Bayesian Ying-Yang harmony learning for local factor analysis: A comparative investigation

Studies in Computational Intelligence

Volumn 155, Issue , 2008, Pages 209-232

  Shi, Lei ^a  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Automatic model selection; Bayesian Ying Yang harmony learning; Data smoothing; Incremental methods; Local Factor Analysis; Model selection; Small sample size; Two phase implementation

Indexed keywords

EID: 51749109145     PISSN: 1860949X     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-540-70829-2_10     Document Type: Article

References (38)

1. Akaike, H.: A new look at the statistical model identification. IEEE Trans. Automatic Control 19(6), 716-723 (1974)
2. Barron, A.R., Rissanen, J., Yu, B.: The Minimum Description Length Principle in Coding and Modeling. IEEE Trans. Infor. Thr. 44(6), 2743-2760 (1998)
3. Bengio, Y., Grandvalet, Y.: No Unbiased Estimator of the Variance of K-Fold Cross-Validation. JMLR 5, 1089-1105 (2004)
4. Bowman, A.W., Azzalini, A.: Applied Smoothing Techniques for Data Analysis. Oxford Statistical Science Series. Oxford Science Publications (1997)
5. Bozdogan, H.: Model selection and Akaike's information criterion (AIC): the general theory and its analytical extensions. Psychometrika 52(3), 345-370 (1987)
6. Bozdogan, H.: Akaike's Information Criterion and Recent Developments in Information Complexity. J. Math. Psychol. 44(1), 62-91 (2000)
7. Burnham, K.P., Anderson, D.: Model Selection and Multi-Model Inference. Springer, Heidelberg (2002)
8. Constantinopoulos, C., Titsias, M.K.: Bayesian Feature and Model Selection for Gaussian Mixture Models. IEEE Trans. Pattern Anal. Mach. Intell. 28(6), 1013-1018 (2006)
9. Figueiredo, M.A.F., Jain, A.K.: Unsupervised Learning of Finite Mixture Models. IEEE Trans. PAMI 24(3), 381-396 (2002)
10. Ghahramani, Z., Beal,M.J.: Variational Inference for BayesianMixtures of Factor Analysers. In: NIPS, pp. 449-455 (1999)
11. Hinton, G.E., Revow, M., Dayan, P.: Recognizing Handwritten Digits Using Mixtures of Linear Models. In: NIPS, pp. 1015-1022 (1994)
12. Mclachlan, G.J., Krishnan, T.: The EM Algorithm and Extensions (Wiley Series in Probability and Statistics). Wiley Series in Probability and Statistics. Wiley-Interscience, Chichester (2007)
13. Parzen, E.: On the estimation of a probability density function and mode. Annals of Mathematical Statistics 33, 1065-1076 (1962)
14. Redner, R., Walker, H.: Mixture Densities, Maximum Likelihood and the EM Algorithm. SIAM Review 26(2), 195-239 (1984)
15. Roberts, S.J., Husmeier, D., Penny, W., Rezek, l.: Bayesian Approaches to Gaussian Mixture Modeling. IEEE Trans. Pattern Anal. Mach. Intell. 20(11), 1133-1142 (1998)
16. Rubin, D., Thayer, D.: EM algorithms for ML factor analysis. Psychometrika 47(1), 69-76 (1982)
17. Salah, A.A., Alpaydin, E.: Incremental Mixtures of Factor Analysers. In: Proc. ICPR, vol. 1, pp. 276-279 (2004)
18. Schwarz, G.: Estimating the dimension of a model. Annals of Statistics 6, 461-464 (1978)
19. Stone, M.: Asymptotics For and Against Cross-Validation. Biometrika 64(1), 29-35 (1977)
20. Tikhonov, A., Arsenin, V.: Solutions of Ill-posed Problems. Winston and Sons (1977)
21. Vapnik, V.: The Nature of Statistical Learning Theory. Springer, New York (1995)
22. Vapnik, V., Sterin, A.: On structural risk minimization or overall risk in a problem of pattern recognition. Automation and Remote Control 10(3), 1495-1503 (1977)
23. Wand, M., Jones, M.: Kernel Smoothing. Monographs on Statistics and Applied Probability. Chapman and Hall, London (1995)
24. Wang, L., Feng, J.: Learning Gaussian mixture models by structural risk minimization. In: Proc. Intnl. Conf. on Machine Learning and Cybernetics 2005, Guangzhou, China, vol. 8, pp. 4858-4863 (2005)
25. Xu, L.: Bayesian Ying Yang Learning. In: Scholarpedia, vol. 2(3) (1809), http://scholarpedia.org/article/Bayesian_Ying_Yang_Learning
26. Xu, L.: Bayesian-Kullback coupled Ying-Yang machines: Unified learnings and new results on vector quantization. In: Proc. of ICONIP 1995, Beijing, China, pp. 977-988 (1995)
27. 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.W., King, I., Leung, D. (eds.) Theoretical aspects of neural computation: A multidisciplinary perspective, pp. 25-42. Springer, Berlin (1997)
28. Xu, L.: RBF nets, mixture experts, and Bayesian Ying-Yang learning. Neurocomputing 19(1-3), 223-257 (1998)
29. Xu, L.: Best harmony, unified RPCL and automated model selection for unsupervised and supervised learning on Gaussian mixtures, ME-RBF models and three-layer nets. International Journal of Neural Systems 11(1), 3-69 (2001)
30. Xu, L.: BYY harmony learning, independent state space, and generalized APT financial analyses. IEEE Trans. Neural Networks 12, 822-849 (2001)
31. Xu, L.: BYY harmony learning, structural RPCL, and topological self-organizing on mixture models. Neural Networks 15(8-9), 1125-1151 (2002)
32. Xu, L.: Data smoothing regularization, multi-sets-learning, and problem solving strategies. Neural Networks 16(5-6), 817-825 (2003)
33. Xu, L.: Advances on BYY harmIny learning: information theoretic perspective, generalized projection geometry, and independent factor auto-determination. IEEE Trans. Neural Networks 15(5), 885-902 (2004)
34. Xu, L.: Bayesian Ying-Yang Learning(I): A unified perspective for statistical modeling. In: Zhong, N., Liu, J. (eds.) Intelligent Technologies for Information Analysis, pp. 615-659. Springer, Heidelberg (2004)
35. Xu, L.: Bayesian Ying-Yang Learning(II): A new mechanism for model selection and regularization. In: Zhong, N., Liu, J. (eds.) Intelligent Technologies for Information Analysis, pp. 661-706. Springer, Heidelberg (2004)
36. Xu, L.: Fundamentals, Challenges, and Advances of Statistical Learning for Knowledge Discovery and Problem Solving: A BYY Harmony Perspective. In: Proc. of Int. Conf. on Neural Networks and Brain, Beijing, China, pp. 24-55 (2005)
37. Xu, L.: Trends on Regularization and Model Selection in Statistical Learning: A Perspective from Bayesian Ying Yang Learning. In: Duch, W., Mandziuk, J., Zurada, J.M. (eds.) Studies in Computational Intelligence, pp. 365-406. Springer, Heidelberg (2007)
38. Xu, L.: A unified perspective and new results on RHT computing, mixture based learning, and multi-learner based problem solving. Pattern Recognition, 2129-2153 (2007)