Random Approximants and Neural Networks

By Yuly Makovoz. 1996

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Approximation rates for neural networks with general activation functions (2019, methodology): “More recently, these results have been improved by a factor of n1/d in [9] using the idea of stratified sampling, based in part on the techniques in [14].”
Sieve extremum estimates for weakly dependent data (1998, unknown): “Recently Makovoz (1996) improved Barron's result to 10- q,0 1 1 = O((i.,,)- , '- ("").”
Chapter 76 Large Sample Sieve Estimation of Semi-Nonparametric Models (2007, methodology): “E[Y1i − ho(Y2i )|Xi] = 0 studied by Newey and Powell (2003), Darolles, Florens and Renault (2002), Blundell, Chen and Kristensen (2007), Hall and Horowitz (2005) and Carrasco, Florens and Renault (2006).”
Neural network approximation (2020, methodology): “Important generalizations of (7.6) were given in (Makovoz 1996), where it was shown that the above result for the class KΩ holds for approximation in Lq, 1 ≤ q ∞, and moreover, the rate of approximation can be improved to O(n−1/2−1/(q∗d)), where q∗ is smallest even integer ≥ q.”
Approximation theory of the MLP model in neural networks (1999, background): “(Makovoz 1996) LetK be a bounded subset of a Hilbert space H .”
Improved Rates and Asymptotic Normality for Nonparametric Neural Network Estimators (1999, methodology): “Recently, for the feedforward networks with sigmoid activation functions of [1], [ 12 ] obtained an improved root-mean-square approximation rate , where is the dimension of the domain of the target function.”
The importance of convexity in learning with squared loss (1998, methodology): “We use the following result (see [ 15 ]) to bound the number of terms in the convex combination needed to achieve a desired accuracy.”