Neural networks: A review from a statistical perspective

Statistical Science

Volumn 9, Issue 1, 1994, Pages 2-30

  Cheng, Bing ^a   Titterington, D M ^b  

^a UNIVERSITY OF KENT   (United Kingdom)

^b UNIVERSITY OF GLASGOW   (United Kingdom)

Author keywords

Artificial intelligence; Artificial neural networks; Cluster analysis; Discriminant analysis; Gibbs distributions; Incomplete data; Nonparametric regression; Statistical pattern recognition

Indexed keywords

EID: 84972539015     PISSN: 08834237     EISSN: None     Source Type: Journal    
DOI: 10.1214/ss/1177010638     Document Type: Article

References (206)

1. Aarts, E. H. L. and Korst, J. H. M. (1989). Simulated Annealing and Boltzmann Machines. Wiley, New York.
2. Ackley, D. H., Hinton, G. E. and Sejnowski, T. J. (1985). A learning algorithm for Boltzmann machiiles. Cognitive Science 9 147-169.
3. Akaike, H. (1974). Information theory and an extension of the maximum likelihood principle. In Second International Symposium on Information Theory (B. N. Petrov and F. Csaki, eds.) 261-281. Akademia Kiedo, Budapest.
4. Aleksander, I., Ed. (1989). Neural Computing Architectures: The Design of Brain-Like Machines. North Oxford, London.
5. Amari, S. I. (1990). Mathematical foundations of neurocomputing. Proc. IEEE 78 1443-1463.
6. Amari, S. I., Kurato, K. and Nagaoka, W. (1992). Information geometry of Boltzmann machines. IEEE Trans. Neural Networks 3 260-271.
7. Amit, D. (1989). Modelling Brain Function. Cambridge Univ. Press.
8. Amit, D. J., Gutfreund, H. and Sompolinsky, H. (1985a). Spinglass models of neural networks. Phys. Rev. A 32 1007-1018.
9. Amit, D. J., Gutfreund, H. and Sompolinsky, H. (1985b). Storing infinite numbers of patterns in a spin-glass model of neural networks. Phys. Rev. Lett. 55 1530-1533.
10. Anderson, J. A. and Rosenfeld, E., Eds. (1988). Neurocomputing: Foundations of Research. MIT Press.
11. Anderson, N. H. and Titterington, D. M. (1993). Beyond the binary Boltzmann machine. Preprint.
12. Antognetti, P. and Milutinovic, V. (1991). Neural Networks: Concepts, Applications and Implementations. Vol. I. Prentice-Hall, Englewood Cliffs, NJ.
13. Barron, A. R. (1989). Statistical properties of artificial neural networks. Proceedings of the 28th IEEE International Conference on Decision and Control 1 280-285. IEEE, New York.
14. Barron, A. R. (1991). Complexity regularization with application to artificial neural networks. In Nonparametric Function Estimation and Related Topics (G. Roussas, ed.) 561-576. Kluwer, Dordrecht.
15. Barron, A. R. (1992). Neural net approximation. In Proc. 7th Yale Workshop on Adaptive and Learning Systems (K S. Narendra, ed.) 69-72. Yale Univ., New Haven.
16. Barron, A. R. (1993). Universal approximation bounds for superpositions of a sigmoidal function. IEEE Trans. Inform. Theory 39 930-945.
17. Barron, A. R. (1994). Approximation and estimation bounds for artificial neural networks. Machine Learning 14 115-133.
18. Barron, A. R. and Barron, R. L (1988). Statistical learning networks: a unifying view. In Computing Science and Statistics: Proceedings of the 10th Symposium on the Interface (E. G. Wegman, ed.) 192-203. Amer. Statist. Assoc., Washington, DC.
19. Barron, A. R. and Xiao, X. (1991). Comment on "Multivariate adaptive regression splines," by J. H. Friedman. Ann. Statist. 19 67-82.
20. Bas, C. F. and Marks, R. J. (1991). Layered perceptron versus Neyman-Pearson optimal detection. In Proceedings of the 1991 IEEE Conference on Neural Networks 1486-1489. IEEE, New York.
