Abstract
The computational complexity of a new class of combinatorial optimization problems that are induced by optimal machine learning procedures in the class of collective piecewise linear classifiers of committee type is studied.
Similar content being viewed by others
References
A. A. Borovkov, Mathematical Statistics (Nauka, Novosibirsk, 1997; Gordon & Breach, Amsterdam, 1998).
V. N. Vapnik, Statistical Learning Theory (Wiley, New York, 1998).
A. Blum and R. L. Rivest, in Advances in Neural Information Processing Systems, Ed. by D. S. Touretzky (M. Kaufmann, San Mateo, 1988), pp. 494–501.
J. H. Lin and J. S. Vitter, Machine Learning 6, 211 (1991).
M. Khachay, J. Math. Model. Algorithms 6(4), 547 (2007).
M. Khachai and M. Poberii, Informatica 20(2), 217 (2009).
I. Dinur, J. ACM 54(3), Paper 12 (2007).
Vl. D. Mazurov, Kibernetika 3, 140 (1971).
M. Khachai, V. Mazurov, and A. Rybin, Proc. Steklov Inst. Math., Suppl. 1, S67 (2002).
M. Khachai, Pattern Recogn. Image Anal. 18(2), 237 (2008).
N. Megiddo and A. Tamir, Oper. Res. Lett. 1(5), 194 (1982).
S. V. Yablonskii, Introduction to Discrete Mathematics (Nauka, Moscow, 1986) [in Russian].
D. S. Johnson and F. P. Preparata, Theor. Comput. Sci. 6, 93 (1978).
M. Yu. Khachai, Zh. Vychisl. Mat. Mat. Fiz. 42(10), 1609 (2002).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © M.Yu.Khachai, 2010, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2010, Vol. 16, No. 3.
Rights and permissions
About this article
Cite this article
Khachai, M.Y. Computational complexity of combinatorial optimization problems induced by collective procedures in machine learning. Proc. Steklov Inst. Math. 272 (Suppl 1), 46–54 (2011). https://doi.org/10.1134/S0081543811020040
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0081543811020040