordt, A. (1998) Random Walks in Field Theory In Meyer-Ortmanns, H, Klümper A. (eds.) (1998) Field Theoretical Tools for Polymer and Particle Physics. Berlin: Springer Verlag.

196

Press, W.H., Teukolsky, S.A., Vetterling, W.T., & Flannery, B.P. (1992) Numerical Recipes in C. Cambridge: Cambridge University Press.

197

Ring, P., & Schuck, P. (1980) The Nuclear Many-Body Problem. New York: Springer Verlag.

198

Ripley, B.D. (1977) Modelling spatial patterns (with discussion). Journal of the Royal Statistical Society series B 39, 172-212.

199

Ripley, B.D. (1987) Stochastic Simulation. New York: Wiley.

200

Ripley, B.D. (1996) Pattern Recognition and Neural Networks. Cambridge: Cambridge University Press.

201

Robert, C.P. (1994) The Bayesian Choice. New York: Springer Verlag.

202

Rodriguez, C.C. (1997) Cross validated Non Parametric Bayesianism by Markov Chain Monte Carlo. arXiv:physics/9712041.

203

Rose, K., Gurewitz, E., & Fox, G.C. (1990) Statistical mechanics and phase transitions in clustering. Phys. Rev. Lett. 65, 945-948.

204

Rothe, H.J. (1992) Lattice Gauge Theories. Singapore: World Scientific.

205

Rumelhart, D.E., McClelland, J.L., and the PDP Research Group (1986) Parallel Distributed Processing, vol.1& 2, Cambridge, MA: MIT Press.

206

Ryder, L.H. (1996) Quantum Field Theory. Cambridge: Cambridge University Press.

207

Schervish, M.J. (1995) Theory of Statistics. New York: Springer Verlag.

208

Schölkopf, B., Burges C., & Smola, A. (1998) Advances in Kernel Methods: Support Vector Machines. Cambridge, MA: MIT Press.

209

Schwefel, H.-P. (1995) Evolution and Optimum Seeking. New York: Wiley.

210

Silverman, B.W. (1984) Spline smoothing: The equivalent variable kernel method. Ann. Statist. 12, 898-916.

211

Silverman, B.W. (1986) Density Estimation for Statistics and Data Analysis. London: Chapman & Hall.

212

Sivia, D.S. (1996) Data Analysis: A Bayesian Tutorial. Oxford: Oxford University Press.

213

Skilling, J. (1991) On parameter estimation and quantified MaxEnt. In Grandy, W.T. & Schick, L.H. (eds.) Maximum Entropy and Bayesian Methods. Laramie, 1990, 267 -273, Dordrecht: Kluwer.

214

Smola, A.J. & Schölkopf, B., (1998) From regularization operators to support vector kernels. In: Jordan, M.I., Kearns, M.J., & Solla S.A. (Eds.): Advances in Neural Information Processing Systems 10. Cambridge, MA: MIT Press.

215

Smola, A.J., Schölkopf, B., & Müller, K-R. (1998) The connection between regularization operators and support vector kernels. Neural Networks 11, 637-649.

216

Stone, M. (1974) Cross-validation choice and assessment of statistical predictions. Journal of the Royal Statistical Society B 36, 111-147.

217

Stone, M. (1977) An asymptotic equivalence of choice of model by cross-validation and Akaike's criterion. Journal of the Royal Statistical Society B 39, 44.

218

Stone, C.J. (1985) Additive regression and other nonparametric models. Ann. Statist. 13,689-705.

219

Tierney, L. (1994) Markov chains for exploring posterior distributions (with discussion). Annals of Statistics 22, 1701-1762.

220

Tikhonov, A.N. (1963) Solution of incorrectly formulated problems and the regularization method. Soviet Math. Dokl. 4, 1035-1038.

221

Tikhonov, A.N. & Arsenin, V.Y. (1977) Solution of Ill-posed Problems. Washington, DC: W.H.Winston.

222

Uhlig, J. (2000) PhD Thesis, Münster University.

223

Uhlig, J., Lemm, J., & Weiguny, A. (1998) Mean field methods for atomic and nuclear reactions: The link between time-dependent and time-independent approaches. Eur. Phys. A 2, 343-354.

