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Volumn , Issue , 2012, Pages 139-172

The EM algorithm

Author keywords

[No Author keywords available]

Indexed keywords

EM ALGORITHMS;

EID: 84985896218     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-3-642-21551-3__6     Document Type: Chapter
Times cited : (87)

References (70)
  • 1
    • 0002020687 scopus 로고
    • A simple method for computing the observed information matrix when using the EM algorithm with categorical data
    • Baker, S.G.: A simple method for computing the observed information matrix when using the EM algorithm with categorical data. J. Comput. Graph. Stat. 1, 63-76 (1992)
    • (1992) J. Comput. Graph. Stat. , vol.1 , pp. 63-76
    • Baker, S.G.1
  • 4
    • 0033475053 scopus 로고    scopus 로고
    • Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm
    • Booth, J.G., Hobert, J.P.: Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm. J. Roy. Stat. Soc. B 61, 265-285 (1999)
    • (1999) J. Roy. Stat. Soc. B , vol.61 , pp. 265-285
    • Booth, J.G.1    Hobert, J.P.2
  • 5
    • 0011241944 scopus 로고
    • Approximate inference in generalized linear mixed models
    • Breslow, N.E., Clayton, D.G.: Approximate inference in generalized linear mixed models. J. Am. Stat. Assoc. 88, 9-25 (1993)
    • (1993) J. Am. Stat. Assoc. , vol.88 , pp. 9-25
    • Breslow, N.E.1    Clayton, D.G.2
  • 6
    • 84937730674 scopus 로고
    • Explaining the Gibbs sampler
    • Casella, G., George, E.I.: Explaining the Gibbs sampler. Am. Stat. 46, 167-174 (1992)
    • (1992) Am. Stat. , vol.46 , pp. 167-174
    • Casella, G.1    George, E.I.2
  • 7
    • 0032876594 scopus 로고    scopus 로고
    • Improved learning algorithms for mixture of experts in multiclass classification
    • Chen, K., Xu, L., Chi, H.: Improved learning algorithms for mixture of experts in multiclass classification. Neural Netw. 12, 1229-1252 (1999)
    • (1999) Neural Netw. , vol.12 , pp. 1229-1252
    • Chen, K.1    Xu, L.2    Chi, H.3
  • 10
    • 0001560954 scopus 로고
    • Information geometry and alternating minimization procedure
    • Dudewicz, E.J., Plachky, D., Sen, P.K. (eds.), R. Oldenbourg, Munich
    • Csiszár, I., Tusnády, G.: Information geometry and alternating minimization procedure. In:Dudewicz, E.J., Plachky, D., Sen, P.K. (eds.) Recent Results in Estimation Theory and Related Topics, pp. 205-237. R. Oldenbourg, Munich (1984)
    • (1984) Recent Results in Estimation Theory and Related Topics , pp. 205-237
    • Csiszár, I.1    Tusnády, G.2
  • 11
    • 0002629270 scopus 로고
    • Maximum likelihood from incomplete data via the EM algorithm
    • Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Stat. Soc. B 39, 1-38 (1977)
    • (1977) J. Roy. Stat. Soc. B , vol.39 , pp. 1-38
    • Dempster, A.P.1    Laird, N.M.2    Rubin, D.B.3
  • 12
    • 0002344794 scopus 로고
    • Bootstrap methods: another look at the jackknife
    • Efron, B.: Bootstrap methods: another look at the jackknife. Ann. Stat. 7, 1-26 (1979)
    • (1979) Ann. Stat. , vol.7 , pp. 1-26
    • Efron, B.1
  • 14
    • 0028517016 scopus 로고
    • Space-alternating generalized expectation-maximization algorithm
    • Fessler, J.A., Hero, A.O.: Space-alternating generalized expectation-maximization algorithm. IEEE Trans. Signal. Process. 42, 2664-2677 (1994)
