메뉴 건너뛰기




Volumn 35, Issue 5, 2007, Pages 1931-1946

Estimation in spin glasses: A first step

Author keywords

Consistency; Estimation; Exponential families; Neural networks; Spin glass

Indexed keywords


EID: 50449103822     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053607000000109     Document Type: Article
Times cited : (57)

References (26)
  • 1
    • 0003124865 scopus 로고
    • Some rigorous results on the Sherrington-Kirkpatrick spin glass model
    • AIZENMAN, M., LEBOWITZ, J. L. and RUELLE, D. (1987). Some rigorous results on the Sherrington-Kirkpatrick spin glass model. Comm. Math. Phys. 112 3-20.
    • (1987) Comm. Math. Phys , vol.112 , pp. 3-20
    • AIZENMAN, M.1    LEBOWITZ, J.L.2    RUELLE, D.3
  • 2
    • 1642452967 scopus 로고    scopus 로고
    • Extended variational principle for the Sherrington-Kirkpatrick spin-glass model
    • AIZENMAN, M., SIMS, R. and STARR, S. (2003). Extended variational principle for the Sherrington-Kirkpatrick spin-glass model. Phys. Rev. B 68 214403.
    • (2003) Phys. Rev. B , vol.68 , pp. 214403
    • AIZENMAN, M.1    SIMS, R.2    STARR, S.3
  • 3
    • 0347989448 scopus 로고    scopus 로고
    • Methodologies in spectral analysis of large-dimensional random matrices, a review (with discussion)
    • BAI, Z. D. (1999). Methodologies in spectral analysis of large-dimensional random matrices, a review (with discussion). Statist. Sinica 9 611-677.
    • (1999) Statist. Sinica , vol.9 , pp. 611-677
    • BAI, Z.D.1
  • 4
    • 0000913755 scopus 로고
    • Spatial interaction and the statistical analysis of lattice systems (with discussion)
    • BESAG, J. (1974). Spatial interaction and the statistical analysis of lattice systems (with discussion). J. Roy. Statist. Soc. Ser. B 36 192-236.
    • (1974) J. Roy. Statist. Soc. Ser. B , vol.36 , pp. 192-236
    • BESAG, J.1
  • 5
    • 0000582521 scopus 로고
    • Statistical analysis of non-lattice data
    • BESAG, J. (1975). Statistical analysis of non-lattice data. Statistician 24 179-195.
    • (1975) Statistician , vol.24 , pp. 179-195
    • BESAG, J.1
  • 6
    • 0004340648 scopus 로고    scopus 로고
    • Hopfield models as generalized random mean field models
    • A. Bovier and P. Picco, eds, Birkhäuser, Boston
    • BOVIER, A. and GAYRARD, V. (1998). Hopfield models as generalized random mean field models. In Mathematical Aspects of Spin Glasses and Neural Networks (A. Bovier and P. Picco, eds.) 3-89. Birkhäuser, Boston.
    • (1998) Mathematical Aspects of Spin Glasses and Neural Networks , pp. 3-89
    • BOVIER, A.1    GAYRARD, V.2
  • 7
    • 50449109701 scopus 로고    scopus 로고
    • CHATTERJEE, S. (2005). Concentration inequalities with exchangeable pairs. Ph.D. dissertation, Stanford Univ. Available at arxiv.org/abs/math/0507526.
    • CHATTERJEE, S. (2005). Concentration inequalities with exchangeable pairs. Ph.D. dissertation, Stanford Univ. Available at arxiv.org/abs/math/0507526.
  • 8
    • 33947318684 scopus 로고    scopus 로고
    • Concentration of Haar measures, with an application to random matrices
    • CHATTERJEE, S. (2007). Concentration of Haar measures, with an application to random matrices. J. Funct. Anal. 245 379-389.
    • (2007) J. Funct. Anal , vol.245 , pp. 379-389
    • CHATTERJEE, S.1
  • 9
    • 33847617461 scopus 로고    scopus 로고
    • Stein's method for concentration inequalities
    • CHATTERJEE, S. (2007). Stein's method for concentration inequalities. Probab. Theory Related Fields 138 305-321.
    • (2007) Probab. Theory Related Fields , vol.138 , pp. 305-321
    • CHATTERJEE, S.1
  • 10
    • 0000695777 scopus 로고
    • On consistency of a class of estimators for exponential families of Markov random fields on the lattice
    • COMETS, F. (1992). On consistency of a class of estimators for exponential families of Markov random fields on the lattice. Ann. Statist. 20 455-468.
    • (1992) Ann. Statist , vol.20 , pp. 455-468
    • COMETS, F.1
  • 11
    • 34249756647 scopus 로고
    • The Sherrington-Kirkpatrick model of spin glasses and stochastic calculus: The high temperature case
    • COMETS, F. and NEVEU, J. (1995). The Sherrington-Kirkpatrick model of spin glasses and stochastic calculus: The high temperature case. Comm. Math. Phys. 166 549-564.
    • (1995) Comm. Math. Phys , vol.166 , pp. 549-564
    • COMETS, F.1    NEVEU, J.2
  • 12
    • 0000051109 scopus 로고
