Skip to main content

Bayesian Ying Yang System, Best Harmony Learning, and Gaussian Manifold Based Family

  • Chapter
Computational Intelligence: Research Frontiers (WCCI 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5050))

Included in the following conference series:

Abstract

Two intelligent abilities and three inverse problems are re-elaborated from a probability theory based two pathway perspective, with challenges of statistical learning and efforts towards the challenges overviewed. Then, a detailed introduction is provided on the Bayesian Ying-Yang (BYY) harmony learning. Proposed firstly in (Xu,1995) and systematically developed in the past decade, this approach consists of a two pathway featured BYY system as a general framework for unifying a number of typical learning models, and a best Ying-Yang harmony principle as a general theory for parameter learning and model selection. The BYY harmony learning leads to not only a criterion that outperforms typical model selection criteria in a two-phase implementation, but also model selection made automatically during parameter learning for several typical learning tasks, with computing cost saved significantly. In addition to introducing the fundamentals, several typical learning approaches are also systematically compared and re-elaborated from the BYY harmony learning perspective. Moreover, a further brief is made on the features and applications of a particular family called Gaussian manifold based BYY systems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Akaike, H.: A new look at the statistical model identification. IEEE Tr. Automatic Control 19, 714–723 (1974)

    Google Scholar 

  2. Akaike, H.: Likelihood of a model and information criteria. Journal of Econometrics 16, 3–14 (1981)

    Article  MATH  Google Scholar 

  3. Amari, S., Cichocki, A., Yang, H.: A new learning algorithm for blind signal separation. In: Advances in NIPS, vol. 8, pp. 757–763. MIT Press, Cambridge (1996)

    Google Scholar 

  4. An, Y.J., et al.: A Comparative Investigation on Model Selection in Independent Factor Analysis. J. Mathematical Modelling and Algorithms 5, 447–473 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  5. Barndorff-Nielson, O.E.: Methods of Information and Exponential Families. Wiley, Chichester (1978)

    Google Scholar 

  6. Bourlard, H., Kamp, Y.: Auto-association by multilayer Perceptrons and singular value decomposition. Biological Cybernetics 59, 291–294 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  7. Bozdogan, H.: Model Selection and Akaike’s Information Criterion: The general theory and its analytical extension. Psychometrika 52, 345–370 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  8. Bozdogan, H., Ramirez, D.E.: FACAIC: Model selection algorithm for the orthogonal factor model using AIC and FACAIC. Psychometrika 53(3), 407–415 (1988)

    Article  MATH  Google Scholar 

  9. Brown, L.: Fundamentals of Statistical Exponential Families. Institute of Mathematical Statistics, Hayward, CA (1986)

    Google Scholar 

  10. Cavanaugh, J.E.: Unifying the derivations for the Akaike and corrected Akaike information criteria. Statistics & Probability Letters 33, 201–208 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  11. Dayan, P., Hinton, G.E., Neal, R.M., Zemel, R.S.: The Helmholtz machine. Neural Computation 7(5), 889–904 (1995)

    Article  Google Scholar 

  12. Gilks, W.R., Richardson, S., Spiegelhakter, D.J.: Markov Chain Monte carlo in Practice. Chapman and Hall, London (1996)

    MATH  Google Scholar 

  13. Girosi, F., et al.: Regularization theory and neural architectures. Neural Computation 7, 219–269 (1995)

    Article  Google Scholar 

  14. Grossberg, S.: Adaptive patten classification and universal recording: I&II. Biological Cybernetics 23, 187–202 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  15. Hinton, G.E., Zemel, R.S.: Autoencoders, minimum description length and Helmholtz free energy. In: Advances in NIPS, vol. 6, pp. 3–10 (1994)

    Google Scholar 

  16. Hinton, G.E., Dayan, P., Frey, B.J., Neal, R.N.: The wake-sleep algorithm for unsupervised learning neural networks. Science 268, 1158–1160 (1995)

    Article  Google Scholar 

  17. Hu, X.L., Xu, L.: A Comparative Study on Selection of Cluster Number and Local Subspace Dimension in the Mixture PCA Models. In: Wang, J., Yi, Z., Żurada, J.M., Lu, B.-L., Yin, H. (eds.) ISNN 2006. LNCS, vol. 3971, pp. 1214–1221. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  18. Hu, X.L., Xu, L.: A comparative investigation on subspace dimension determination. Neural Networks 17, 1051–1059 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  19. Jaakkola, T.S.: Tutoiral on variational approximation methods. In: Opper, Saad (eds.) Advanced Mean Field methods: Theory & Pratice, pp. 129–160. MIT Press, Cambridge (2001)