    • (1994) IEEE Trans. Signal. Process. , vol.42 , pp. 2664-2677
    • Fessler, J.A.1    Hero, A.O.2
  • 15
    • 0034362341 scopus 로고    scopus 로고
    • Exercises in EM
    • Flury, B., Zoppé, A.: Exercises in EM. Am. Stat. 54, 207-209 (2000)
    • (2000) Am. Stat. , vol.54 , pp. 207-209
    • Flury, B.1    Zoppé, A.2
  • 17
    • 84950453304 scopus 로고
    • Sampling-based approaches to calculating marginal densities
    • Gelfand, A.E., Smith, A.F.M.: Sampling-based approaches to calculating marginal densities. J. Am. Stat. Assoc. 85, 398-409 (1990)
    • (1990) J. Am. Stat. Assoc. , vol.85 , pp. 398-409
    • Gelfand, A.E.1    Smith, A.F.M.2
  • 18
    • 38049135335 scopus 로고
    • Another interpretation of the EM algorithm for mixture distributions
    • Hathaway, R.J.: Another interpretation of the EM algorithm for mixture distributions. Stat. Probab. Lett. 4, 53-56 (1986)
    • (1986) Stat. Probab. Lett. , vol.4 , pp. 53-56
    • Hathaway, R.J.1
  • 19
    • 77956890234 scopus 로고
    • Monte Carlo sampling methods using Markov chains and their applications
    • Hastings, W.K.: Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 97-109 (1970)
    • (1970) Biometrika , vol.57 , pp. 97-109
    • Hastings, W.K.1
  • 23
    • 0000262562 scopus 로고
    • Hierarchical mixtures of experts and the EMalgorithm
    • Jordan,M.I., Jacobs, R.A.: Hierarchical mixtures of experts and the EMalgorithm. Neural Comput. 6, 181-214 (1994)
    • (1994) Neural Comput. , vol.6 , pp. 181-214
    • Jordan, M.I.1    Jacobs, R.A.2
  • 24
    • 0029617280 scopus 로고
    • Convergence results for the EM approach to mixtures of experts architectures
    • Jordan, M.I., Xu, L.: Convergence results for the EM approach to mixtures of experts architectures. Neural Netw. 8, 1409-1431 (1995)
    • (1995) Neural Netw. , vol.8 , pp. 1409-1431
    • Jordan, M.I.1    Xu, L.2
  • 25
    • 11144327550 scopus 로고    scopus 로고
    • An adaptive window width/center adjustment system with online training capabilities for MR images
    • Lai, S.H., Fang, M.: An adaptive window width/center adjustment system with online training capabilities for MR images. Artif. Intell. Med. 33, 89-101 (2005)
    • (2005) Artif. Intell. Med. , vol.33 , pp. 89-101
    • Lai, S.H.1    Fang, M.2
  • 26
    • 0034730124 scopus 로고    scopus 로고
    • Importance of replication in microarray gene expression studies: statistical methods and evidence from repetitive cDNA hybridizations
    • Lee, M.L.T., Kuo, F.C., Whitmore, G.A., Sklar, J.: Importance of replication in microarray gene expression studies: statistical methods and evidence from repetitive cDNA hybridizations. Proc. Natl. Acad. Sci. USA 97, 9834-9838 (2000)
    • (2000) Proc. Natl. Acad. Sci. USA , vol.97 , pp. 9834-9838
    • Lee, M.L.T.1    Kuo, F.C.2    Whitmore, G.A.3    Sklar, J.4
  • 27
    • 2442599184 scopus 로고    scopus 로고
    • An automated (Markov chain) Monte Carlo EM algorithm
    • Levine, R., Fan, J.J.: An automated (Markov chain) Monte Carlo EM algorithm. J. Stat. Comput. Simulat. 74, 349-359 (2004)
    • (2004) J. Stat. Comput. Simulat. , vol.74 , pp. 349-359
    • Levine, R.1    Fan, J.J.2
  • 29
    • 0000315742 scopus 로고