21. Baum, E. B. and Haussler, D. (1989). What size net gives valid generalization? Neural Computation 1 151-160.
22. Bengio, Y., Demori, R., Flammia, G. and Kompe, R. (1992). Global optimization of a neural network-hidden Markov model hybrid. IEEE Trans. Neural Networks 3 252-258.
23. Besag, J. and Green, P. J. (1993). Spatial statistics and Bayesian computation. J. Roy. Statist. Soc. Ser. B 55 25-37.
24. Bienenstock, E. L. and Von Der Malsburg, C. (1987). A neural network for invariant pattern recognition. Europhysics Letters 4 121-126.
25. Bishop, Y. M. M., Fienberg, S. E. and Holland, P.W. (1975). Discrete Multivariate Analysis. MIT Press.
26. Bornholdt, S. and Graudenz, D (1992). General asymmetric neural networks and structure design by genetic algorithms. Neural Networks 5 327-334.
27. Bourlard, H. E. (1990). How connectionist models could improve Markov models for speech recognition. In Advanced Neural Computers (R. E. Eckmiller, ed.) 247-254. North-Holland, Amsterdam.
28. Bourlard, H. E. and Morgan, N. (1991). Merging multilayer perceptron and hidden Markov models: some experiments in continuous speech recognition. In Neural Networks: Advances and Applications (E. Gelenbe, ed.) 215-239. North-Holland, Amsterdam.
29. Breiman, L. (1993). Hinging hyperplanes for regression classification and function approximation. IEEE Trans. Inform. Theory 39 999-1013.
30. Breiman, L. Friedman, J. H., Olshen, R. A. and Stone, C. J. (1984). Classification and Regression Trees. Wadsworth, Belmont, CA.
31. Breiman, L. and Ihaka, R. (1984). Nonlinear discriminant analysis via ACE and scaling. Tech. Report 40, Dept. Statistics, Univ. California, Berkeley.
32. Bresshoff, P. C. and Taylor, J. G. (1990). Random iterative networks. Phys. Rev. A 41 1126-1137.
33. Bridle, J. S. (1990). Probabilistic interpretation of feedforward classification network outputs, with relationships to statistical pattern recognition. In Neuro-computing: Algorithms, Architectures and Applications (F. Fougleman-Soulie and J. Herault, eds.) 227-236. Springer, New York.
34. Bridle, J. S. (1992). Neural networks or hidden Markov models for automatic speech recognition: is there a choice? In Speech Recognition and Understanding: Recent Advances, Trends and Application (P. LaFace, ed.) 225-236. Springer, New York.
35. Broomhead, D. S. and Lowe, D. (1988). Multivariate functional interpolation and adaptive networks. Complex Systems 2 321-355.
36. Bryson, A. E. and Ho, Y. C. (1969). Applied Optimal Control. Blaisdell, New York.
37. Buntine, W. L. and Weigend, A. S. (1991). Bayesian back-propagation. Complex Systems 5 603-643.
38. Byrne, W. (1992) Alternating minimization and Boltzmann machine learning. IEEE Trans. Neural Networks 3 612-620.
39. Campbell, C., Sherrington, D. and Wong, K Y. M. (1989). Statistical mechanics and neural networks. In Neural Computing Architectures: The Design of Brain-Like Machines (I. Aleksander, ed.) 239-257. North Oxford, London.
40. Carpenter, G. A. and Grossberg, S. (1988). The ART of adaptive pattern recognition by a self-organizing neural network. Computer 21 77-88.
41. Casdagli, M. (1989). Nonlinear prediction of chaotic time series. Phys. D 35 335-356.
42. Cheng, B. and Titterington, D. M. (1994). A small selection of neural network methods and their statistical connections. In Statistics and Images II (K. V. Mardia, ed.) Carfax, Abingdon, lb appear.
43. Cox, D. R. and Snell, E. J. (1989). Analysis of Binary Data. Chapman and Hall, London.
44. Craven, P. and Wahba, G. (1979). Smoothing noisy data with spline functions. Numer. Math. 31 377-403.
45. Csiszar, I. and Tusnady, G. (1984). Information geometry and alternating minimization procedures. In Statist. Decisions Suppl. 1 205-237. Oldenbourg, Munich.
