ON THE APPLICATION OF ELIMINATION IDEAL FOR STATISTICAL MODEL

  • Tadashi Takahashi Department of Intelligence and Informatics Konan University 8-9-1 Okamoto, Higashinada, Kobe
  • Tomohiro Washino
Keywords: statistical model, elimination ideal, Gröbner basis

Abstract

The set of parameters that by which the true density function
is realizable by a statistical model is a common set of zero
points defined by finite polynomials by applying Hilbert’s basis theorem.
We calculate the parameterization of the this algebraic set
by considering the elimination ideal of the ideal defined by the finite
polynomials. In this paper, we show the calculation results for
recurrence formula by using computer algebra system

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References

Buchberger, B. 1985. Greobner Bases, an algorithmic methodin polynomial ideal theory, in Multidimensional Systems Theory, edited by N. K. Bose. D. Reidel Publishing Company, Dordrecht, 184-232.

Fukumizu, K. and Amari, S. "Local minima and plateaus

in hierarchical structures of multilayer perceptrons",

Neural Networks, vol. 13, no. 3, 317-327, 2000.

Published
2020-05-31
How to Cite
Takahashi, T., & Washino, T. (2020). ON THE APPLICATION OF ELIMINATION IDEAL FOR STATISTICAL MODEL. COMPUSOFT: An International Journal of Advanced Computer Technology, 9(5). Retrieved from https://ijact.in/index.php/ijact/article/view/1156