    • Constrained Monte Carlo maximum likelihood for dependent data (with discussion)
    • GEYER, C. J. and THOMPSON, E. A. (1992). Constrained Monte Carlo maximum likelihood for dependent data (with discussion). J. Roy. Statist. Soc. Ser. B 54 657-699.
    • (1992) J. Roy. Statist. Soc. Ser. B , vol.54 , pp. 657-699
    • GEYER, C.J.1    THOMPSON, E.A.2
  • 13
    • 0009856498 scopus 로고
    • Consistency of maximum likelihood and pseudolikelihood estimators for Gibbs distributions
    • W. Fleming and P.-L. Lions, eds, Springer, New York
    • GIDAS, B. (1988). Consistency of maximum likelihood and pseudolikelihood estimators for Gibbs distributions. In Stochastic Differential Systems, Stochastic Control Theory and Applications (W. Fleming and P.-L. Lions, eds.) 129-145. Springer, New York.
    • (1988) Stochastic Differential Systems, Stochastic Control Theory and Applications , pp. 129-145
    • GIDAS, B.1
  • 14
    • 0037329695 scopus 로고    scopus 로고
    • Broken replica symmetry bounds in the mean field spin glass model
    • GUERRA, F. (2003). Broken replica symmetry bounds in the mean field spin glass model. Comm. Math. Phys. 233 1-12.
    • (2003) Comm. Math. Phys , vol.233 , pp. 1-12
    • GUERRA, F.1
  • 15
    • 0036768858 scopus 로고    scopus 로고
    • The thermodynamic limit in mean field spin glass models
    • GUERRA, F. and TONINELLI, F. L. (2002). The thermodynamic limit in mean field spin glass models. Comm. Math. Phys. 230 71-79.
    • (2002) Comm. Math. Phys , vol.230 , pp. 71-79
    • GUERRA, F.1    TONINELLI, F.L.2
  • 16
    • 0002446794 scopus 로고
    • A lower bound for the critical probability in a certain percolation process
    • HARRIS, T. E. (1960). A lower bound for the critical probability in a certain percolation process. Proc. Cambridge Philos. Soc. 56 13-20.
    • (1960) Proc. Cambridge Philos. Soc , vol.56 , pp. 13-20
    • HARRIS, T.E.1
  • 17
    • 0020118274 scopus 로고
    • Neural networks and physical systems with emergent collective computational abilities
    • HOPFIELD, J. J. (1982). Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. U.S.A. 79 2554-2558.
    • (1982) Proc. Natl. Acad. Sci. U.S.A , vol.79 , pp. 2554-2558
    • HOPFIELD, J.J.1
  • 18
    • 33947716431 scopus 로고
    • Beitrag zur Theorie des Ferromagnetismus.
    • ISING, E. (1925). Beitrag zur Theorie des Ferromagnetismus. Z. Physik 31 253-258.
    • (1925) Z. Physik , vol.31 , pp. 253-258
    • ISING, E.1
  • 19
    • 0000849716 scopus 로고
    • Pseudolikelihood for exponential family models of spatial point processes
    • JENSEN, J. L. and MØLLER, J. (1991). Pseudolikelihood for exponential family models of spatial point processes. Ann. Appl. Probab. 1 445-461.
    • (1991) Ann. Appl. Probab , vol.1 , pp. 445-461
    • JENSEN, J.L.1    MØLLER, J.2
  • 20
    • 0027677367 scopus 로고
    • Polynomial-time approximation algorithms for the Ising model
    • JERRUM, M. and SINCLAIR, A. (1993). Polynomial-time approximation algorithms for the Ising model. SIAM J. Comput. 22 1087-1116.
    • (1993) SIAM J. Comput , vol.22 , pp. 1087-1116
    • JERRUM, M.1    SINCLAIR, A.2
  • 21
    • 36149012281 scopus 로고
    • Crystal statistics. I. A two-dimensional model with an order-disorder transition
    • ONSAGER, L. (1944). Crystal statistics. I. A two-dimensional model with an order-disorder transition. Phys. Rev. (2) 65 117-149.
    • (1944) Phys. Rev , vol.65 , Issue.2 , pp. 117-149
    • ONSAGER, L.1
  • 22
    • 23944456403 scopus 로고    scopus 로고
    • Free energy in the generalized Sherrington-Kirkpatrick mean field model
    • PANCHENKO, D. (2005). Free energy in the generalized Sherrington-Kirkpatrick mean field model. Rev. Math. Phys. 17 793-857.
    • (2005) Rev. Math. Phys , vol.17 , pp. 793-857
    • PANCHENKO, D.1
  • 23
    • 0000862452 scopus 로고    scopus 로고
    • On the replica symmetric solution for the Sherrington-Kirkpatrick model
    • SHCHERBINA, M. V. (1997). On the replica symmetric solution for the Sherrington-Kirkpatrick model. Helv. Phys. Acta 70 838-853.
    • (1997) Helv. Phys. Acta , vol.70 , pp. 838-853
    • SHCHERBINA, M.V.1
  • 24
  • 26
    • 33645683399 scopus 로고    scopus 로고
    • The Parisi formula
    • TALAGRAND, M. (2006). The Parisi formula. Ann. of Math. (2) 163 221-263.
    • (2006) Ann. of Math. (2) , vol.163 , pp. 221-263
    • TALAGRAND, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.