    • The ECME algorithm: a simple extension of EM and ECM with faster monotone convergence
    • Liu, C., Rubin, D.B.: The ECME algorithm: a simple extension of EM and ECM with faster monotone convergence. Biometrika 81, 633-648 (1994)
    • (1994) Biometrika , vol.81 , pp. 633-648
    • Liu, C.1    Rubin, D.B.2
  • 30
    • 0032397180 scopus 로고    scopus 로고
    • Maximum likelihood estimation of factor analysis using the ECME algorithm with complete and incomplete data
    • Liu, C., Rubin, D.B.:Maximum likelihood estimation of factor analysis using the ECME algorithm with complete and incomplete data. Stat. Sin. 8, 729-747 (1998)
    • (1998) Stat. Sin. , vol.8 , pp. 729-747
    • Liu, C.1    Rubin, D.B.2
  • 31
    • 0001508169 scopus 로고    scopus 로고
    • Parameter expansion to accelerate EM: the PX-EM algorithm
    • Liu, C., Rubin, D.B., Wu, Y.N.: Parameter expansion to accelerate EM: the PX-EM algorithm. Biometrika 85, 755-770 (1998)
    • (1998) Biometrika , vol.85 , pp. 755-770
    • Liu, C.1    Rubin, D.B.2    Wu, Y.N.3
  • 32
    • 0001044972 scopus 로고
    • Finding the observed information matrix when using the EM algorithm
    • Louis, T.A.: Finding the observed information matrix when using the EM algorithm. J. Roy. Stat. Soc. B 44, 226-233 (1982)
    • (1982) J. Roy. Stat. Soc. B , vol.44 , pp. 226-233
    • Louis, T.A.1
  • 34
    • 0031479575 scopus 로고    scopus 로고
    • Maximum likelihood algorithms for generalized linear mixed models
    • McCulloch, C.E.: Maximum likelihood algorithms for generalized linear mixed models. J. Am. Stat. Assoc. 92, 162-170 (1997)
    • (1997) J. Am. Stat. Assoc. , vol.92 , pp. 162-170
    • McCulloch, C.E.1
  • 36
    • 0036203115 scopus 로고    scopus 로고
    • A mixture model-based approach to the clustering of microarray expression data
    • McLachlan, G.J., Bean, R.W., Peel, D.: A mixture model-based approach to the clustering of microarray expression data. Bioinformatics 18, 413-422 (2002)
    • (2002) Bioinformatics , vol.18 , pp. 413-422
    • McLachlan, G.J.1    Bean, R.W.2    Peel, D.3
  • 40
    • 0001232538 scopus 로고
    • A fast improvement of the EM algorithm in its own terms
    • Meilijson, I.: A fast improvement of the EM algorithm in its own terms. J. Roy. Stat. Soc. B 51, 127-138 (1989)
    • (1989) J. Roy. Stat. Soc. B , vol.51 , pp. 127-138
    • Meilijson, I.1
  • 41
    • 21344477603 scopus 로고
    • On the rate of convergence of the ECM algorithm
    • Meng, X.L.: On the rate of convergence of the ECM algorithm. Ann. Stat. 22, 326-339 (1994)
    • (1994) Ann. Stat. , vol.22 , pp. 326-339
    • Meng, X.L.1
  • 42
    • 84864615423 scopus 로고
    • Using EM to obtain asymptotic variance-covariance matrices: the SEM algorithm
    • Meng, X.L., Rubin, D.B.: Using EM to obtain asymptotic variance-covariance matrices: the SEM algorithm. J. Am. Stat. Assoc. 86, 899-909 (1991)
    • (1991) J. Am. Stat. Assoc. , vol.86 , pp. 899-909
    • Meng, X.L.1    Rubin, D.B.2
  • 43
    • 0000251971 scopus 로고
    • Maximum likelihood estimation via the ECM algorithm: a general framework
    • Meng, X.L., Rubin, D.B.: Maximum likelihood estimation via the ECM algorithm: a general framework. Biometrika 80, 267-278 (1993)
    • (1993) Biometrika , vol.80 , pp. 267-278
    • Meng, X.L.1    Rubin, D.B.2
  • 44
