메뉴 건너뛰기




Volumn 68, Issue 3, 2007, Pages 201-233

Annealing stochastic approximation Monte Carlo algorithm for neural network training

Author keywords

Back propagation; Convergence rate; Markov chain Monte Carlo; Multiple layer perceptron; Simulated annealing; Stochastic approximation; Wang Landau algorithm

Indexed keywords

APPROXIMATION ALGORITHMS; NEURAL NETWORKS; SIMULATED ANNEALING; STOCHASTIC MODELS;

EID: 34548179892     PISSN: 08856125     EISSN: 15730565     Source Type: Journal    
DOI: 10.1007/s10994-007-5017-7     Document Type: Article
Times cited : (37)

References (79)
  • 1
    • 0008752912 scopus 로고
    • A statistical analysis of the effect of noise injection during neural network training
    • Abunawass, A. M., & Owen, C. B. (1993). A statistical analysis of the effect of noise injection during neural network training. SPIE Proceedings, 1966, 362-371.
    • (1993) SPIE Proceedings , vol.1966 , pp. 362-371
    • Abunawass, A.M.1    Owen, C.B.2
  • 3
    • 33244461073 scopus 로고    scopus 로고
    • Stability of Stochastic Approximation under Verifiable Conditions
    • Andrieu, C., Moulines, E., & Priouret, P. (2005). Stability of Stochastic Approximation Under Verifiable Conditions. SIAM J. Control and Optimization, 44, 283-312.
    • (2005) SIAM J. Control and Optimization , vol.44 , pp. 283-312
    • Andrieu, C.1    Moulines, E.2    Priouret, P.3
  • 4
    • 0027599793 scopus 로고
    • Universal approximation bounds for superposition of a sigmoidal function
    • Barron, A. (1993). Universal approximation bounds for superposition of a sigmoidal function. IEEE Transactions on Information Theory, 3, 930-945.
    • (1993) IEEE Transactions on Information Theory , vol.3 , pp. 930-945
    • Barron, A.1
  • 5
    • 0000389960 scopus 로고
    • Constructing hidden units using examples and queries
    • Kaufmann San Mateo
    • Baum, E. B., & Lang, K. J. (1991). Constructing hidden units using examples and queries. In Advances in neural information processing systems (Vol. 3, pp. 904-910). San Mateo: Kaufmann.
    • (1991) Advances in Neural Information Processing Systems , vol.3 , pp. 904-910
    • Baum, E.B.1    Lang, K.J.2
  • 7
    • 0033329123 scopus 로고    scopus 로고
    • Stochastic approximation algorithms: Overview and recent trends
    • Bharath, B., & Borkar, V. S. (1999). Stochastic approximation algorithms: overview and recent trends. Sadhana, 24, 425-452.
    • (1999) Sadhana , vol.24 , pp. 425-452
    • Bharath, B.1    Borkar, V.S.2
  • 10
  • 11
    • 19944366594 scopus 로고
    • The convergence of a class of double rank minimization algorithms, part II
    • Broyden, C. G. (1970b). The convergence of a class of double rank minimization algorithms, part II. Journal of the Institute of Mathematics and Applications, 6, 222-231.
    • (1970) Journal of the Institute of Mathematics and Applications , vol.6 , pp. 222-231
    • Broyden, C.G.1
  • 12
    • 3342921861 scopus 로고    scopus 로고
    • On approximating weighted sums with exponentially many terms
    • Chawla, D., Li, L., & Scott, S. (2004). On approximating weighted sums with exponentially many terms. Journal of Computer and System Sciences, 69, 196-234.
    • (2004) Journal of Computer and System Sciences , vol.69 , pp. 196-234
    • Chawla, D.1    Li, L.2    Scott, S.3
  • 13
    • 0024861871 scopus 로고
    • Approximation by superpositions of a sigmoidal function
    • Cybenko, G. (1989). Approximation by superpositions of a sigmoidal function. Mathematics of Control, Signals, and Systems, 3, 303-314.
