메뉴 건너뛰기




Volumn 29, Issue 1, 2009, Pages 45-59

Singularity and slow convergence of the em algorithm for gaussian mixtures

Author keywords

EM algorithm; Gradient descent learning; Learning dynamics; Singularity; Slow convergence

Indexed keywords

ALGORITHMS; ARRAY PROCESSING; CONVERGENCE OF NUMERICAL METHODS; DYNAMICS; EDUCATION; ELECTRIC NETWORK ANALYSIS; LEARNING SYSTEMS; MAXIMUM LIKELIHOOD; MAXIMUM LIKELIHOOD ESTIMATION; TRELLIS CODES;

EID: 60449094542     PISSN: 13704621     EISSN: 1573773X     Source Type: Journal    
DOI: 10.1007/s11063-009-9094-4     Document Type: Article
Times cited : (37)

References (23)
  • 2
    • 0034201611 scopus 로고    scopus 로고
    • Adaptive method of realizing natural gradient learning for multilayer perceptrons
    • S Amari H Park K Fukumizu 2000 Adaptive method of realizing natural gradient learning for multilayer perceptrons Neural Comput 12 1399 1409
    • (2000) Neural Comput , vol.12 , pp. 1399-1409
    • Amari, S.1    Park, H.2    Fukumizu, K.3
  • 4
    • 0038030649 scopus 로고    scopus 로고
    • Learning and inference in hierarchical models with singularities
    • S Amari T Ozeki H Park 2003 Learning and inference in hierarchical models with singularities Syst Comput Jpn 34 34 42
    • (2003) Syst Comput Jpn , vol.34 , pp. 34-42
    • Amari, S.1    Ozeki, T.2    Park, H.3
  • 5
    • 33646407804 scopus 로고    scopus 로고
    • Singularities affect dynamics of learning in neuromanifolds
    • 5
    • S Amari H Park T Ozeki 2006 Singularities affect dynamics of learning in neuromanifolds Neural Comput 18 5 1007 1065
    • (2006) Neural Comput , vol.18 , pp. 1007-1065
    • Amari, S.1    Park, H.2    Ozeki, T.3
  • 6
    • 0042311289 scopus 로고    scopus 로고
    • Likelihood ratio of unidentifiable models and multilayer neural networks
    • 3
    • K Fukumizu 2003 Likelihood ratio of unidentifiable models and multilayer neural networks Ann Stat 31 3 833 851
    • (2003) Ann Stat , vol.31 , pp. 833-851
    • Fukumizu, K.1
  • 7
    • 0034018074 scopus 로고    scopus 로고
    • Local minima and plateaus in hierarchical structures of multilayer perceptrons
    • K Fukumizu S Amari 2000 Local minima and plateaus in hierarchical structures of multilayer perceptrons Neural Netw 13 317 327
    • (2000) Neural Netw , vol.13 , pp. 317-327
    • Fukumizu, K.1    Amari, S.2
  • 8
    • 0040079861 scopus 로고    scopus 로고
    • On the problem in model selection of neural network regression in overrealizable scenario
    • K Hagiwara 2002 On the problem in model selection of neural network regression in overrealizable scenario Neural Comput 14 1979 2002
    • (2002) Neural Comput , vol.14 , pp. 1979-2002
    • Hagiwara, K.1
  • 9
    • 0035200563 scopus 로고    scopus 로고
    • Upper bound of the expected training error of neural network regression for a Gaussian noise sequence
    • K Hagiwara T Hayasaka N Toda S Usui K Kuno 2001 Upper bound of the expected training error of neural network regression for a Gaussian noise sequence Neural Netw 14 1419 1429
    • (2001) Neural Netw , vol.14 , pp. 1419-1429
    • Hagiwara, K.1    Hayasaka, T.2    Toda, N.3    Usui, S.4    Kuno, K.5
  • 11
    • 0038323312 scopus 로고    scopus 로고
    • On-line learning theory of soft committee machines with correlated hidden units-steepest gradient descent and natural gradient descent
    • 4
    • M Inoue H Park M Okada 2003 On-line learning theory of soft committee machines with correlated hidden units-steepest gradient descent and natural gradient descent J Phys Soc Jpn 72 4 805 810
    • (2003) J Phys Soc Jpn , vol.72 , pp. 805-810
    • Inoue, M.1    Park, H.2    Okada, M.3
  • 13
    • 24144442632 scopus 로고    scopus 로고
