On the application of elimination ideal for statistical model
Keywords:
statistical model, elimination ideal, Gröbner basisAbstract
The set of parameters 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 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.
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.
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