    • (1989) Mathematics of Control, Signals, and Systems , vol.3 , pp. 303-314
    • Cybenko, G.1
  • 14
    • 0003264499 scopus 로고
    • Variable metric method for minimization
    • Davidon, W. C. (1959). Variable metric method for minimization. AEC Res. and Dev. Report ANL-5990.
    • (1959) AEC Res. and Dev. Report , vol.ANL-5990
    • Davidon, W.C.1
  • 15
    • 0000979403 scopus 로고    scopus 로고
    • Sequential Monte Carlo methods to train neural network models
    • de Freitas, N., Niranjan, M., Gee, A. H., & Doucet, A. (2000). Sequential Monte Carlo methods to train neural network models. Neural Computation, 12, 955-993.
    • (2000) Neural Computation , vol.12 , pp. 955-993
    • De Freitas, N.1    Niranjan, M.2    Gee, A.H.3    Doucet, A.4
  • 16
    • 0033243858 scopus 로고    scopus 로고
    • Convergence of a stochastic approximation version of the em algorithm
    • Delyon, B., Lavielle, M., & Moulines, E. (1999). Convergence of a stochastic approximation version of the EM algorithm. Annals of Statistics, 27, 94-128.
    • (1999) Annals of Statistics , vol.27 , pp. 94-128
    • Delyon, B.1    Lavielle, M.2    Moulines, E.3
  • 17
    • 34548168330 scopus 로고    scopus 로고
    • Technical Report, Department of Mathematical Science, Norwegian University of Science and Technology
    • Erland, S. (2003). Adaptive Markov chain Monte Carlo review. Technical Report, Department of Mathematical Science, Norwegian University of Science and Technology.
    • (2003) Adaptive Markov Chain Monte Carlo Review
    • Erland, S.1
  • 19
    • 0030616346 scopus 로고    scopus 로고
    • Analyzing a self-organizing algorithm
    • Flanagan, J. A. (1997). Analyzing a self-organizing algorithm. Neural Networks, 10, 875-883.
    • (1997) Neural Networks , vol.10 , pp. 875-883
    • Flanagan, J.A.1
  • 20
    • 0014825610 scopus 로고
    • A new approach to variable metric algorithms
    • Fletcher, R. (1970). A new approach to variable metric algorithms. The Computer Journal, 13, 317-322.
    • (1970) The Computer Journal , vol.13 , pp. 317-322
    • Fletcher, R.1
  • 22
    • 0000387235 scopus 로고
    • A rapidly convergent descent method for minimization
    • Fletcher, R., & Powell, M. J. D. (1963). A rapidly convergent descent method for minimization. The Computer Journal, 6, 163-168.
    • (1963) The Computer Journal , vol.6 , pp. 163-168
    • Fletcher, R.1    Powell, M.J.D.2
  • 23
    • 0024866495 scopus 로고
    • On the approximate realization of continuous mappings by neural networks
    • Funahashi, K. (1989). On the approximate realization of continuous mappings by neural networks. Neural Networks, 2, 183-192.
    • (1989) Neural Networks , vol.2 , pp. 183-192
    • Funahashi, K.1
  • 27
    • 84966251980 scopus 로고
    • A family of variable metric methods derived by variational means
    • Goldfarb, D. (1970). A family of variable metric methods derived by variational means. Mathematics of Computation, 24, 23-26.
    • (1970) Mathematics of Computation , vol.24 , pp. 23-26
    • Goldfarb, D.1
  • 29
    • 13144294075 scopus 로고    scopus 로고
    • A stochastic approximation algorithm with Markov chain Monte Carlo method for incomplete data estimation problems
    • Gu, M. G., & Kong, F. H. (1998). A stochastic approximation algorithm with Markov chain Monte Carlo method for incomplete data estimation problems. Proceedings of the National Academy of Sciences USA, 95, 7270-7274.
