The KIPS Transactions:PartB (정보처리학회논문지B)

Korea Information Processing Society (한국정보처리학회)
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Computation of Noncentral F Probabilities using multilayer neural network

다층 신경 망을 이용한 비중심F분포 확률계산

  • 구선희 (전주대학교 교양학부 컴퓨터강의전담)
  • Published : 2002.06.01
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Abstract

The test statistic in ANOVA tests has a single or doubly noncentral F distribution and the noncentral F distribution is applied to the calculation of the power functions of tests of general linear hypotheses. Although various approximations of noncentral F distribution are suggested, they are troublesome to compute. In this paper, the calculation of noncentral F distribution is applied to the neural network theory, to solve the computation problem. The neural network consists of the multi-layer perceptron structure and learning process has the algorithm of the backpropagation. Using fables and figs, comparisons are made between the results obtained by neural network theory and the Patnaik's values. Regarding of accuracy and calculation, the results by neural network are efficient than the Patnaik's values.

ANOVA 검정에서 검정통계량은 단일 또는 이중 비중심F분포를 따르며 비중심F분포는 일반적인 선형 가설 검정에서 검정함수 계산에 적용되고 있다. 기존 비중심F분포의 함수 계산에 대한 연구로 여러 접근 방법이 제시되었지만, 하나의 정확한 함수값을 구하는데도 많은 시간이 소요되는 문제점이 발생되었다. 본 논문에서는 기존 함수 계산의 문제점을 해결하기 위하여 다층 퍼셉트론 네트워크로부터 역전파 학습 알고리즘을 적용하여 비중심F분포의 함수값을 구하는 방법을 제안하였다. 제안된 신경망에 의한 함수값과 기존 Patnaik이 제시한 분포식에 의한 함수값의 차이를 표와 그림을 통하여 비교하였으며, 정확성과 계산속도를 고려할 때 Patnaik의 함수식에 의한 방법보다 신경망을 이용한 방법이 효율적임을 알 수가 있다.

Keywords

References

  1. 김대수, '신경망 이론과 응용 (I),(II),' 하이테크정보, 1994
  2. P.J. Bickel and K.A. Doksum, 'Mathematical Statistics : Basic ideas and selected topics,' SanFrancisco : HoldenDay, 1977
  3. R. Chattamvelli, 'On the doubly non-central F distribution,' Computational Statistics and Data Analysis, Vol.20, pp.481-489, 1995 https://doi.org/10.1016/0167-9473(94)00054-M
  4. B. Cheng and D.M. Titterington, 'Neural Networks : A review from a statistical perspective,' Statistical Science, Vol.9, pp.2-54, 1994 https://doi.org/10.1214/ss/1177010638
  5. R.A. Fisher, 'The general sampling distribution of the multiple correlation coefficient,' Proceedings of the Royal Society of London, Series A, Vol.1, pp.654-673, 1928
  6. J.N. Hwang and H. Li. M. Maechler and D. Martin and J. Schimert, 'Regression modeling in backpropaga-tion and projection pursuit learning,' IEEE transactions on neural networks, Vol.5, pp.342-353, 1994 https://doi.org/10.1109/72.286906
  7. L.K. Jones, 'A simple lemma on greedy approximation in Hilbert space and convergence rates for projection pursuit regression and neural network training,' The Annals of Statistics, Vol.20, pp.608-613, 1992 https://doi.org/10.1214/aos/1176348546
  8. H. John and K. Anders and G.P. Richard, 'Introduction to the Theory Neural Computation,' Addison Wesley Publishing Co. Inc, 1991
  9. N.L. Johnson, 'On an extension of the connexion between the Poisson and ${\chi}^2$ distributions,' Biometrika, Vol.46, pp.352-363, 1993 https://doi.org/10.2307/2333532
  10. N.L. Johnson and S. Kotz, 'Continuous Univariate Distributions,' Boston : Houghton Mifflin, 1970
  11. P.B. Patnaik, 'The noncentral ${\chi}^2$ and F-distributions and their applications,' Biometrika, Vol.36, pp.202-232, 1949 https://doi.org/10.2307/2332542
  12. R. Price, 'Some noncentral F-distributions expressed in closed form,' Biometrika, Vol.51, pp.107-122, 1964 https://doi.org/10.2307/2334200
  13. D.E. Rumelhart and E.H. Geoffrey and J.W. Ronald, 'Learning representations by backpropagating errors,' Nature, Vol.323, pp.533-536, 1986 https://doi.org/10.1038/323533a0
  14. G.A.F. Seber, 'The noncentral chi-squared and beta distributions,' Biometrika, Vol.50, pp.542-544, 1963 https://doi.org/10.2307/2333927
  15. M. Sibuya, 'On the noncentral beta distribution function,' Unpublished manuscript, 1967
  16. M. Simth, 'Neural Networks for Statistical Modeling,' New York : Van Nostrand Reinhold
  17. D.F. Specht, 'A general regression neural network,' IEEE transactions on neural networks, Vol.2, pp.568-576, 1991 https://doi.org/10.1109/72.97934
  18. P.C. Tang, 'The power function of the analysis of variance tests with tables and illustrations of their use,' Statistical Research Memoirs, Vol.2, pp.126-150, 1938
  19. M.L. Tiku, 'A note on approximating to the noncentral F-distribution,' Biometrika, Vol.53, pp.606-610, 1975
  20. H. White, 'Learning in artificial net-works : A Statistical perspective,' Neural Computation, Vol.1(4), pp.425-469, 1989 https://doi.org/10.1162/neco.1989.1.4.425
  21. H. White, 'Connectionist nonpara-metric regression : multilayer feed-forward networks can learn arbitrary mappings,' Neural Networks, Vol.3, pp.535-549, 1990 https://doi.org/10.1016/0893-6080(90)90004-5

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