Function approximation with neural networks
Theory on the optimal network size
V. Vysniauskas, F. Groen, and B. Kröse
In many applications it is necessary to know the accuracy with which a neural
computational model can approximate a function. This accuracy is a function
of the size of the network and the size of the learning set. Because of
computational constraints, a finite network size and a finite learning set
size has to be chosen. A grant from the UvA made it possible to
invite again V. Vysniauskas from
Vilnius, Lithuania for 6 months. The methodology for estimating
the optimal network size and learning set size for
a given desired accuracy which was developed
in the previous year was refined and compared with other
models in the literature.
The nested network
P. van der Smagt, F. Groen, A. Jansen, F. van het Groenewoud
We present a method for accurate representation of high-dimensional unknown
functions from random samples drawn from its input space.
The method builds representations of the function
by recursively splitting the input space in smaller subspaces,
while in each of these subspaces a linear approximation is computed.
The representations of the function at all levels (i.e., depths in the
tree) are retained during the learning process, such that a good
generalisation is available as well as more accurate representations
in some subareas. Therefore, fast and accurate learning are combined
in this method.