    • (1998) Proceedings of the National Academy of Sciences USA , vol.95 , pp. 7270-7274
    • Gu, M.G.1    Kong, F.H.2
  • 30
    • 0035532138 scopus 로고    scopus 로고
    • Maximum likelihood estimation for spatial models by Markov chain Monte Carlo stochastic approximation
    • Gu, M. G., & Zhu, H. T. (2001). Maximum likelihood estimation for spatial models by Markov chain Monte Carlo stochastic approximation. Journal of the Royal Statistical Society, Series B, 63, 339-355.
    • (2001) Journal of the Royal Statistical Society, Series B , vol.63 , pp. 339-355
    • Gu, M.G.1    Zhu, H.T.2
  • 32
    • 0016303884 scopus 로고
    • Alopex: A stochastic method for determining visual receptive fields
    • Harth, E., & Tzanakou, E. (1974). Alopex: a stochastic method for determining visual receptive fields. Vision Research, 14, 1475-1482.
    • (1974) Vision Research , vol.14 , pp. 1475-1482
    • Harth, E.1    Tzanakou, E.2
  • 34
    • 77956890234 scopus 로고
    • Monte Carlo sampling methods using Markov chains and their applications
    • Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97-109.
    • (1970) Biometrika , vol.57 , pp. 97-109
    • Hastings, W.K.1
  • 37
    • 0000688106 scopus 로고
    • Asymptotic of the spectral gap with applications to the theory of simulated annealing
    • Holley, R. A., Kusuoka, S., & Stroock, D. (1989). Asymptotic of the spectral gap with applications to the theory of simulated annealing. Journal of Functional Analysis, 83, 333-347.
    • (1989) Journal of Functional Analysis , vol.83 , pp. 333-347
    • Holley, R.A.1    Kusuoka, S.2    Stroock, D.3
  • 38
    • 0024880831 scopus 로고
    • Multilayer feedforward networks are universal approximators
    • Hornik, K., Stinchcombe, M., & White, H. (1989). Multilayer feedforward networks are universal approximators. Neural Networks, 2, 359-366.
    • (1989) Neural Networks , vol.2 , pp. 359-366
    • Hornik, K.1    Stinchcombe, M.2    White, H.3
  • 39
    • 0025901642 scopus 로고
    • Local minimization escape using thermodynamic properties of neural networks
    • Ingman, D., & Merlis, Y. (1991). Local minimization escape using thermodynamic properties of neural networks. Neural Networks, 4, 395-404.
    • (1991) Neural Networks , vol.4 , pp. 395-404
    • Ingman, D.1    Merlis, Y.2
  • 40
    • 0002734223 scopus 로고    scopus 로고
    • The Markov chain Monte Carlo method: An approach to approximate counting and integration
    • PWS Publishing Company Boston
    • Jerrum, M., & Sinclair, A. (1997). The Markov chain Monte Carlo method: an approach to approximate counting and integration. In D. S. Hochbaum (Ed.), Approximation algorithms for NP-hard problems (pp. 482-520). Boston: PWS Publishing Company.
    • (1997) Approximation Algorithms for NP-hard Problems , pp. 482-520
    • Jerrum, M.1    Sinclair, A.2    Hochbaum, D.S.3
  • 43
    • 26444479778 scopus 로고
    • Optimization by simulated annealing
    • Kirkpatrick, S., Gelatt, C. D., & Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220, 671-680.
    • (1983) Science , vol.220 , pp. 671-680
    • Kirkpatrick, S.1    Gelatt, C.D.2    Vecchi, M.P.3
  • 46
    • 0000873069 scopus 로고
    • A method for the solution of certain non-linear problems in least squares
    • Levenberg, K. (1944). A method for the solution of certain non-linear problems in least squares. Quarterly Journal of Applied Mathematics, 2, 164-168.