    • Asymptotic convergence properties of the em algorithm with respect to the overlap in the mixtures
    • J Ma L Xu 2005 Asymptotic convergence properties of the EM algorithm with respect to the overlap in the mixtures Neurocomputing 68 105 129
    • (2005) Neurocomputing , vol.68 , pp. 105-129
    • Ma, J.1    Xu, L.2
  • 14
    • 0037735771 scopus 로고    scopus 로고
    • Asymptotic convergence rate of the em algorithm for Gaussian mixtures
    • J Ma L Xu MI Jordan 2000 Asymptotic convergence rate of the EM algorithm for Gaussian mixtures Neural Comput 12 2881 2907
    • (2000) Neural Comput , vol.12 , pp. 2881-2907
    • Ma, J.1    Xu, L.2    Jordan, M.I.3
  • 15
    • 0034266869 scopus 로고    scopus 로고
    • Adaptive natural gradient learning algorithms for various stochastic models
    • H Park S Amari K Fukumizu 2000 Adaptive natural gradient learning algorithms for various stochastic models Neural Netw 13 755 764
    • (2000) Neural Netw , vol.13 , pp. 755-764
    • Park, H.1    Amari, S.2    Fukumizu, K.3
  • 16
    • 0345581643 scopus 로고    scopus 로고
    • Online learning dynamics of multilayer perceptrons with unidentifiable parameters
    • H Park M Inoue M Okada 2003 Online learning dynamics of multilayer perceptrons with unidentifiable parameters J Phys A Math Gen 36 11753 11764
    • (2003) J Phys A Math Gen , vol.36 , pp. 11753-11764
    • Park, H.1    Inoue, M.2    Okada, M.3
  • 17
    • 22144437704 scopus 로고    scopus 로고
    • Slow dynamics due to singularities of hierarchical learning machines
    • H Park M Inoue M Okada 2004 Slow dynamics due to singularities of hierarchical learning machines Prog Theor Phys Suppl 157 275 279
    • (2004) Prog Theor Phys Suppl , vol.157 , pp. 275-279
    • Park, H.1    Inoue, M.2    Okada, M.3
  • 18
    • 0021404166 scopus 로고
    • Mixture densities, maximum likelihood and the em algorithm
    • RA Redner HF Walker 1984 Mixture densities, maximum likelihood and the EM algorithm SIAM Rev 26 159 239
    • (1984) SIAM Rev , vol.26 , pp. 159-239
    • Redner, R.A.1    Walker, H.F.2
  • 19
    • 4243234689 scopus 로고
    • On-line learning in soft committee machines
    • D Saad A Solla 1995 On-line learning in soft committee machines Phys Rev E 52 4225 4243
    • (1995) Phys Rev e , vol.52 , pp. 4225-4243
    • Saad, D.1    Solla, A.2
  • 20
    • 0035316373 scopus 로고    scopus 로고
    • Algebraic analysis for non-identifiable learning machines
    • S Watanabe 2001 Algebraic analysis for non-identifiable learning machines Neural Comput 13 899 933
    • (2001) Neural Comput , vol.13 , pp. 899-933
    • Watanabe, S.1
  • 21
    • 0034842476 scopus 로고    scopus 로고
    • Algebraic geometrical methods for hierarchical learning machines
    • 8
    • S Watanabe 2001 Algebraic geometrical methods for hierarchical learning machines Neural Netw 14 8 1049 1060
    • (2001) Neural Netw , vol.14 , pp. 1049-1060
    • Watanabe, S.1
  • 22
    • 41549141920 scopus 로고    scopus 로고
    • Dynamics of learning near singularities in layered networks
    • H Wei J Zhang F Cousseau T Ozeki S Amari 2006 Dynamics of learning near singularities in layered networks Neural Comput 20 813 843
    • (2006) Neural Comput , vol.20 , pp. 813-843
    • Wei, H.1    Zhang, J.2    Cousseau, F.3    Ozeki, T.4    Amari, S.5
  • 23
    • 2342533082 scopus 로고    scopus 로고
    • On convergence properties of the em algorithm for gaussian mixtures
    • L Xu MI Jordan 1996 On convergence properties of the EM algorithm for gaussian mixtures Neural Comput 8 129 151
    • (1996) Neural Comput , vol.8 , pp. 129-151
    • Xu, L.1    Jordan, M.I.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.