46. Cybenko, G. (1989). Approximation by superpositions of a sigmoidal function. Math. Control Signals System 2 303-314.
47. Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm (with discussion). J. Roy. Statist. Soc. Ser. B 39 1-38.
48. Duane, S., Kennedy, A. D., Pendleton, B. J. and Roweth, D. (1987). Hybrid Monte Carlo. Phys. Lett. B 195 216-222.
49. Duda, R. O. and Hart, P. E. (1973). Pattern Classification and Scene Analysis. Wiley, New York
50. Eckmiller, R. E. (Ed.) (1990). Advanced Neural Computers. North-Holland, Amsterdam.
51. Eckmiller, R. E., Hartmann, G. and Hauske, G., Eds. (1990). Parallel Processing in Neural Systems and Computers. North-Holland, Amsterdam.
52. Eckmiller, R. E. and Von Der Malsburg, C., Eds. (1988). Neural Computers. NATO ASI Series. Springer, Berlin.
53. Efron, B. (1964). The perceptron correction procedure in non-separable situations. Technical report RADC-TDR-63-533. Rome Air Development Center, Rome, NY.
54. Fabian, V. (1968). On asymptotic normality in stochastic approximation. Ann. Math. Statist. 39 1327-1332.
55. Farmer, J. D. and Sidorowich, J. J. (1989). Predicting chaotic dynamics. In Dynamic Patterns in Complex Systems (Kelso, J. A. S., Mandell, A. J. and Shlesinger, M. F., eds.) 265-292. World Scientific, Singapore.
56. Fisher, R. A. (1936). The use of multiple measurements in taxonomic problems. Ann. Eugenics 7 179-184.
57. Friedman, J. H. (1989). Regularized discriminant analysis. J. Amer. Statist. Assoc. 84 165-188.
58. Friedman, J. H. (1991). Multivariate adaptive regression splines (with discussion). Ann. Statist. 19 1-141.
59. Friedman, J. H. and Silverman, B. W. (1989). Flexible parsimonious smoothing and additive modeling (with discussion). Technometrics 31 3-39.
60. Friedman, J. H. and Stuetzle, W. (1981). Projection pursuit regression. J. Amer. Statist. Assoc. 76 817-823.
61. Fukumi, M., Omatu, S., Takeda, F. and Kosaka, T. (1992). Rotation invariant neural pattern recognition systems with application to coin recognition. IEEE Trans. Neural Networks 3 272-279.
62. Gawthrop, R J. and Sbarbaro, D. G. (1990). Stochastic approximation and multilayer perceptrons: the gain backpropagation algorithm. Complex Systems 4 51-74.
63. Gelenbe, E. (1991a). Theory of the random neural network model. In Neural Networks: Advances and Applications 1-20. North-Holland, Amsterdam.
64. Gelenbe, E., Ed. (1991b). Neural Networks: Advances and Applications. North-Holland, Amsterdam.
65. Geman, S., Bienenstock, E. and Doursat, R. (1992). Neural networks and the bias/variance dilemma. Neural Computation 4 1-58.
