Codimensional matrix pairing perspective of BYY harmony learning: Hierarchy of bilinear systems, joint decomposition of data-covariance, and applications of network biology

Frontiers of Electrical and Electronic Engineering in China

Volumn 6, Issue 1, 2011, Pages 86-119

  Lei, Xu ^a  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Automatic model selection; Bayesian Ying Yang (BYY) harmony learning; Bi clustering; Bi linear stochastic system; Co dimensional matrix pair; De noise embedded local factor analysis (LFA); Denoise embedded Gaussian mixture; Gene transcriptional regulatory; Generalized linear model (GLM); Manifold learning; Network alignment; Network integration; Semi blind learning; Sparse learning; Temporal factor analysis (TFA)

Indexed keywords

EID: 79952291896     PISSN: 16733460     EISSN: 16733584     Source Type: Journal    
DOI: 10.1007/s11460-011-0135-1     Document Type: Article

References (149)

1. Xu L. Bayesian Ying-Yang system, best harmony learning, and five action circling. A special issue on Emerging Themes on Information Theory and Bayesian Approach, Frontiers of Electrical and Electronic Engineering in China, 2010, 5(3): 281-328.
2. Anderson T W, Rubin H. Statistical inference in factor analysis. In: Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability. 1956, 5: 111-150.
3. Rubi D, Thayer D. EM algorithm for ML factor analysis. Psychometrika, 1976, 57: 69-76.
4. Bozdogan H, Ramirez D E. FACAIC: model selection algorithm for the orthogonal factor model using AIC and FACAIC. Psychometrika, 1988, 53(3): 407-415.
5. Belouchrani A, Cardoso J. Maximum likelihood source separation by the expectation maximization technique: deterministic and stochastic implementation. In: Proceedings of NOLTA95. 1995, 49-53.
6. Xu L. Bayesian Kullback Ying-Yang dependence reduction theory. Neurocomputing, 1998, 22(1-3): 81-111.
7. Xu L. BYY learning, regularized implementation, and model selection on modular networks with one hidden layer of binary units, Neurocomputing, 2003, 51: 277-301.
8. Xu L. Advances on BYY harmony learning: Information theoretic perspective, generalized projection geometry, and independent factor auto-determination. IEEE Transactions on Neural Networks, 2004, 15(4): 885-902.
9. Xu L. Independent component analysis and extensions with noise and time: a Bayesian Ying-Yang learning perspective. Neural Information Processing-Letters and Reviews, 2003, 1(1): 1-52.
10. Moulines E, Cardoso J, Gassiat E. Maximum likelihood for blind separation and deconvolution of noisy signals using mixture models. In: Proc. ICASSP97. 1997, 3617-3620.
11. Attias H. Independent factor analysis. Neural Computation, 1999, 11(4): 803-851.
12. Liu Z Y, Chiu K C, Xu L. Investigations on non-Gaussian factor analysis. IEEE Signal Processing Letters, 2004, 11(7): 597-600.
13. Xu L. Independent subspaces. In: Ramón J, Dopico R, Dorado J, Pazos A, eds. Encyclopedia of Artificial Intelligence, Hershey (PA): IGI Global. 2008, 903-912.
14. Saund E. A multiple cause mixture model for unsupervised learning. Neural Computation, 1995, 7(1): 51-71.
15. Zhang B L, Xu L, Fu M Y. Learning multiple causes by competition enhanced least mean square error reconstruction. International Journal of Neural Systems, 1996, 7(3): 223-236.
16. Reckase M D. The past and future of multidimensional item response theory. Applied Psychological Measurement, 1997, 21(1): 25-36.
17. Moustaki I, Knott M. Generalized latent trait models. Psychometrika, 2000, 65(3): 391-411.
18. Bartholomew D J, Knott M. Latent variable models and factor analysis, Kendalls, Library of Statistics, Vol. 7. New York: Oxford University Press, 1999.
19. Paatero P, Tapper U. Positive matrix factorization: a nonnegative factor model with optimal utilization of error estimates of data values. Environmetrics, 1994, 5(2): 111-126.