    • (1944) Quarterly Journal of Applied Mathematics , vol.2 , pp. 164-168
    • Levenberg, K.1
  • 47
    • 0041825287 scopus 로고    scopus 로고
    • An effective Bayesian neural network classifier with a comparison study to support vector machine
    • Liang, F. (2003). An effective Bayesian neural network classifier with a comparison study to support vector machine. Neural Computation, 15, 1959-1989.
    • (2003) Neural Computation , vol.15 , pp. 1959-1989
    • Liang, F.1
  • 48
    • 29144446035 scopus 로고    scopus 로고
    • Generalized Wang-Landau algorithm for Monte Carlo computation
    • Liang, F. (2005a). Generalized Wang-Landau algorithm for Monte Carlo computation. Journal of the American Statistical Association, 100, 1311-1327.
    • (2005) Journal of the American Statistical Association , vol.100 , pp. 1311-1327
    • Liang, F.1
  • 49
    • 18444399665 scopus 로고    scopus 로고
    • Evidence evaluation for Bayesian neural networks using contour Monte Carlo
    • Liang, F. (2005b). Evidence evaluation for Bayesian neural networks using contour Monte Carlo. Neural Computation, 17, 1385-1410.
    • (2005) Neural Computation , vol.17 , pp. 1385-1410
    • Liang, F.1
  • 50
    • 1542573405 scopus 로고    scopus 로고
    • Real parameter evolutionary Monte Carlo with applications in Bayesian mixture models
    • Liang, F., & Wong, W. H. (2001). Real parameter evolutionary Monte Carlo with applications in Bayesian mixture models. Journal of the American Statistical Association, 96, 653-666.
    • (2001) Journal of the American Statistical Association , vol.96 , pp. 653-666
    • Liang, F.1    Wong, W.H.2
  • 52
    • 0002704818 scopus 로고
    • A practical Bayesian framework for backprop networks
    • MacKay, D. J. C. (1992a). A practical Bayesian framework for backprop networks. Neural Computation, 4, 448-472.
    • (1992) Neural Computation , vol.4 , pp. 448-472
    • MacKay, D.J.C.1
  • 53
    • 0000234257 scopus 로고
    • The evidence framework applied to classification problems
    • MacKay, D. J. C. (1992b). The evidence framework applied to classification problems. Neural Computation, 4, 720-736.
    • (1992) Neural Computation , vol.4 , pp. 720-736
    • MacKay, D.J.C.1
  • 55
    • 0030551974 scopus 로고    scopus 로고
    • Rates of convergence of the Hastings and Metropolis algorithms
    • Mengersen, K. L., & Tweedie, R. L. (1996). Rates of convergence of the Hastings and Metropolis algorithms. The Annals of Statistics, 24, 101-121.
    • (1996) The Annals of Statistics , vol.24 , pp. 101-121
    • Mengersen, K.L.1    Tweedie, R.L.2
  • 58
    • 0028862414 scopus 로고
    • Statistical analysis of self-organization
    • Mulier, F. M., & Cherkassky, V. S. (1995). Statistical analysis of self-organization. Neural Networks, 8, 717-727.
    • (1995) Neural Networks , vol.8 , pp. 717-727
    • Mulier, F.M.1    Cherkassky, V.S.2
  • 59
    • 0347128520 scopus 로고    scopus 로고
    • Issues in Bayesian analysis of neural network models
    • Müller, P., & Insua, D. R. (1998). Issues in Bayesian analysis of neural network models. Neural Computation, 10, 749-770.
    • (1998) Neural Computation , vol.10 , pp. 749-770
    • Müller, P.1    Insua, D.R.2
  • 61
    • 0742301621 scopus 로고
    • Applications of simulated annealing to the back-propagation model improves convergence
    • Owen, C. B., & Abunawass, A. M. (1993). Applications of simulated annealing to the back-propagation model improves convergence. SPIE Proceedings, 1966, 269-276.