    Google Scholar 

  20. Jordan, M., Ghahramani, Z., Jaakkola, T., Saul, L.: Introduction to variational methods for graphical models. Machine Learning 37, 183–233 (1999)

    Article  MATH  Google Scholar 

  21. Kass, R.E., Raftery, A.E.: Bayes Factors. Journal of the American Statistical Association 90, 773–795 (1995)

    Article  MATH  Google Scholar 

  22. MacKay, D.J.C.: Information Theory, Inference, and Learning Algorithms. Cambridge University Press, Cambridge (2003)

    MATH  Google Scholar 

  23. Neath, A.A., Cavanaugh, J.E.: Regression and time series model selection using variants of the Schwarz information criterion. Communications in Statistics A 26, 559–580 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  24. Neal, R., 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. MIT Press, Cambridge (1999)

    Google Scholar 

  25. Press, S.J.: Bayesian statistics: principles, models, and applications. Factors. John Wiley & Sons, Inc., Chichester (1989)

    Google Scholar 

  26. Poggio, T., Girosi, F.: Networks for approximation and learning. Proc. of IEEE 78, 1481–1497 (1990)

    Article  Google Scholar 

  27. Redner, R.A., Walker, H.F.: Mixture densities, maximum likelihood, and the EM algorithm. SIAM Review 26, 195–239 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  28. Rissanen, J.: Stochastic complexity and modeling. Annals of Statistics 14(3), 1080–1100 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  29. Rissanen, J.: Stochastic Complexity in Statistical Inquiry. World Scientific, Singapore (1989)

    MATH  Google Scholar 

  30. Rivals, I., Personnaz, L.: On Cross Validation for Model Selection. Neural Computation 11, 863–870 (1999)

    Article  Google Scholar 

  31. Rockafellar, R.: Convex Analysis. Princeton University Press, Princeton (1972)

    Google Scholar 

  32. Ruanaidh, O., Joseph, J.K.: Numerical Bayesian methods applied to signal processing. Springer, New York (1996)

    MATH  Google Scholar 

  33. Rustagi, J.: Variational Method in Statistics. Academic Press, New York (1976)

    Google Scholar 

  34. Schwarz, G.: Estimating the dimension of a model. Annals of Statistics 6, 461–464 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  35. Shi, L.: Bayesian Ying-Yang harmony learning for local factor analysis: a comparative investigation. In: Tizhoosh, Ventresca (eds.) Oppositional Concepts in Computational Intelligence (Studies in CI). Springer, Heidelberg (2008)

    Google Scholar 

  36. Shi, L., Xu, L.: Local Factor Analysis with Automatic Model Selection: A Comparative Study and Digits Recognition Application. In: Kollias, S., Stafylopatis, A., Duch, W., Oja, E. (eds.) ICANN 2006. LNCS, vol. 4132, pp. 260–269. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  37. Stone, M.: Cross-validatory choice and assessment of statistical prediction. J. Royal Statistical Society B 36, 111–147 (1974)

    MATH  Google Scholar 

  38. Stone, M.: An asymptotic equivalence of choice of model by cross-validation and Akaike’s criterion. J. Royal Statistical Society B 39(1), 44–47 (1977)

    MATH  Google Scholar 

  39. Stone, M.: Cross-validation: A review. Math. Operat. Statist. 9, 127–140 (1978)

    MATH  Google Scholar 

  40. Tikhonov, A.N., Arsenin, V.Y.: Solutions of Ill-posed Problems. Winston and Sons (1977)

    Google Scholar 

  41. Vapnik, V.N.: The Nature Of Statistical Learning Theory. Springer, Heidelberg (1995)

    MATH  Google Scholar 

  42. Wallace, C.S., Boulton, D.M.: An information measure for classification. Computer Journal 11, 185–194 (1968)

    MATH  Google Scholar 

  43. Wallace, C.S., Freeman, P.R.: Estimation and inference by compact coding. J. of the Royal Statistical Society 49(3), 240–265 (1987)

    MATH  MathSciNet  Google Scholar 

  44. Wang, L., Feng, J.: Learning Gaussian mixture models by structural risk minimization. In: Proc. ICMLC 2005, August 19-21, Guangzhou, China, pp. 4858–4863 (2005)

    Google Scholar 

  45. Xu, L.: Machine learning problems from optimization perspective. Journal of Global Optimization (to appear, 2008)

    Google Scholar 

  46. Xu, L.: A unified perspective and new results on RHT computing, mixture based learning, and multi-learner based problem solving. Pattern Recognition 40, 2129–2153 (2007)

    Article  MATH  Google Scholar 

  47. Xu, L.: Bayesian Ying Yang learning. Scholarpedia 2(3), 1809 (2007), http://scholarpedia.org/article/BayesianYingYangLearning

