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Volumn 34, Issue 2, 1996, Pages 437-472

A dynamical system approach to stochastic approximations

Author keywords

Chain recurrence; Neural networks; Ordinary differential equations; Stochastic approximations

Indexed keywords

ASYMPTOTIC STABILITY; DIFFERENTIAL EQUATIONS; NEURAL NETWORKS; RANDOM PROCESSES;

EID: 0030104967     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012993253534     Document Type: Article
Times cited : (172)

References (35)
  • 1
    • 4243064830 scopus 로고
    • Un théorème de Poincaré-Bendixson pour une classe d'equations différentielles stochastiques
    • M. BENAIM (1994a), Un théorème de Poincaré-Bendixson pour une classe d'equations différentielles stochastiques, C. R. Acad. Sci. Paris Sér. I, 318, pp. 837-839.
    • (1994) C. R. Acad. Sci. Paris Sér. I , vol.318 , pp. 837-839
    • Benaim, M.1
  • 2
    • 0000213606 scopus 로고
    • On functional approximation with normalized Gaussian units
    • _ (1994b), On functional approximation with normalized Gaussian units, Neural Computation, 6, pp. 319-333.
    • (1994) Neural Computation , vol.6 , pp. 319-333
  • 4
    • 85033843163 scopus 로고
    • Asymptotic pseudo-trajectories, chain-recurrent flows and stochastic approximations
    • to appear
    • _ (1995b), Asymptotic pseudo-trajectories, chain-recurrent flows and stochastic approximations, J. Dynamics Differential Equations, to appear.
    • (1995) J. Dynamics Differential Equations
  • 5
    • 0002951055 scopus 로고
    • Chain recurrence in surface flows
    • _ (1995c), Chain recurrence in surface flows, Discrete and Continuous Dynamics Systems, 1 (1995), pp. 1-17.
    • (1995) Discrete and Continuous Dynamics Systems , vol.1 , Issue.1995 , pp. 1-17
  • 6
    • 0002168637 scopus 로고
    • Competitive and self-organizing algorithms based on the minimization of an information criterion
    • T. Kohonen, ed., North-Holland, Amsterdam
    • M. BENAIM AND L. TOMASINI (1991), Competitive and self-organizing algorithms based on the minimization of an information criterion, in Artificial Neural Networks I, Vol. 1, T. Kohonen, ed., North-Holland, Amsterdam, pp. 391-396.
    • (1991) Artificial Neural Networks I , vol.1 , pp. 391-396
    • Benaim, M.1    Tomasini, L.2
  • 7
    • 4243144723 scopus 로고
    • Approximating function and predicting time series with multisigmoidal basis functions
    • I. Aleksander and J. Taylor, eds., Elsevier, Amsterdam
    • _ (1992), Approximating function and predicting time series with multisigmoidal basis functions, in Artificial Neural Networks II, Vol. 1, I. Aleksander and J. Taylor, eds., Elsevier, Amsterdam, pp. 407-411.
    • (1992) Artificial Neural Networks II , vol.1 , pp. 407-411
  • 9
    • 0003505303 scopus 로고
    • Translated Masson, Paris
    • A. BENVENISTE, M. MÉTIVIER, AND P. PRIOURET (1990), Stochastic Approximations and Adaptive Algorithms, Springer-Verlag, Berlin, Heidelberg, New York. Translated from Algorithmes adaptatifs et approximations stochastiques, Masson, Paris, 1987.
    • (1987) Algorithmes Adaptatifs et Approximations Stochastiques
  • 11
    • 0003262604 scopus 로고
    • Isolated Invariant Sets and the Morse Index
    • American Mathematical Society, Providence, RI
    • C. C. CONLEY (1978), Isolated Invariant Sets and the Morse Index, Regional Conference Series in Mathematics 38, American Mathematical Society, Providence, RI.
    • (1978) Regional Conference Series in Mathematics 38
    • Conley, C.C.1
  • 12
    • 0000771328 scopus 로고
    • Quadratic mean and almost sure convergence of unbounded stochastic approximation algorithms with correlated observations
    • E. EWEDA AND O. MACCHI (1983), Quadratic mean and almost sure convergence of unbounded stochastic approximation algorithms with correlated observations, Ann. Inst. H. Poincaré, 19, pp. 235-255.
    • (1983) Ann. Inst. H. Poincaré , vol.19 , pp. 235-255
    • Eweda, E.1    Macchi, O.2
  • 14
    • 0007298844 scopus 로고
    • On stochastic approximation
    • E. G. GLADYSHEV (1965), On stochastic approximation, Theory Probab. Appl., 10, pp. 275-278.
    • (1965) Theory Probab. Appl. , vol.10 , pp. 275-278
    • Gladyshev, E.G.1
  • 16
    • 3042936998 scopus 로고
    • Asymptotic phase, shadowing and reaction-diffusion systems
    • K. D. Elworthy, W. N. Everitt, and E. B. Lee, eds., Marcel Dekker, New York
