ACCURACY ANALYSIS FOR WAVELET APPROXIMATIONS

''Constructive wavelet networks'' are investigated as a universal tool for function approximation. The parameters of such networks are obtai ned via some ''direct'' Monte-Carlo procedures. Approximation bounds a re given. Typically, it is shown that such networks with one layer of ''wavelons'' achieve an L(2)-error of order O(N--rho/d), where N is th e number of nodes, d is the problem dimension and rho is the number of summable derivatives of the approximated function, An algorithm is al so proposed to estimate this approximation based on noisy input-output data observed from the function under consideration. Unlike neural ne twork training, this estimation procedure does not rely on stochastic gradient type techniques such as the celebrated ''backpropagation,'' a nd it completely avoids the problem of poor convergence or undesirable local minima.