224

Vapnik, V.N. (1982) Estimation of dependencies based on empirical data. New York: Springer Verlag.

225

Vapnik, V.N. (1995) The Nature of Statistical Learning Theory. New York: Springer Verlag.

226

Vapnik, V.N. (1998) Statistical Learning Theory. New York: Wiley.

227

Vico, G. (1858, original 1710) De antiquissima Italorum sapientia Naples: Stamperia de' Classici Latini.

228

Wahba, G. (1990) Spline Models for Observational Data. Philadelphia: SIAM.

229

Wahba, G. (1997) Support vector machines, reproducing kernel Hilbert spaces and the randomized GACV. Technical Report 984, University of Wisconsin.

230

Wahba, G. & Wold, S. 1975) A completely automatic French curve. Commun. Statist. 4, 1-17.

231

Watkin, T.L.H., Rau, A., & Biehl, M. (1993) The statistical mechanics of learning a rule. Rev. Mod. Phys. 65, 499-556.

232

Watzlawick, P. (ed.) (1984) The Invented Reality. New York: Norton.

233

Weinstein, S. (1995) The Quantum Theory of Fields. Vol.1 Cambridge: Cambridge University Press.

234

Weinstein, S. (1996) The Quantum Theory of Fields. Vol.2 Cambridge: Cambridge University Press.

235

West, M. & Harrison, J. (1997) Bayesian Forecasting and Dynamic Models. New York, Springer Verlag.

236

Williams, C.K.I. & Barber, D. (1998) Bayesian Classification With Gaussian Processes IEEE Trans. on Pattern Analysis and Machine Intelligence. 20(12), 1342-1351.

237

Williams, C.K.I. & Rasmussen, C.E. (1996) Gaussian Processes for Regression. in Advances in Neural Information Processing Systems 8, D.S. Touretzky et al (eds.), 515-520, Cambridge, MA: MIT Press.

238

Winkler, G. (1995) Image Analysis, Random Fields and Dynamic Monte Carlo Methods. Berlin: Springer Verlag.

239

Wolpert, D.H. (ed.) (1995) The Mathematics of Generalization. The Proceedings of the SFI/CNLS Workshop on Formal Approaches to Supervised Learning. Santa Fe Institute, Studies in the Sciences of Complexity. Reading, MA: Addison-Wesley.

240

Wolpert, D.H. (1996) The Lack of A Priori Distinctions between Learning Algorithms. Neural Computation 8 (7), 1341-1390.

241

Wolpert, D.H. (1996) The Existence of A Priori Distinctions between Learning Algorithms. Neural Computation 8 (7), 1391-1420.

242

Yakowitz, S.J. & Szidarovsky, F. (1985) A Comparison of Kriging With Nonparametric Regression Methods. J.Multivariate Analysis. 16, 21-53.

243

Yuille, A.L., (1990) Generalized deformable models, statistical physics and matching problems. Neural Computation, 2, (1) 1-24.

244

Yuille, A.L. & Kosowski, J.J. (1994) Statistical Physics Algorithm That Converge. Neural Computation 6 (3), 341-356.

245

Yuille, A.L., Stolorz, P., & Utans, J. (1994) Statistical Physics, Mixtures of Distributions, and EM Algorithm. Neural Computation, 6 (2), 334-340.

246

Zhu, S.C. & Mumford, D.´ (1997) Prior Learning and Gibbs Reaction-Diffusion. IEEE Trans. on Pattern Analysis and Machine Intelligence 19 (11), 1236-1250.

247

Zhu, S.C. & Yuille, A.L. (1996) Region Competition: Unifying Snakes, Region Growing, and Bayes/MDL for Multiband Image Segmentation. IEEE Trans. on Pattern Analysis and Machine Intelligence 18 (9), 884-900.

248

Zhu, S.C., Wu, Y.N., & Mumford, D. (1997) Minimax Entropy principle and Its Application to Texture Modeling. Neural Computation, 9 (8).

249

Zinn-Justin, J. (1989) Quantum Field Theory and Critical Phenomena. Oxford: Oxford Science Publications.

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