    Google Scholar 

  48. Xu, L.: Rival penalized competitive learning. Scholarpedia 2(8), 1810 (2007), http://scholarpedia.org/article/RivalPenalizedCompetitiveLearning

    Google Scholar 

  49. Xu, L.: A trend on regularization and model selection in statistical learning: a Bayesian Ying Yang learning perspective. In: Duch, W., Mandziuk, J. (eds.) Challenges for Computational Intelligence, pp. 365–406. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  50. Xu, L.: Temporal BYY encoding, Markovian state spaces, and space dimension determination. IEEE Tr. Neural Networks 15, 1276–1295 (2004)

    Article  Google Scholar 

  51. Xu, L.: Advances on BYY harmony learning: information theoretic perspective, generalized projection geometry, and independent factor auto-determination. IEEE Tr. Neural Networks 15, 885–902 (2004)

    Article  Google Scholar 

  52. Xu, L.: Bayesian Ying Yang learning (I) & (II). In: Zhong, Liu (eds.) Intelligent Technologies for Information Analysis, pp. 615–706. Springer, Heidelberg (2004)

    Google Scholar 

  53. Xu, L.: BI-directional BYY learning for mining structures with projected polyhedra and topological map. In: Lin, Smale, Poggio, Liau (eds.) Proc. of FDM 2004: Foundations of Data Mining, Brighton, UK, pp. 5–18 (2004)

    Google Scholar 

  54. Xu, L.: BYY learning, regularized implementation, and model selection on modular networks with One hidden layer of binary units. Neurocomputing 51, 227–301 (2003)

    Article  Google Scholar 

  55. Xu, L.: Data smoothing regularization, multi-sets-learning, and problem solving strategies. Neural Networks 15(5-6), 817–825 (2003)

    Article  Google Scholar 

  56. Xu, L.: Independent component analysis and extensions with noise and time: a Bayesian Ying-Yang learning perspective. Neural Information Processing Letters and Reviews 1, 1–52 (2003)

    Google Scholar 

  57. Xu, L.: BYY harmony learning, structural RPCL, and topological self-organizing on unsupervised and supervised mixture models. Neural Networks 15, 1125–1151 (2002)

    Article  Google Scholar 

  58. Xu, L.: Bayesian Ying Yang harmony learning. In: Arbib, M.A. (ed.) The Handbook of Brain Theory and Neural Networks, pp. 1231–1237. The MIT Press, Cambridge (2002)

    Google Scholar 

  59. Xu, L.: BYY harmony learning, independent state space and generalized APT financial analyses. IEEE Tr. Neural Networks 12, 822–849 (2001)

    Article  Google Scholar 

  60. 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. Intl J. Neural Systems 11, 3–69 (2001)

    Google Scholar 

  61. Xu, L.: Temporal BYY learning for state space approach, hidden Markov model and blind source separation. IEEE Tr. on Signal Processing 48, 2132–2144 (2000)

    Article  MATH  Google Scholar 

  62. Xu, L.: RBF nets, mixture experts, and Bayesian Ying-Yang learning. Neurocomputing 19(1-3), 223–257 (1998)

    Article  MATH  Google Scholar 

  63. Xu, L.: Bayesian Ying-Yang machine, clustering and number of clusters. Pattern Recognition Letters 18(11-13), 1167–1178 (1997)

    Article  Google Scholar 

  64. Xu, L.: Bayesian-Kullback coupled YING-YANG machines: unified learnings and new results on vector quantization. In: Proc. ICONIP 1995, Beijing, October 30-November 3, pp. 977–988 (1995)

    Google Scholar 

  65. Xu, L., Krzyzak, A., Oja, E.: Rival penalized competitive learning for clustering analysis, RBF net and curve detection. IEEE Tr. on Neural Networks 4, 636–649 ( Its early version on In: Proc. of 11th ICPR92. vol.I, pp. 672–675 (1992& 1993))

    Google Scholar 

  66. Xu, L.: Least mean square error reconstruction for self-organizing neural-nets. Neural Networks 6, 627–648 (1993) (Its early version on Proc. IJCNN 1991 Singapore. pp. 2363–2373 (1991& 1993))

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Jacek M. Zurada Gary G. Yen Jun Wang

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Xu, L. (2008). Bayesian Ying Yang System, Best Harmony Learning, and Gaussian Manifold Based Family. In: Zurada, J.M., Yen, G.G., Wang, J. (eds) Computational Intelligence: Research Frontiers. WCCI 2008. Lecture Notes in Computer Science, vol 5050. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68860-0_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-68860-0_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-68858-7

  • Online ISBN: 978-3-540-68860-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics