Abstract
For estimation algorithms, the problem of building correct algorithms by modifying weights of features and weights of objects is examined. Criteria for the possibility to build a correct algorithm are obtained for certain cases. Conditions of the possibility to build a correct algorithm are obtained in terms of solving a constrained optimization problem. An optimization method is proposed. Under these conditions, the proposed method significantly reduces the computational complexity of synthesizing a correct algorithm.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Yu. I. Zhuravlev, “Correct Algorithms over Sets of Incorrect (Heuristic) Algorithms: Part II,” Kibernetika, No. 6, 21–27 (1977).
Yu. I. Zhuravlev, “Correct Algorithms over Sets of Incorrect (Heuristic) Algorithms: Part III,” Kibernetika, No. 2, 35–43 (1978).
Yu. I. Zhuravlev and I. V. Isaev, “Constructing Recognition Algorithms That are Correct for a Given Validation Sample” Zh. Vychisl. Mat. Mat. Fiz. 19, 726–738 (1979).
K. V. Rudakov, On Certain Classes of Recognition Algorithms (General Results) (Vychisl. Tsentr Akad. Nauk SSSR, Moscow, 1980) [in Russian].
K. V. Rudakov, On Certain Classes of Recognition Algorithms (Parametric Models) (Vychisl. Tsentr Akad. Nauk SSSR, Moscow, 1981) [in Russian].
V. V. Ryazanov, “Optimization of Estimation Algorithms Using Parameters Describing the Representative Property of Reference Rows,” Zh. Vychisl. Mat. Mat. Fiz. 16, 1559–1570 (1976).
V. V. Ryazanov, “Optimal Group Decisions in Recognition and Classification,” Doctoral Dissertation in Mathematics and Physics (VTs RAN, Moscow, 1994).
N. N. Katerinochkina, “Methods for Finding a Maximal Consistent Subsystem of a System of Linear Inequalities,” in Communications in Applied Mathematics (Vychisl. Tsentr, Ross. Akad. Nauk, Moscow, 1997) [in Russian].
B. T. Polyak, Introduction to Optimization (Nauka, Moscow, 1983) [in Russian].
S. B. Pshenichnikov and A. G. Shtern, “Methods for Solving Systems of Nonlinear Algebraic Equations,” in Mathematical Methods and Computer-Aided Systems in Geology: A Survey (Moscow, 1995) [in Russian].
S. B. Pshenichnikov, “Spinor Elimination and Formulae for Relations between Unknowns in Systems of Nonlinear Algebraic Equations,” Latv. Mat. Ezhegodnik, No. 30, 150–161 (1986).
G. A. Zaitsev, Algebraic Problems in Mathematical and Theoretical Physics (Nauka, Moscow, 1974) [in Russian].
K. A. Rybnikov, Introduction to Combinatorial Analysis (Mosk. Gos. Univ., Moscow, 1985) [in Russian].
J. Edmonds, “Matroids and the Greedy Algorithm,” Math. Program. 1, 127–136 (1971).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.Yu. Smetanin, 2008, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2008, Vol. 48, No. 3, pp. 529–535.
Rights and permissions
About this article
Cite this article
Smetanin, A.Y. Building correct estimation algorithms as a constrained optimization problem. Comput. Math. and Math. Phys. 48, 500–506 (2008). https://doi.org/10.1134/S0965542508030123
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0965542508030123