20. Lee D D, Seung H S. Learning the parts of objects by nonnegative matrix factorization. Nature, 1999, 401(6755): 788-791.
21. Lee D D, Seung H S. Algorithms for non-negative matrix factorization. Adv. Neural Inf. Process, 2001, 13: 556-562.
22. Kim H, Park H. Nonnegative matrix factorization based on alternating nonnegativity constrained least squares and active set method. SIAM Journal on Matrix Analysis and Applications, 2008, 30(2): 713-730.
23. Kim H, Park H. Sparse non-negative matrix factorizations via alternating non-negativity-constrained least squares for microarray data analysis. Bioinformatics (Oxford, England), 2007, 23(12): 1495-1502.
24. Chen Y, Rege M, Dong M, Hua J. Non-negative matrix factorization for semi-supervised data clustering. Knowledge and Information Systems, 2008, 17(3): 355-379.
25. Ho N, Vandooren P. Non-negative matrix factorization with fixed row and column sums. Linear Algebra and Its Applications, 2008, 429(5-6): 1020-1025.
26. Cemgil A T. Bayesian Inference for Nonnegative Matrix Factorisation Models, Computational Intelligence and Neuroscience, 2009.
27. Yang Z, Zhu Z, Oja E. Automatic rank determination in projective nonnegative matrix factorization. Lecture Notes in Computer Science: Latent Variable Analysis and Signal Separation, 2010, (6365): 514-521.
28. Tu S, Chen R, Xu L. A binary matrix factorization algorithm for protein complex prediction. In: Proceedings of the BIBM 2010 International Workshop on Computational Proteomics, Hong Kong, December 18-21, 2010.
29. Redner R A, Walker H F. Mixture densities, maximum likelihood, and the EM algorithm. SIAM Review, 1984, 26(2): 195-239.
30. Xu L, Jordan M I. On convergence properties of the EM algorithm for Gaussian mixtures. Neural Computation, 1996, 8(1): 129-151.
31. McLachlan G J, Geoffrey J. The EM Algorithms and Extensions. Wiley, 1997.
32. Xu L. Multisets modeling learning: a unified theory for supervised and unsupervised learning. In: Proceedings of IEEE ICNN94. 1994, I: 315-320.
33. Xu L. A unified learning framework: multisets modeling learning. In: Proceedings of WCNN95. 1995, 1: 35-42.
34. Xu L. Rival penalized competitive learning, finite mixture, and multisets clustering. In: Proceedings of IEEE-INNS IJCNN98, Anchorage, Alaska, vol. II. 1998, 2525-2530.
35. Xu L. BYY harmony learning, structural RPCL, and topological self-organizing on unsupervised and supervised mixture models. Neural Networks, 2002, (8-9): 1125-1151.
36. Xu L. Data smoothing regularization, multi-sets-learning, and problem solving strategies. Neural Networks, 2003, 16(5-6): 817-825.
37. Belkin M, Niyogi P. Laplacian eigenmaps for dimensionality reduction and data representation. Neural Computation, 2003, 15(6): 1373-1396.
38. He X, Niyogi P. Locality Preserving Projections. In: Advances in Neural Information Processing Systems 16. Cambridge, MA: MIT Press, 2003, 152-160.
39. Wallace C S, Dowe D R. Minimum message length and Kolmogorov complexity. Computer Journal, 1999, 42(4): 270-283.
40. Figueiredo M A F, Jain A K. Unsupervised learning of finite mixture models. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2002, 24(3): 381-396.
41. Williams P M. Bayesian regularization and pruning using a Laplace prior. Neural Computation, 1995, 7(1): 117-143.
42. Tibshirani R. Regression shrinkage and selection via the lasso. J. Royal. Statist. Soc B., 1996, 58(1): 267-288.
43. Hansen L K, Goutte C. Regularization with a pruning prior. Neural Networks, 1997, 10(6): 1053-1059.
44. Schwarz G. Estimating the dimension of a model. Annals of Statistics, 1978, 6(2): 461-464.
45. Rissanen J. Modeling by shortest data description. Automatica, 1978, 14: 465-471.
46. Rissanen J. Basics of estimation. Frontiers of Electrical and Electronic Engineering in China, 2010, 5(3): 274-280.
47. Corduneanu A, Bishop CM. Variational Bayesian model selection for mixture distributions. In: Jaakkola T, Richardson T, eds. Artificial Intelligence and Statistics, Morgan Kaufmann. 2001, 27-34.
