Leaning Theory and Approximation By Neural Networks (pp.108-121)
V. Maiorov · Azerbaijan Journal of Mathematics · 2013
This paper quanties the approximation capability of Neural Networks and their applicationin machine leaning theory. The problem of Learning Neural Networks from samples isconsidered. The sample size which is sucient for obtaining the almost-optimal stochastic approximationof function classes is obtained. In the terms of the accuracy condence function weshow that the least square estimator is almost-optimal for the problem. Moreover, we considerthe analogous problems connecting with leaning by radial basis functions.Learning theory is a growing eld of research which attracts a wide body of researchers fromdisciplines such as computer science, economic and neural networks. Mathematics is importantfor investigating learning problems since it provides the necessary level of rigorous analysis thatleads to understanding the fundamental concepts and properties of learning. Specically, thelearning problem is reduced to nding a regression function (the average function of a givenrandom processes) using the corresponding manifold under the condition that the function isnot known but belongs to some given class of functions. The learning network problems havethe long history in statistic, see the works of V. Vapnik, M.G.D. Powell, P.L. Bartlett et all.