66. Geman, S. and Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence 6 721-741.
67. Gersho, A. (1982). On the structure of vector quantizers. IEEE Trans. Inform. Theory 28 157-166.
68. Girosi, F. and Poggio, T. (1990). Networks and the best approximation property. Biol. Cybernet. 63 169-176.
69. Goldberg, D. E. (1989). Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading, MA.
70. Gordon, A. (1981). Classification. Chapman and Hall, London.
71. Gray, R. M. (1982). Editorial for special issue. IEEE Trans. Inform. Theory 28 127-128.
72. Gray, R. M. (1990). Source Coding Theory. Kluwer, Boston.
73. Hand, D. J. (1981). Discrimination and Classification. Wiley, New York.
74. Hartigan, J. A. (1975). Clustering Algorithms. Wiley, New York.
75. Hartigan, J. A. (1978). Asymptotic distributions for clustering criteria. Ann. Statist. 6 117-131.
76. Hastie, T., Buja, A. and Tibshirani, R. (1992). Penalized discriminant analysis. Preprint.
77. Hastie, T. and Tibshirani, R. (1990). Generalized Additive Models. Chapman and Hall, London.
78. Hastie, T., Tibshirani, R., and Buja, A. (1992). Flexible discriminant analysis. Preprint.
79. Hebb, D. O. (1949). The Organization of Behavior: A Neurophysiological Theory. Wiley, New York.
80. Hecht-Nielsen, R. (1990). Neurocomputing. Addison-Wesley, Reading, MA.
81. Hertz, J., Krogh, A. and Palmer, R. G. (1991). Introduction to the Theory of Neural Computation. Addison-Wesley, Reading, MA.
82. Hinton, G. E. (1986). Learning distributed representations of ' concepts. In Proceedings of the Eighth Annual Conference of the Cognitive Science Society 1-12. Erlbaum, Hillsdale, NJ.
83. Hinton, G. E. (1989). Connectionist learning procedures. Artif. Intell. 40 185-234.
84. Hinton, G. E. (1992). How neural networks learn from experience. Scientific American 267 104-109.
85. Hinton, G. E. and Sejnowski, T. J. (1986). Learning and relearning in Boltzmann machines. In Parallel Distributed Processing: Explorations in the Microstructure of Cognition, Vol. 1 (D. E. Rumelhart, G. E. Hintori and R. J. Williams, eds.) 282-317. MIT Press.
86. Hopfield, J. J. (1982). Neural networks and physical systems with emergent collective computational abilities. Proc. Nat. Acad. Sci, U.S.A. 79 2554-2558.
87. Hopfield, J. J. (1984). Neurons with graded response have collective computational properties like those of two-state neurons. Proc. Nat. Acad. Sci. U.S.A. 81 3088-3092.
88. Hopfield, J. J. and Tank, D. W. (1985). Neural computation of decisions in optimization problems. Biol. Cybernet. 52 141-152.
89. Hornik, K, Stinchcombe, M. and White, H. (1989). Multilayer feedforward networks are universal approximators. Neural Networks 2 359-366.
90. Hunt, K J., Sbarbaro, D., Zbikowski, R. and Gawthrop, P.J. (1992). Neural networks for control systems-a survey. Automatica 28 1083-1112.
91. Johnson, R. C. and Brown, C. (1988). Cognizers: Neural Networks and Machines That Think. Wiley, New York.
92. Jones, L. K. (1992). A simple lemma on greedy approximation in Hilbert Space and convergence rates for projection pursuit regression and neural network training. Ann. Statist. 20 608-613.
93. Kanal, L. (1993). On patterns, categories and alternate realities. Pattern Recognition Letters 14 241-255.
94. Kass, R. E. and Raftery, A. E. (1993). Bayes factors and model uncertainty. Technical Report 571, Dept. Statistics, Carnegie Mellon Univ.
95. Kieffer, J. C. (1982). Exponential rate of convergence for Lloyd’s method 1. IEEE Trans. Inform. Theory 28 205-210.
96. Kohonen, T. (1982). Self-organized formation of topologically correct feature maps. Biol. Cybernet. 43 59-69.
97. Kohonen, T. (1989). Self-organization and Associative Memory, 3rd ed. Springer, Berlin.
98. Kohonen, T. (1990) Internal representations and associative memory. In Parallel Processing in Neural Systems and Computers (R. E. Eckmiller, G. Hartman and G. Hauske, eds.) 177-182. North-Holland, Amsterdam.
99. Kohonen, T., Makisara, K., Simula, O. and Kangas, J., Eds. (1991). Artificial Neural Networks 1, 2. North-Holland, Amsterdam.
100. Komlos, J. and Paturi, R. (1988). Convergence results in an associative memory model. Neural Networks 1 239-250.
101. Kressel, U. W-G. (1991). The impact of the learning-set size in handwritten-digit recognition. In Artificial Neural Networks (T. Kohonen, K. Makisara, O. Simula and J. Kangas, eds.) 2 1685-1690. North-Holland, Amsterdam.
102. Kuhnel, H. and Traven, P. (1991). A network for discriminant analysis. In Artificial Neural Networks (T. Kohonen, K. Makisara, O. Simula and J. Kangas, eds.) 2 1053-1056. North Holland, Amsterdam.