48. Choudrey R A, Roberts S J. Variational mixture of Bayesian independent component analyzers. Neural Computation, 2003, 15(1): 213-252.
49. McGrory C A, Titterington D M. Variational approximations in Bayesian model selection for finite mixture distributions. Computational Statistics & Data Analysis, 2007, 51(11): 5352-5367.
50. Umeyama S. An eigendecomposition approach to weighted graph matching problems. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1988, 10(5): 695-703.
51. Xu L, Oja E. Improved Simulated Annealing, Boltzmann Machine and Attributed Graph Matching. In: Goos G, Hartmanis J, eds. Lecture Notes in Computer Sciences, Springer-Verlag, 1989, 412: 151-160.
52. Conte D, Foggiay P, Sansoney C, Vento M. Thirty years of Graph Matching in Pattern Recognition. International Journal of Pattern Recognition and Artificial Intelligence, 2004, 18(3): 265-298.
53. Xu L, Klasa S. A PCA like rule for pattern classification based on attributed graph. In: Proceedings of 1993 International Joint Conference on Neural Networks (IJCNN93), Nagoya. 1993, 1281-1284.
54. Xu L, King I. A PCA approach for fast retrieval of structural patterns in attributed graphs. IEEE Transactions on Systems, Man and Cybernetics, Part B, 2001, 31(5): 812-817.
55. Li H B, Stoica P, Li J. Computationally efficient maximum likelihood estimation of structured covariance matrices. IEEE Transactions on Signal Processing, 1999, 47(5): 1314-1323.
56. Burg J, Luenberger D, Wenger D. Estimation of structured covariance matrices. Proceedings of the IEEE, 1982, 70(9): 963-974.
57. Xu L. Beyond PCA learning: from linear to nonlinear and from global representation to local representation. In: Proceedings of ICONIP94. 1994, 2: 943-949.
58. Xu L. Vector quantization by local and hierarchical LMSER. In: Proceedings of 1995 Intl Conf. on Artificial Neural Networks (ICANN95), Paris. 1995, II: 575-579.
59. Hinton G E, Dayan P, Revow M. Modeling the manifolds of images of handwritten digits. IEEE Transactions on Neural Networks, 1997, 8(1): 65-74.
60. Liu Z Y, Chiu K C, Xu L. Strip line detection and thinning by RPCL-based local PCA. Pattern Recognition Letters, 2003, 24(14): 2335-2344.
61. Liu Z Y, Xu L. Topological local principal component analysis. Neurocomputing, 2003, 55(3-4): 739-745.
62. Tipping M E, Bishop C M. Mixtures of probabilistic principal component analyzers. Neural Computation, 1999, 11(2): 443-482.
63. Salah A A, Alpaydin E. Incremental mixtures of factor analyzers. In: Proceedings of the 17th International Conference on Pattern Recognition. Cambridge: IEEE Press, 2004, 1: 276-279.
64. Utsugi A, Kumagai T. Bayesian analysis of mixtures of factor analyzers. Neural Computation, 2001, 13(5): 993-1002.
65. Ghahramani Z, Beal M. Variational inference for Bayesian mixtures of factor analysers, Advances in neural information processing systems 12. Cambridge, MA: MIT Press, 2000, 449-455.
66. Xu L, Bayesian Ying Yang System, Best Harmony Learning, and Gaussian Manifold Based Family. In: Zurada et al, eds. Computational Intelligence: Research Frontiers (WCCI2008 Plenary/Invited Lectures), LNCS5050, 2008, 48-78.