    • 18244387717 scopus 로고    scopus 로고
    • The EM algorithm - an old folk song sung to a fast new tune
    • Meng, X.L., van Dyk, D.: The EM algorithm - an old folk song sung to a fast new tune. J. Roy. Stat. Soc. B 59, 511-567 (1997)
    • (1997) J. Roy. Stat. Soc. B , vol.59 , pp. 511-567
    • Meng, X.L.1    van Dyk, D.2
  • 45
    • 84899029127 scopus 로고    scopus 로고
    • Very fast EM-based mixture model clustering using multiresolution kd-trees
    • Kearns, M.S., Solla, S.A., Cohn, D.A. (eds.), MIT Press, MA
    • Moore, A.W.: Very fast EM-based mixture model clustering using multiresolution kd-trees. In:Kearns, M.S., Solla, S.A., Cohn, D.A. (eds.) Advances in Neural Information Processing Systems 11, pp. 543-549. MIT Press, MA (1999)
    • (1999) Advances in Neural Information Processing Systems , vol.11 , pp. 543-549
    • Moore, A.W.1
  • 46
    • 0002788893 scopus 로고    scopus 로고
    • A view of the EM algorithm that justifies incremental, sparse, and other variants
    • Jordan, M.I. (ed.), Kluwer, Dordrecht
    • Neal, R.M., Hinton, G.E.: A view of the EM algorithm that justifies incremental, sparse, and other variants. In: Jordan, M.I. (ed.) Learning in Graphical Models, pp. 355-368. Kluwer, Dordrecht (1998)
    • (1998) Learning in Graphical Models , pp. 355-368
    • Neal, R.M.1    Hinton, G.E.2
  • 47
    • 0033260540 scopus 로고    scopus 로고
    • Convergence properties of the EM algorithm in constrained parameter spaces
    • Nettleton, D.: Convergence properties of the EM algorithm in constrained parameter spaces. Can. J. Stat. 27, 639-648 (1999)
    • (1999) Can. J. Stat. , vol.27 , pp. 639-648
    • Nettleton, D.1
  • 48
    • 0345832327 scopus 로고    scopus 로고
    • On the choice of the number of blocks with the incremental EM algorithm for the fitting of normal mixtures
    • Ng, S.K., McLachlan, G.J.: On the choice of the number of blocks with the incremental EM algorithm for the fitting of normal mixtures. Stat. Comput. 13, 45-55 (2003)
    • (2003) Stat. Comput. , vol.13 , pp. 45-55
    • Ng, S.K.1    McLachlan, G.J.2
  • 49
    • 2542607597 scopus 로고    scopus 로고
    • Using the EM algorithm to train neural networks: misconceptions and a new algorithm for multiclass classification
    • Ng, S.K., McLachlan, G.J (2004a). Using the EM algorithm to train neural networks: misconceptions and a new algorithm for multiclass classification. IEEE Trans. Neural Netw. 15, 738-749.
    • (2004) IEEE Trans. Neural Netw. , vol.15 , pp. 738-749
    • Ng, S.K.1    McLachlan, G.J.2
  • 50
    • 2642550607 scopus 로고    scopus 로고
    • Speeding up the EM algorithm for mixture model-based segmentation of magnetic resonance images
    • Ng, S.K., McLachlan, G.J (2004b). Speeding up the EM algorithm for mixture model-based segmentation of magnetic resonance images. Pattern Recogn. 37, 1573-1589.
    • (2004) Pattern Recogn. , vol.37 , pp. 1573-1589
    • Ng, S.K.1    McLachlan, G.J.2
  • 51
    • 33644857556 scopus 로고    scopus 로고
    • An incremental EM-based learning approach for on-line prediction of hospital resource utilization
    • Ng, S.K., McLachlan, G.J., Lee, A.H (2006a). An incremental EM-based learning approach for on-line prediction of hospital resource utilization. Artif. Intell. Med. 36, 257-267.
    • (2006) Artif. Intell. Med. , vol.36 , pp. 257-267
    • Ng, S.K.1    McLachlan, G.J.2    Lee, A.H.3
  • 52
    • 33747890494 scopus 로고    scopus 로고
    • A mixture model with random-effects components for clustering correlated gene-expression profiles
    • Ng, S.K., McLachlan, G.J., Wang, K., Ben-Tovim Jones, L., Ng, S.W (2006b). A mixture model with random-effects components for clustering correlated gene-expression profiles. Bioinformatics 22, 1745-1752.
    • (2006) Bioinformatics , vol.22 , pp. 1745-1752
    • Ng, S.K.1    McLachlan, G.J.2    Wang, K.3    Ben-Tovim Jones, L.4    Ng, S.W.5
  • 53
    • 4444257472 scopus 로고    scopus 로고
    • Modelling the distribution of ischaemic stroke-specific survival time using an EM-based mixture approach with random effects adjustment
    • Ng, S.K., McLachlan, G.J., Yau, K.K.W., Lee, A.H.: Modelling the distribution of ischaemic stroke-specific survival time using an EM-based mixture approach with random effects adjustment. Stat. Med. 23, 2729-2744 (2004)
    • (2004) Stat. Med. , vol.23 , pp. 2729-2744
    • Ng, S.K.1    McLachlan, G.J.2    Yau, K.K.W.3    Lee, A.H.4
  • 54
    • 77956387580 scopus 로고    scopus 로고
    • A gradient-based algorithm for matrix factorization applied to dimensionality reduction
    • Fred, A., Filipe, J., Gamboa, H. (eds.), Institute for Systems and Technologies of Information, Control and Communication, Portugal
    • Nikulin, V., McLachlan, G.J.: A gradient-based algorithm for matrix factorization applied to dimensionality reduction. In: Fred, A., Filipe, J., Gamboa, H. (eds.) Proceedings of BIOSTEC 2010, the 3rd International Joint Conference on Biomedical Engineering Systems and Technologies, pp. 147-152. Institute for Systems and Technologies of Information, Control and Communication, Portugal (2010)
    • (2010) Proceedings of BIOSTEC 2010, the 3rd International Joint Conference on Biomedical Engineering Systems and Technologies , pp. 147-152
    • Nikulin, V.1    McLachlan, G.J.2
  • 55
    • 0141626917 scopus 로고    scopus 로고
    • The effect of replication on gene expression microarray experiments
    • Pavlidis, P., Li, Q., Noble, W.S.: The effect of replication on gene expression microarray experiments. Bioinformatics 19, 1620-1627 (2003)
    • (2003) Bioinformatics , vol.19 , pp. 1620-1627
    • Pavlidis, P.1    Li, Q.2    Noble, W.S.3
  • 56
    • 24344483148 scopus 로고    scopus 로고
    • Genetic-based EM algorithm for learning Gaussian mixture models
    • Pernkopf, F., Bouchaffra, D.: Genetic-based EM algorithm for learning Gaussian mixture models. IEEE Trans. Pattern Anal. Mach. Intell. 27, 1344-1348 (2005)
    • (2005) IEEE Trans. Pattern Anal. Mach. Intell. , vol.27 , pp. 1344-1348
    • Pernkopf, F.1    Bouchaffra, D.2
  • 57
    • 0031691761 scopus 로고    scopus 로고
    • Use of an artificial neural network to predict length of stay in acute pancreatitis
    • Pofahl, W.E., Walczak, S.M., Rhone, E., Izenberg, S.D.: Use of an artificial neural network to predict length of stay in acute pancreatitis. Am. Surg. 64, 868-872 (1998)
    • (1998) Am. Surg. , vol.64 , pp. 868-872
    • Pofahl, W.E.1    Walczak, S.M.2    Rhone, E.3    Izenberg, S.D.4
  • 59
    • 0000481620 scopus 로고
    • On the geometric convergence of the Gibbs sampler
    • Roberts, G.O., Polson, N.G.: On the geometric convergence of the Gibbs sampler. J. Roy. Stat. Soc. B 56, 377-384 (1994)
    • (1994) J. Roy. Stat. Soc. B , vol.56 , pp. 377-384
    • Roberts, G.O.1    Polson, N.G.2
  • 60
    • 0041375875 scopus 로고    scopus 로고
    • On convergence of the EM algorithm and the Gibbs sampler
    • Sahu, S.K., Roberts, G.O.: On convergence of the EM algorithm and the Gibbs sampler. Stat. Comput. 9, 55-64 (1999)
    • (1999) Stat. Comput. , vol.9 , pp. 55-64
    • Sahu, S.K.1    Roberts, G.O.2
  • 61
    • 0034131785 scopus 로고    scopus 로고
    • On-line EM algorithm for the normalized Gaussian network
    • Sato, M., Ishii, S.: On-line EM algorithm for the normalized Gaussian network. Neural Comput. 12, 407-432 (2000)
    • (2000) Neural Comput. , vol.12 , pp. 407-432
    • Sato, M.1    Ishii, S.2
  • 62
    • 33746386802 scopus 로고    scopus 로고
    • ECM algorithms that converge at the rate of EM
    • Sexton, J., Swensen, A.R.: ECM algorithms that converge at the rate of EM. Biometrika 87, 651-662 (2000)
    • (2000) Biometrika , vol.87 , pp. 651-662
    • Sexton, J.1    Swensen, A.R.2
  • 64
    • 0001593436 scopus 로고
    • Recursive parameter estimation using incomplete data
    • Titterington, D.M.: Recursive parameter estimation using incomplete data. J. Roy. Stat. Soc. B 46, 257-267 (1984)
    • (1984) J. Roy. Stat. Soc. B , vol.46 , pp. 257-267
    • Titterington, D.M.1
  • 65
    • 0032029288 scopus 로고    scopus 로고
    • Deterministic annealing EM algorithm
    • Ueda, N., Nakano, R.: Deterministic annealing EM algorithm. Neural Netw. 11, 271-282 (1998)
    • (1998) Neural Netw. , vol.11 , pp. 271-282
    • Ueda, N.1    Nakano, R.2
  • 66
    • 0347724152 scopus 로고    scopus 로고
    • The one-step-late PXEM algorithm
    • van Dyk, D.A., Tang, R.: The one-step-late PXEM algorithm. Stat. Comput. 13, 137-152 (2003)
    • (2003) Stat. Comput. , vol.13 , pp. 137-152
    • van Dyk, D.A.1    Tang, R.2
  • 67
    • 26844482934 scopus 로고    scopus 로고
    • Two-slice EM algorithms for fitting generalized linear mixed models with binary response
    • Vaida, F., Meng, X.L.: Two-slice EM algorithms for fitting generalized linear mixed models with binary response. Stat. Modelling 5, 229-242 (2005)
    • (2005) Stat. Modelling , vol.5 , pp. 229-242
    • Vaida, F.1    Meng, X.L.2
  • 68
    • 84950432017 scopus 로고
    • A Monte Carlo implementation of the EM algorithm and the poor man's data augmentation algorithms
    • Wei, G.C.G., Tanner, M.A.: A Monte Carlo implementation of the EM algorithm and the poor man's data augmentation algorithms. J. Am. Stat. Assoc. 85, 699-704 (1990)
    • (1990) J. Am. Stat. Assoc. , vol.85 , pp. 699-704
    • Wei, G.C.G.1    Tanner, M.A.2
  • 69
    • 23044519568 scopus 로고    scopus 로고
    • An interval analysis approach to the EM algorithm
    • Wright, K., Kennedy, W.J.: An interval analysis approach to the EM algorithm. J. Comput. Graph. Stat. 9, 303-318 (2000)
    • (2000) J. Comput. Graph. Stat. , vol.9 , pp. 303-318
    • Wright, K.1    Kennedy, W.J.2
  • 70
    • 0002210265 scopus 로고
    • On the convergence properties of the EM algorithm
    • Wu, C.F.J.: On the convergence properties of the EM algorithm. Ann. Stat. 11, 95-103 (1983)
    • (1983) Ann. Stat. , vol.11 , pp. 95-103
    • Wu, C.F.J.1


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