    • (1993) SPIE Proceedings , vol.1966 , pp. 269-276
    • Owen, C.B.1    Abunawass, A.M.2
  • 66
    • 0040673435 scopus 로고    scopus 로고
    • Two timescale analysis of the Alopex algorithm for optimization
    • Sastry, P. S., Magesh, M., & Unnikrishnan, K. P. (2002). Two timescale analysis of the Alopex algorithm for optimization. Neural Computation, 14, 2729-2750.
    • (2002) Neural Computation , vol.14 , pp. 2729-2750
    • Sastry, P.S.1    Magesh, M.2    Unnikrishnan, K.P.3
  • 67
    • 0000547544 scopus 로고
    • A useful convergence theorem for probability distributions
    • Scheffé, H. (1947). A useful convergence theorem for probability distributions. Annals of Mathematical Statistics, 18, 434-438.
    • (1947) Annals of Mathematical Statistics , vol.18 , pp. 434-438
    • Scheffé, H.1
  • 68
    • 84968497764 scopus 로고
    • Conditioning of quasi-Newton methods for function minimization
    • Shanno, D. F. (1970). Conditioning of quasi-Newton methods for function minimization. Mathematics of Computation, 24, 647-656.
    • (1970) Mathematics of Computation , vol.24 , pp. 647-656
    • Shanno, D.F.1
  • 70
    • 0026839090 scopus 로고
    • Multivariate stochastic approximation using a simultaneous perturbation gradient approximation
    • Spall, J. C. (1992). Multivariate stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Transactions on Automatic Control, 37, 332-341.
    • (1992) IEEE Transactions on Automatic Control , vol.37 , pp. 332-341
    • Spall, J.C.1
  • 72
    • 0042879436 scopus 로고    scopus 로고
    • An algorithm of supervised learning for multilayer neural networks
    • Tang, Z., Wang, X., Tamura, H., & Ishii, M. (2003). An algorithm of supervised learning for multilayer neural networks. Neural Computation, 15, 1125-1142.
    • (2003) Neural Computation , vol.15 , pp. 1125-1142
    • Tang, Z.1    Wang, X.2    Tamura, H.3    Ishii, M.4
  • 73
    • 0002855385 scopus 로고
    • Scaling relations in back-propagation learning
    • Tesauro, G., & Janssens, B. (1988). Scaling relations in back-propagation learning. Complex System, 2, 39-44.
    • (1988) Complex System , vol.2 , pp. 39-44
    • Tesauro, G.1    Janssens, B.2
  • 76
    • 6644221271 scopus 로고    scopus 로고
    • Efficient, multiple-range random walk algorithm to calculate the density of states
    • Wang, F., & Landau, D. P. (2001). Efficient, multiple-range random walk algorithm to calculate the density of states. Physical Review Letters, 86, 2050-2053.
    • (2001) Physical Review Letters , vol.86 , pp. 2050-2053
    • Wang, F.1    Landau, D.P.2
  • 77
    • 0033333990 scopus 로고    scopus 로고
    • Training neural networks with additive noise in the desired signal
    • Wang, C., & Principe, J. C. (1999). Training neural networks with additive noise in the desired signal. IEEE Transactions on Neural Networks, 10, 1511-1517.
    • (1999) IEEE Transactions on Neural Networks , vol.10 , pp. 1511-1517
    • Wang, C.1    Principe, J.C.2
  • 79
    • 0033285473 scopus 로고    scopus 로고
    • On the use of simultaneous perturbation stochastic approximation for neural network training
    • San Diego, CA
    • Wouwer, A. V., Renotte, C., & Remy, M. (1999) On the use of simultaneous perturbation stochastic approximation for neural network training. In Proceedings of the American control conference (pp. 388-392), San Diego, CA.
    • (1999) Proceedings of the American Control Conference , pp. 388-392
    • Wouwer, A.V.1    Renotte, C.2    Remy, M.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.