67. Xu L. Learning algorithms for RBF functions and subspace based functions. In: Olivas E S, et al, eds. Handbook of Research on Machine Learning, Applications and Trends: Algorithms, Methods and Techniques, Hershey (PA): IGI Global. 2009, 60-94.
68. Brown R G, Hwang P Y C. Introduction to random signals and applied Kalman filtering. John Wiley & Sons, Inc., 1997.
69. Xu L. Bayesian Ying Yang System and Theory as a Unified Statistical Learning Approach (II): From Unsupervised Learning to Supervised Learning and Temporal Modeling. In: Wong K M, Yeung D Y, King I, et al, eds. Theoretical Aspects of Neural Computation: A Multidisciplinary Perspective. Berlin: Springer-Verlag, 1997, 25-60.
70. Xu L. Temporal BYY learning and its applications to extended Kalman filtering, hidden Markov model, and sensormotor integration. In: Proceedings of IEEE-INNS 1999 Intl J. Conf on Neural Networks, Washington. 1999, 2: 949-954.
71. Xu L. Bayesian Ying-Yang system and theory as a unified statistical learning approach:(V) temporal modeling for temporal perception and control. In: Proceedings of ICONIP98, Kitakyushu. 1998, 2: 877-884.
72. Ghahramani Z, Hinton G E. Variational learning for switching state-space models. Neural Computation, 2000, 12(4): 831-864.
73. Xu L. Temporal BYY learning for state space approach, hidden Markov model and blind source separation. IEEE Transactions on Signal Processing, 2000, 48(7): 2132-2144.
74. Xu L. BYY harmony learning, independent state space, and generalized APT financial analyses. IEEE Transactions on Neural Networks, 2001, 12(4): 822-849.
75. Xu L. Temporal BYY encoding, Markovian state spaces, and space dimension determination. IEEE Transactions on Neural Networks, 2004, 15(5): 1276-1295.
76. Liao J C, Boscolo R, Yang Y L, Tran L M, Sabatti C, Roychowdhury V P. Network component analysis: reconstruction of regulatory signals in biological systems. Proceedings of the National Academy of Sciences of the United States of America, 2003, 100(26): 15522-15527.
77. Boulesteix A L, Strimmer K. Predicting transcription factor activities from combined analysis of microarray and ChIP data: a partial least squares approach. Theoretical Biology & Medical Modelling, 2005, 2(1): 23.
78. Brynildsen M P, Tran L M, Liao J C. A Gibbs sampler for the identification of gene expression and network connectivity consistency. Bioinformatics (Oxford, England), 2006, 22(24): 3040-3046.
79. Brynildsen M P, Wu T Y, Jang S S, Liao J C. Biological network mapping and source signal deduction. Bioinformatics (Oxford, England), 2007, 23(14): 1783-1791.
80. Stockham T G, Cannon T M, Ingebretsen R B. Blind deconvolution through digital signal processing. Proceedings of the IEEE, 1975, 63(4): 678-692.
81. Kundur D, Hatzinakos D. Blind image deconvolution revisited. IEEE Signal Processing Magazine, 1996, 13(6): 61-63.
82. Xu L, Yan P F, Chang T. Semi-blind deconvolution of finite length sequence: (I) linear problem & (II). Nonlinear Problem, SCIENTIA SINICA, Series A, 1987, (12): 1318-1344.
83. Zhou Z H. When semi-supervised learning meets ensemble learning. Frontiers of Electrical and Electronic Engineering in China, 2011, 6(1): 6-16.
84. De Las Rivas J, Fontanillo C. Protein-protein interactions essentials: key concepts to building and analyzing interactome networks. PLoS Comput Biol, 2010, 6(6): e1000807.
85. Han J D. Understanding biological functions through molecular networks. Cell Research, 2008, 18(2): 224-237.
86. Davies M. Identifiability Issues in Noisy ICA. IEEE SIGNAL PROCESSING LETTERS, 2004, 11(5): 470-473.
87. Morris C. Natural exponential families with quadratic variance functions. Annals of Statistics, 1982, 10(1): 65-80.
88. McCullagh P, Nelder J. Generalized Linear Models. 2nd ed. Boca Raton: Chapman and Hall/CRC, 1989.
89. Gorman J W, Toman R J. Selection of variables for fitting equations to data. Technometrics, 1966, 8: 27-51.
90. Mallows C L. Some comments on Cp. Technometrics, 1973, 15: 661-675.
91. Wallace C S, Boulton D M. An information measure for classification. Computer Journal, 1968, 11(2): 185-194.
92. Akaike H. A new look at the statistical model identification. IEEE Transactions on Automatic Control, 1974, 19(6): 714-723.
93. Solomonoff R J. A formal theory of inductive inference. Part I. Information and Control, 1964, 7(1): 1-22.
94. Kolmogorov A N. Three approaches to the quantitative definition of information. Problems of Information Transmission, 1965, 1(1): 1-11.
95. Vapnik V. The Nature of Statistical Learning Theory, Springer-Verlag, New York, 1995.
96. Xu L, Krzyzak A, Oja E. Rival penalized competitive learning for clustering analysis, RBF net and curve detection. IEEE Transactions on Neural Networks, 1993, 4(4): 636-649.
97. Xu L, Krzyzak A, Oja E. Unsupervised and supervised classifications by rival penalized competitive learning. In: Proceedings of the 11th International Conference on Pattern Recognition. 1992, I: 672-675.
98. Tu S K, Xu L. Parameterizations make different model selections: empirical findings from factor analysis, to appear on Frontiers of Electrical and Electronic Engineering in China, 2011.
99. Sun K, Tu S, Gao D Y, Xu L. Canonical dual approach to binary factor analysis. In: Adali T, Jutten C, Romano J M T, Barros A K, eds. Independent Component Analysis and Signal Separation. Lecture Notes in Computer Science, 2009, 5441: 346-353.
100. Xu L. Machine learning problems from optimization perspective. Journal of Global Optimization, 2010, 47(3): 369-401.
101. He X F, Lin B B. Tangent space learning and generalization. Frontiers of Electrical and Electronic Engineering in China, 2011, 6(1): 27-42.
102. Luxburg U. A tutorial on spectral clustering. Statistics and Computing, 2007, 17(4): 395-416.
103. Chung F R. Spectral Graph Theory. Amer. Math. Soc., Providence, RI. MR1421568, 1997.
104. Xu L. Distribution approximation, combinatorial optimization, and Lagrange-Barrier. In: Proceedings of International Joint Conference on Neural Networks 2003 (IJCNN 03), Jantzen Beach, Portland. 2003, 2354-2359.
105. Xu L. Combinatorial optimization neural nets based on a hybrid of Lagrange and transformation approaches. In: Proceedings Of World Congress on Neural Networks. San Diego, CA. 1994, 399-404.
106. Xu L. On the hybrid LT combinatorial optimization: new U-shape barrier, sigmoid activation, least leaking energy and maximum entropy. In: Proceedings of Intl. Conf. on Neural Information Processing, Beijing. 1995, 309-312.
107. Xu L. One-bit-matching ICA theorem, convex-concave programming, and combinatorial optimization. In: Advances in neural networks: ISNN 2005, LNCS 3496. Berlin: Springer-Verlag, 2005, 5-20.
108. Xu L. One-bit-matching theorem for ICA, convex-concave programming on polyhedral set, and distribution approximation for combinatorics. Neural Computation, 2007, 19(2): 546-569.
109. Xu L, Amari S I. Combining Classifiers and Learning Mixture-of-Experts, In: Ramón J, Dopico R, Dorado J, Pazos A, eds. Encyclopedia of Artificial Intelligence. IGI Global (IGI) publishing company, 2008, 318-326.
110. Xu L. A unified perspective and new results on RHT computing, mixture based learning, and multi-learner based problem solving. Pattern Recognition, 2007, 40(8): 2129-2153.
111. Sun N, Zhao H Y. Reconstructing transcriptional regulatory networks through genomics data. Statistical Methods in Medical Research, 2009, 18(6): 595-617.
112. Bar-Joseph Z, Gerber G K, Lee T I, Rinaldi N J, Yoo J Y, Robert F, Gordon D B, Fraenkel E, Jaakkola T S, Young R A, Gifford D K. Computational discovery of gene modules and regulatory networks. Nature Biotechnology, 2003, 21(11): 1337-1342.
113. De Las Rivas J, Fontanillo C. Protein-protein interactions essentials: key concepts to building and analyzing interactome networks. PLoS Comput Biol, 2010, 6(6): e1000807.
114. Singh R, Xu J B, Berger B. Global alignment of multiple protein interaction networks with application to functional orthology detection. Proceedings of the National Academy of Sciences of the United States of America, 2008, 105(35): 12763-12768.
115. Spirin V, Mirny L A. Protein complexes and functional modules in molecular networks. Proceedings of the National Academy of Sciences of the United States of America, 2003, 100(21): 12123-12128.
116. Bu D, Zhao Y, Cai L, Xue H, Zhu X, Lu H, Zhang J, Sun S, Ling L, Zhang N, Li G, Chen R. Topological structure analysis of the protein-protein interaction network in budding yeast. Nucleic Acids Research, 2003, 31(9): 2443-2450.
117. Sharan R, Ulitsky I, Shamir R. Network-based prediction of protein function. Molecular Systems Biology, 2007, 3: 88.
118. Pinkert S, Schultz J, Reichardt J. Protein interaction networks more than mere modules. PLoS Computational Biology, 2010, 6(1): e1000659.
119. Segal E, Shapira M, Regev A, Peer D, Botstein D, Koller D, Friedman N. Module networks: identifying regulatory modules and their condition-specific regulators from gene expression data. Nature Genetics, 2003, 34(2): 166-176.
120. Reiss D J, Baliga N S, Bonneau R. Integrated biclustering of heterogeneous genome-wide datasets for the inference of global regulatory networks. BMC Bioinformatics, 2006, 7(1): 280.
121. Lemmens K, Dhollander T, De Bie T, Monsieurs P, Engelen K, Smets B, Winderickx J, De Moor B, Marchal K. Inferring transcriptional modules from ChIP-chip, motif and microarray data. Genome Biology, 2006, 7(5): R37(1-14).
122. Youn A, Reiss D J, Stuetzle W. Learning transcriptional networks from the integration of ChIP-chip and expression data in a non-parametric model. Bioinformatics (Oxford, England), 2010, 26(15): 1879-1886.
123. Holter N S, Mitra M, Maritan A, Cieplak M, Banavar J R, Fedoroff N V. Fundamental patterns underlying gene expression profiles: simplicity from complexity. Proceedings of the National Academy of Sciences of the United States of America, 2000, 97(15): 8409-8414.
124. Yeung M K, Tegnr J, Collins J J. Reverse engineering gene networks using singular value decomposition and robust regression. Proceedings of the National Academy of Sciences of the United States of America, 2002, 99(9): 6163-6168.
125. Alter O, Brown P O, Botstein D. Singular value decomposition for genome-wide expression data processing and modeling. Proceedings of the National Academy of Sciences of the United States of America, 2000, 97(18): 10101-10106.
126. Alter O, Brown P O, Botstein D. Generalized singular value decomposition for comparative analysis of genome-scale expression data sets of two different organisms. Proceedings of the National Academy of Sciences of the United States of America, 2003, 100(6): 3351-3356.
127. Bussemaker H J, Li H, Siggia E D. Regulatory element detection using correlation with expression. Nature Genetics, 2001, 27(2): 167-174.
128. Lee S I, Batzoglou S. Application of independent component analysis to microarrays. Genome Biology, 2003, 4(11): R76.
129. Liebermeister W. Linear modes of gene expression determined by independent component analysis. Bioinformatics (Oxford, England), 2002, 18(1): 51-60.
130. Sun N, Carroll R J, Zhao H. Bayesian error analysis model for reconstructing transcriptional regulatory networks. Proceedings of the National Academy of Sciences of the United States of America, 2006, 103(21): 7988-7993.
131. Sabatti C, James G M. Bayesian sparse hidden components analysis for transcription regulation networks. Bioinformatics, 2006, 22(6): 739-746.
132. Liu X, Jessen W J, Sivaganesan S, Aronow B J, Medvedovic M. Bayesian hierarchical model for transcriptional module discovery by jointly modeling gene expression and ChIPchip data. BMC Bioinformatics, 2007, 8(1): 283.
133. Xing B, van der Laan M J. A statistical method for constructing transcriptional regulatory networks using gene expression and sequence data. Journal of Computational Biology, 2005, 12(2): 229-246.
134. Pournara I, Wernisch L. Factor analysis for gene regulatory networks and transcription factor activity profiles. BMC Bioinformatics, 2007, 8(1): 61.
135. Gardner T S, di Bernardo D, Lorenz D, Collins J J. Inferring genetic networks and identifying compound mode of action via expression profiling. Science, 2003, 301(5629): 102-105.
136. Rangel C, Angus J, Ghahramani Z, Lioumi M, Sotheran E, Gaiba A, Wild D L, Falciani F. Modeling T-cell activation using gene expression profiling and state-space models. Bioinformatics (Oxford, England), 2004, 20(9): 1361-1372.
137. Beal M J, Falciani F, Ghahramani Z, Rangel C, Wild D L. A Bayesian approach to reconstructing genetic regulatory networks with hidden factors. Bioinformatics (Oxford, England), 2005, 21(3): 349-356.
138. Sanguinetti G, Lawrence N D, Rattray M. Probabilistic inference of transcription factor concentrations and genespecific regulatory activities. Bioinformatics (Oxford, England), 2006, 22(22): 2775-2781.
139. Yamaguchi R, Higuchi T. State-space approach with the maximum likelihood principle to identify the system generating time-course gene expression data of yeast. International Journal of Data Mining and Bioinformatics, 2006, 1(1): 77-87.
140. Li Z, Shaw S M, Yedwabnick M J, Chan C. Using a statespace model with hidden variables to infer transcription factor activities. Bioinformatics (Oxford, England), 2006, 22(6): 747-754.
141. Inoue L Y, Neira M, Nelson C, Gleave M, Etzioni R. Cluster-based network model for time-course gene expression data. Biostatistics (Oxford, England), 2007, 8(3): 507-525.
142. Martin S, Zhang Z, Martino A, Faulon J L. Boolean dynam ics of genetic regulatory networks inferred from microarray time series data. Bioinformatics (Oxford, England), 2007, 23(7): 866-874.
143. Hirose O, Yoshida R, Imoto S, Yamaguchi R, Higuchi T, Charnock-Jones D S, Print C, Miyano S. Statistical inference of transcriptional module-based gene networks from time course gene expression profiles by using state space models. Bioinformatics (Oxford, England), 2008, 24(7): 932-942.
144. Xiong H, Choe Y. Structural systems identification of genetic regulatory networks. Bioinformatics (Oxford, England), 2008, 24(4): 553-560.
145. Wu F X, Zhang W J, Kusalik A J. State-space model with time delays for gene regulatory networks. Journal of Biological System, 2004, 12(4): 483-500.
146. Shiraishi Y, Kimura S, Okada M. Inferring cluster-based networks from differently stimulated multiple time-course gene expression data. Bioinformatics (Oxford, England), 2010, 26(8): 1073-1081.
147. Kim T Y, Kim H U, Lee S Y. Data integration and analysis of biological networks. Current Opinion in Biotechnology, 2010, 21(1): 78-84.
148. Xu L, Pearl J. Structuring causal tree models with continuous variables. In: Proceedings of the 3rd Annual Conference on Uncertainty in Artificial Intelligence. 1987, 170-179.
149. Xu L, Pearl J. Structuring Causal Tree Models with Continuous Variables. In: Kanal L N, Levitt T S, Lemmer J F, eds. Uncertainty in Artificial Intelligence 3. North Holland, Amsterdam, 1989, 209-219.