ICONIP 2006: Neural Information Processing pp 660-669 | Cite as
Optimality of Kernel Density Estimation of Prior Distribution in Bayes Network
Conference paper
Abstract
The key problem of inductive-learning in Bayes network is the estimator of prior distribution. This paper adopts general naive Bayes to handle continuous variables, and proposes a kind of kernel function constructed by orthogonal polynomials, which is used to estimate the density function of prior distribution in Bayes network. The paper then makes further researches into optimality of the kernel estimation of density and derivatives. When the sample is fixed, the estimators can keep continuity and smoothness, and when the sample size tends to infinity, the estimators can keep good convergence rates.
Keywords
Kernel Function Prior Distribution Orthogonal Polynomial Total Space Kernel Density Estimation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
- 1.Zhang, H., Ling, C.: Numeric mapping and learnability of naive Bayes. Applied Artificial Intelligence 17, 507–518 (2003)CrossRefGoogle Scholar
- 2.Tang, Y., Pan, W.M., Li, H.M.: Fuzzy native Bayes classifier Based on fuzzy clustering. In: Proceedings of the IEEE International Conference on Systems, vol. 5, pp. 452–458 (2002)Google Scholar
- 3.Li, X.S., Li, D.Y.: A New Method Based on Density Clustering for Discretization of Continuous Attributes. Acta Simulata Systematica Sinica 6, 804–809 (2003)Google Scholar
- 4.Dougherty, J., Kohavi, R., Sahami, M.: Supervised and unsupervised discretization of continuous features. In: Proc. of the 12th International Conference on Machine Learning, pp. 194–202. Morgan Kaufmann Publishers, San Francisco (2003)Google Scholar
- 5.Li, B.C., Yuan, S.M., Wang, L.M.: The Simplified Expression of Bayesian Network. Chinese Journal of Scientific Instrument 10, 1070–1073 (2005)Google Scholar
- 6.Lin, P.E.: Rates of convergence in empirical Bayes estimation problems: continuous case. Ann. Statist. 3, 155–164 (1975)MATHCrossRefMathSciNetGoogle Scholar
- 7.Ronald, R.Y.: An extension of the naive Bayesian classifier. Information Sciences 176(5), 577–588 (2006)CrossRefMathSciNetGoogle Scholar
- 8.Eugene, S., Yan, V.: Universal results for correlations of characteristic polynomials: Riemann-Hilbert approach. Communications in Mathematical Physics 241, 343–382 (2003)MATHMathSciNetGoogle Scholar
- 9.Freilikher, V., Kanzieper, E., Yurkevich, I.: Theory of random matrices with strong level confinement: orthogonal polynomial approach. Physical Review E 54, 210–219 (1996)CrossRefMathSciNetGoogle Scholar
- 10.Gajek, L.: On improving density estimators which are not bona fide functions. Ann. Statist. 11, 1612–1618 (1986)CrossRefMathSciNetGoogle Scholar
- 11.Roder, H., et al.: Kernel polynomial method for a nonorthogonal electronicstructure calculation of amorphous diamond. Physical Review B 55, 15382–15385 (1997)CrossRefGoogle Scholar
- 12.Li, J.J., Gupta, S.S.: Empirical Bayes tests based on kernel sequence estimation. Statistica Sinica 12, 1061–1072 (2002)MATHMathSciNetGoogle Scholar
- 13.Jones, M.C.: On kernel density derivative estimation. Communications in Statistics (Theory and Methods) 23, 2133–2139 (1994)MATHCrossRefMathSciNetGoogle Scholar
- 14.Girolami, M.: Orthogonal series density estimation and the kernel eigenvalue problem. Neural Computation 14, 669–688 (2002)MATHCrossRefGoogle Scholar
- 15.Messer, K.: A comparison of spline estimate to its equivalent kernel estimate. Ann. Statist. 19, 817–829 (1991)MATHCrossRefMathSciNetGoogle Scholar
- 16.Parzen, E.: On estimation of a probability density function and model. Ann. Math. Statist. 33, 1065–1076 (1962)MATHCrossRefMathSciNetGoogle Scholar
- 17.Tong, H.Q.: Convergence rates for empirical Bayes estimators of parameters in multi-parameter exponential families. Communications in Statistics (Theory and Methods) 25, 1089–1098 (1996)MATHCrossRefMathSciNetGoogle Scholar
- 18.Vanlessen, M.: Universal behavior for averages of characteristic polynomials at the origin of the spectrum. Communications in Mathematical Physics 253, 535–560 (2005)MATHCrossRefMathSciNetGoogle Scholar
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