103. Lachenbruch, P.A. and Mickey, M.R. (1968). Estimation of error rates in discriminant analysis. Technometrics 10 1-10.
104. Lapedes, A. and Farber, R. (1987). Nonlinear signal processing using neural networks. Technical Report LA-UR-87-2662, Los Alamos National Laboratory, Los Alamos, NM.
105. Lauritzen, S. L. and Spiegelhalter, D. J. (1988). Local computations with probabilities in graphical structures and their applications to expert systems (with discussion). J. Roy. Statist. Soc. Ser. B 50 157-224.
106. Le Cun, Y., Boser, B., Denker, J. S., Henderson, D., Howard, R. E., Hubbard, W. and Jackel, L. D. (1989). Backpropagation applied to handwritten Zip code recognition. Neural Computation 1 541-551.
107. Le Cun, Y., Boser, B., Denker, J. S., Henderson, D., Howard, R. E., Hubbard, W. and Jackel, L.D. (1990). Handwritten digit recognition with a backpropagation network. In Advances in Neural Information Processing Systems II (D. S. Touretzky, eds.) 396-404. Morgan Kaufmann, San Mateo, CA.
108. Levin, E., Tishby, N. and Solla, S. A. (1990). A statistical approach to learning and generalization in layered neural networks. Proc. IEEE 78 1568-1574.
109. Lim, G. S., Alder, M. and Hadingham, P. (1992). Adaptive quadratic neural nets. Pattern Recognition Letters 13 325-329.
110. p, C, cross-validation and generalized cross-validation: Discrete index set. Ann. Statist. 15 958-975.
111. Linde, Y., Buzo, A. and Gray, R. M. (1980). An algorithm for vector quantizer design. IEEE Trans. Communications Technology 28 84-95.
112. Lindsay, B. G. and Roeder, K (1992). Residual diagnostics for mixture models. J. Amer. Statist. Assoc. 87 785-794.
113. Lippmann, R. R (1987). An introduction to computing with neural nets. IEEE Acoustics, Speech and Signal Processing Magazine 4(April) 4-22.
114. Little, W. A. (1974). The existence of persistent states in the brain. Math. Biosci. 19 101-120.
115. Lloyd, S. P. (1957). Least squares quantization in PCM. Bell Labs memorandum. Reprinted (1982) in IEEE Trans. Inform. Theory 28 84-95.
116. Lorentz, G. (1966). Approximation of Functions. Holt, Rinehart and Winston, New York.
117. Lowe, D. (1991). On the statistical inversion of RBF networks: a statistical interpretation. In Proceedings of the Second IEE International Conference on Artificial Neural Networks. IEE, London.
118. Lowe, D. and Webb, A. R. (1990). Exploiting prior knowledge in network optimization: an illustration from medical prognosis. Network 1 299-323.
119. Lowe, D. and Webb, A. R. (1991). Optimal feature extraction and the Bayes decision in feed-forward classifer networks. IEEE Transactions on Pattern Analysis and Machine Intelligence 13 355-364.
120. Luttrell, S. P. (1990). Derivation of a class of training algorithms. IEEE TVans. Neural Networks 1 2.2&-2S2,.
121. Luttrell, S. P. (1991). Code vector density in topographic mappings: scalar case. IEEE Trans. Neural Networks 2 427-436.
122. Luttrell, S. P. (1992). Self-supervized adaptive networks. IEE Proceedings F-Radar and Signal Processing 139 371-377.
123. Mackay, D. J. C. (1992a). Bayesian interpolation. Neural Computation 4 415-447.
124. Mackay, D. J. C. (1992b). A practical Bayesian framework for backpropagation networks. Neural Computation 4 448-472.
125. Mclachlan, G. J. (1992). Discriminant Analysis and Statistical Pattern Recognition. Wiley, New York.
126. Mclachlan, G. J. and Basford, K E. (1988). Mixture Models: Inference and Applications to Clustering. Dekker, New York.
127. Macqueen, J. B. (1967). Some methods for classification and analysis of multivariate observations. In Proc. Fifth Berkeley Symp. Math. Statist. Probab. 281-297. Univ. California Press, Berkeley.
128. Mallows, C. L. (1973). Some comments on Cp. Technometrics 15 661-675.
129. Mardia, K V., Kent, J. T. and Bibby, J. M. (1979). Multivariate Analysis. Academic, New York.
130. Mcculloch, W. S. and Pitts, W. (1943). A logical calculus of ideas immanent in nervous activity. Bulletin of Mathematical Biophysics 5 115-133.
131. Mceliece, R. J., Posner, E. C., Rodemich, E. R., and Venkatesh, S. S. (1987). The capacity of the Hopfield associative memory. IEEE Trans. Inform. Theory 33 461-482.
132. Minsky, M. L. and Papert, S. A. (1969). Perceptrons. MIT Press.
133. Minsky, M. L. and Papert, S. A. (1988). Perceptrons, 2nd ed. MIT Press.
134. Moody, J. E. (1992). The effective number of parameters: an analysis of generalization and regularization in nonlinear learning systems. In Advances in Neural Information Processing Systems 4 (J. E. Moody, S. J. Hanson and R. P. Lippmann, eds.) 847-854. Morgan Kaufmann, San Mateo, CA.
135. Moody, J. E. and Darken, C. (1989). Fast learning in networks of locally-tuned processing units. Neural Computation 1281-294.
136. Mpitsos, G. J. and Burton, R. M. (1992). Convergence and divergence in neural networks: processing of chaos and biological analogy. Neural Networks 5 605-625.
137. Muller, B. and Reinhardt, J. (1990). Neural Networks: An Introduction. Springer, Berlin.
138. Neal, R. M. (1992a). Bayesian training of backpropagation networks by the hybrid Monte Carlo method. Preprint.
139. Neal, R. M. (1992b). Connectionist learning of belief networks. Artif. Intell. 56 71-113.
140. Neal, R. M. (1993). Bayesian learning via stochastic dynamics. In Advances in Neural Information Processing Systems 5 (C. L. Giles, S. J. Hanson and J. D. Cowan, eds.) 475-482. Morgan Kaufmann, San Mateo, CA.
141. Newman, C. M. (1988). Memory capacity in neural network models: rigorous lower bounds. Neural Networks 1 223-238.
142. Nychka, D., Ellner, S., Gallant, A. R. and Mccaffrey, D. (1992). Finding chaos in noisy systems. J. Roy. Statist. Soc. Ser. B 54 399-426.
143. Oja, E. (1982). A simplified neuron model as a principal component analyzer. J. Math. Biol. 15 267-273.
144. Panel on Discriminant Analysis, Classification and Clustering (1989). Discriminant Analysis and Clustering. Statist. Sci. 4 34-69.
145. Parker, D. B. (1985). Learning logic. Technical Report 47, Center for Computational Research in Economics and Management Science, MIT.
146. Pearl, J. (1988). Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Mateo, CA.
147. Perantonis, S. and Lisboa., P. J. G. (1992). Translation, rotation and scale invariant pattern recognition by high-order neural networks and moment classifiers. IEEE Trans. Neural Networks 3 241-251.
148. Poggio, T. (1990). A parallel vision machine that learns. In Models of Brain Functions (R.M. J. Cotterill, ed.) 3-34, Cambridge Univ. Press.
149. Poggio, T. and Girosi, F. (1990). Networks for approximation and learning. Proc. IEEE 78 1481-1497.
150. Pollard, D. (1981). Strong consistency of /£-means clustering. Ann. Statist. 9 135-140.
151. Pollard, D. (1982a). Quantization and the method of HT-means. IEEE Trans. Inform. Theory 28 199-205.
152. Pollard, D. (1982b). A central limit theorem for K-means clustering. Ann. Statist. 10 119-205.
153. Quinlan, J. R. (1983). Learning efficient classification procedures and their application to chess end-games. In Machine Learning (R.S. Michalski, J. G. Carbonelli and T. M. Mitchell, eds.) 463-482. Tioga, Palo Alto, CA.
154. Richard, M. D. and Lippmann, R. P. (1992). Neural network classifiers estimate Bayesian a posteriori probabilities. Neural Computation 3 461-483.
155. Ripley, B. D. (1993a). Statistical aspects of neural networks. In Networks and Chaos-Statistical and Probabilistic Aspects (O. E. Bamdorff-Nielsen, J. L. Jensen and W. S. Kendall, eds.) 40-123. Chapman and Hall, London.
156. Ripley, B. D. (1994a). Neural networks and related methods for classification (with discussion). J. Roy. Statist. Soc. Ser. B 56. Td appear.
157. Rissanen, J. (1987). Stochastic complexity. J. Roy. Statist Soc. Ser. B 49 223-239.
158. Robbins, H. and Monro, S. (1951). A stochastic approximation method. Ann. Math. Statist. 22 400-407.
159. Ritter, H. and Schulten, K (1986). On the stationary state of Kohonen’s self-organizing sensory mapping. Biol. Cybernet. 54 99-106.
160. Rosenblatt, F. (1962). Principles of Neurodynamics. Spartan, New York.
161. Rujan, P. (1991). A fast method for calculating the perceptron with maximal stability. Preprint, Univ. Oldenburg, Germany.
162. Rumelhart, D. E., Hinton, G. E. and Williams, R. J. (1986a). Learning internal representation by back-propagating errors. Nature 323 533-536.
163. Rumelhart, D. E., Hinton, G. E. and Williams, R. J. (1986b). Learning internal representation by back-propagating errors. In Parallel Distributed Processing: Explorations in the Microstructure of Cognition (D. E. Rumelhart, J. L. McClelland and the PDP Research Group, eds.). MIT Press.
164. Rumelhart, D. E., Mcclelland, J. L. and the PDP Research Group (1986). Parallel Distributed Processing: Explorations in the Microstructure of Cognition. MIT Press.
165. Rumelhart, D. E. and Zipser, D. (1985). Feature discovery by competitive learning. Cognitive Science 9 75-112.
166. Sanger, T. D. (1989). Optimal unsupervized learning in a singlelayer linear feedforward neural network. Neural Networks 2 459-473.
167. Schwartz, G. (1978). Estimating the dimension of a model. Ann. Statist. 6 461-464.
168. Seber, G. A. F. and Wild, C. J. (1989). Nonlinear Regression. Wiley, New York.
169. Sejnowski, T. J. and Rosenberg, C. R. (1987). Parallel networks that learn to pronounce English text. Complex Systems 1 145-168.
170. Sethi, I. K and Jain, A. K, Eds. (1991). Artificial Neural Networks and Statistical Pattern Recognition. North-Holland, Amsterdam.
171. Shibata, R. (1981). An optimal selection of regression variables. Biometrika 68 45-54.
172. Silverman, B. W. (1985). Some aspects of the spline smoothing approach to nonparametric regression curve estimation (with discussion). J. Roy. Statist. Soc. Ser. B 47 1-52.
173. Silverman, B. W. (1986) Density Estimation for Statistics and Data Analysis. Chapman and Hall, London.
174. Smith, A. F. M. and Spiegelhalter, D. J. (1980). Bayes factors and choice criteria for linear models. J. Roy. Statist. Soc. Ser. B 42 213-220.
175. Smith, A. F. M. and Roberts, G. O. (1993). Bayesian computation by the Gibbs sampler andxelated Markov chain Monte Carlo methods. J. Roy. Statist. Soc. Ser. B 55 3-23.
176. Smolensky, P. (1986). Information processing in dynamical systems: foundations of harmony theory. In Parallel Distributed Processing: Explorations in the Microstructure of Cognition (D. E. Rumelhart, J. L. McClelland and the PDP Research Group, eds.) 194-281. MIT Press.
177. Sorenson, H. W. and Alspach, D. L. (1971). Recursive Bayesian estimation using Gaussian sums. Automatica 7 465-479.
178. Specht, D. F. (1990). Probabilistic neural networks. Neural Networks 3 109-118.
179. Specht, D. F. (1991). A general regression neural network. IEEE Trans. Neural Networks 2 568-576.
180. Spiegelhalter, D. J. and Lauritzen, S. L. (1990). Sequential updating of conditional probabilities on directed graphical structures. Networks 20 579-605.
181. Stokbro, K., Umberger, D. K. and Hertz, J. A. (1990). Exploiting neurons with localized receptive fields to learn chaos. Complex Systems 4 603-622.
182. Stone, M. (1974). Cross-validatory choice and assessment of statistical predictions (with discussion). J. Roy. Statist. Soc. Ser. B 36 111-147.
183. Tibshirani, R. (1992). Slide functions for projection pursuit regression and neural networks. Preprint, Univ. Toronto.
184. Titterington, D. M. (1984). Comments on "Application of the conditional population-mixture model to image segmentation" by S. C. Sclove. IEEE Transactions on Pattern Analysis and Machine Intelligence 6 656-658.
185. Titterington, D. M. (1985). Common structure of smoothing techniques in statistics. Internat. Statist. Rev. 53 141-170.
186. Titterington, D. M. (1990). Some recent research in the analysis of mixture distributions. Statistics 21 619-641.
187. Titterington, D. M., Murray, G. D., Murray, L. S., Spiegelhalter, D. J., Skene, A. M., Habbema, J. D. F. and Gelpke, G. J. (1981). Comparison of discrimination techniques applied to a complex data set of head injured patients (with discussion). J. Roy. Statist. Soc. Ser. A 144 145-175.
188. Titterington, D. M., Smith, A. F. M. and Makov, U. E. (1985). Statistical Analysis of Finite Mixture Distributions. Wiley, New York.
189. Traven, H. G. C. (1991). A neural network approach to statistical pattern classification by "semiparametric" estimation of probability density functions. IEEE Trans. Neural Networks 2 366-377.
190. Van Ryzin, J. (1977). Classification and Clustering. Academic, New York.
191. Vapnik, V. N. (1982). Estimation of Dependencies Based on Empirical Data. Springer, New York.
192. Vijaya Kumar, B. V. K and Wong, P. H. (1991). Optical associative memories. In Artificial Neural Networks and Statistical Pattern Recognition (I. K Sethi and A. K. Jain, eds.) 219-241. North-Holland, Amsterdam.
193. Wahba, G. (1990). Spline Models for Observational Data. SIAM, Philadelphia.
194. Waltz, D. and Feldman, J. A. (1988). Connectionist Models and their Applications. Ablex, Norwood, NJ.
195. Webb, A. R. Lowe, D. and Bedworth, M. D. (1988). A comparison of nonlinear optimisation strategies for feed-forward adaptive layered networks. Memorandum 4157, RSRE, Great Malvern, UK
196. Wendemuth, A. (1993). Learning optimal threshold and weights for the perceptron of maximal stability. Preprint, Dept. Theoretical Physics, Oxford Univ.
197. Werbos, P. J. (1974). Beyond Regression: new tools for prediction and analysis in the behavioral sciences. Ph.D. Thesis, Harvard Univ.
198. White, H. (1989). Some asymptotic results for learning in single hidden layer feedforward networks. J. Amer. Statist. Assoc. 84 1008-1013.
199. White, H. (1990) Connectionist nonparametric regression: multilayer feedforward networks can learn arbitrary mappings. Neural Networks 3 535-549.
200. White, H. (1992). Artificial Neural Networks: Approximation and Learning Theory. Blackwell, Oxford.
201. Whittaker, J. (1990). Graphical Models in Applied Multivariate Statistics. Wiley, New York.
202. Whittle, P. (1991). Neural nets and implicit inference. Ann. Appl. Probab. 1 173-188.
203. Widrow, B. and Hoff, M. E. (1960). Adaptive switching circuits. In 1960 IRE Western Electric Show and Convention Record 96-104. IRE, New York.
204. Willshaw, D. J. and Von Der Malsburg, C. (1976). How patterned neural connections can be set up by self-organization. Proc. Roy. Soc. London Ser. B 194 431-445.
205. Wolpert, D. H. (1992). Stacked generalization. Neural Networks 5 241-259.
206. Zhang, D. and Benveniste, A. (1992). Wavelet networks. IEEE Trans. Neural Networks 3 889-898.