    • M. W. HIRSCH (1993), Asymptotic phase, shadowing and reaction-diffusion systems, in Control Theory, Dynamical Systems and Geometry of Dynamics, K. D. Elworthy, W. N. Everitt, and E. B. Lee, eds., Marcel Dekker, New York.
    • (1993) Control Theory, Dynamical Systems and Geometry of Dynamics
    • Hirsch, M.W.1
  • 18
    • 0001079593 scopus 로고
    • Stochastic estimation of the maximum of a regression function
    • J. KIEFER AND J WOLFOWITZ (1952), Stochastic estimation of the maximum of a regression function, Ann. Math. Statist., 23, pp. 462-466.
    • (1952) Ann. Math. Statist. , vol.23 , pp. 462-466
    • Kiefer, J.1    Wolfowitz, J.2
  • 19
    • 0041553895 scopus 로고
    • Artificial neural networks: An econometric perspective
    • to be published
    • C. M. KUAN AND H. WHITE (1992), Artificial neural networks: An econometric perspective, Econometric Reviews, to be published.
    • (1992) Econometric Reviews
    • Kuan, C.M.1    White, H.2
  • 21
    • 0017526570 scopus 로고
    • Analysis of recursive stochastic algorithms
    • L. LJUNG (1977), Analysis of recursive stochastic algorithms, IEEE Trans. Automat. Control, AC-22, pp. 551-575.
    • (1977) IEEE Trans. Automat. Control , vol.AC-22 , pp. 551-575
    • Ljung, L.1
  • 22
    • 0001915127 scopus 로고
    • A maximal inequality and dependent strong laws
    • D. L. MCLEISH (1975), A maximal inequality and dependent strong laws, Ann. Probab., 3, pp. 829-839
    • (1975) Ann. Probab. , vol.3 , pp. 829-839
    • Mcleish, D.L.1
  • 23
    • 0021385812 scopus 로고
    • Application of a Kushner and Clark lemma to general classes of stochastic algorithms
    • M. MÉTIVIER AND P. PRIOURET (1984), Application of a Kushner and Clark lemma to general classes of stochastic algorithms, IEEE Trans. Inform. Theory, IT-30, pp. 140-150
    • (1984) IEEE Trans. Inform. Theory , vol.IT-30 , pp. 140-150
    • Métivier, M.1    Priouret, P.2
  • 24
    • 0013198589 scopus 로고
    • Théorèmes de convergence presque sure pour une classe d'algorithmes stochastiques à pas décroissant
    • _ (1987), Théorèmes de convergence presque sure pour une classe d'algorithmes stochastiques à pas décroissant, Probab. Theory Related Fields, 74, pp. 403-428.
    • (1987) Probab. Theory Related Fields , vol.74 , pp. 403-428
  • 25
    • 0000672424 scopus 로고
    • Fast learning in networks of locally-tuned processing units
    • J. MOODY AND C. DARKEN (1989), Fast learning in networks of locally-tuned processing units, Neural Computation, 1, pp. 281-582.
    • (1989) Neural Computation , vol.1 , pp. 281-582
    • Moody, J.1    Darken, C.2
  • 26
    • 0004263792 scopus 로고
    • Stochastic Approximation and Recursive Estimation
    • American Mathematical Society, Providence, RI
    • M. B. NEVEL'SON AND R. Z. HAS'MINSKII (1974), Stochastic Approximation and Recursive Estimation, Translation of Math. Monographs 47, American Mathematical Society, Providence, RI.
    • (1974) Translation of Math. Monographs 47
    • Nevel'son, M.B.1    Has'minskii, R.Z.2
  • 29
    • 49849128478 scopus 로고
    • On Morse-Smale dynamical systems
    • J. PALIS (1969), On Morse-Smale dynamical systems, Topology, 8, pp. 385-405.
    • (1969) Topology , vol.8 , pp. 385-405
    • Palis, J.1
  • 30
    • 0001000786 scopus 로고
    • Nonconvergence to unstable points in urn models and stochastic approximations
    • R. PEMANTLE (1990), Nonconvergence to unstable points in urn models and stochastic approximations, Ann. Probab., 18, pp. 698-712.
    • (1990) Ann. Probab. , vol.18 , pp. 698-712
    • Pemantle, R.1
  • 31
    • 0025056697 scopus 로고
    • Regularization algorithms for learning that are equivalent to multilayer networks
    • T. POGGIO AND F. GIROSI (1990), Regularization algorithms for learning that are equivalent to multilayer networks, Science, 247, pp. 979-982.
    • (1990) Science , vol.247 , pp. 979-982
    • Poggio, T.1    Girosi, F.2
  • 32
    • 0000016172 scopus 로고
    • A stochastic approximation method
    • H. ROBBINS AND S. MONRO (1951), A stochastic approximation method, Ann. Math. Statist., 22, pp. 400-407.
    • (1951) Ann. Math. Statist. , vol.22 , pp. 400-407
    • Robbins, H.1    Monro, S.2
  • 33
    • 0001570568 scopus 로고
    • Stability theorems and hyperbolicity in dynamical systems
    • C. ROBINSON (1977), Stability theorems and hyperbolicity in dynamical systems, Rocky J. Math., 7, pp. 425-434.
    • (1977) Rocky J. Math. , vol.7 , pp. 425-434
    • Robinson, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.