Monthly
288 pp. per issue
6 x 9, illustrated
ISSN
0899-7667
E-ISSN
1530-888X
2014 Impact factor:
2.21

Neural Computation

November 15, 1998, Vol. 10, No. 8, Pages 2159-2173
(doi: 10.1162/089976698300017016)
© 1998 Massachusetts Institute of Technology
Almost Linear VC-Dimension Bounds for Piecewise Polynomial Networks
Article PDF (116.29 KB)
Abstract

We compute upper and lower bounds on the VC dimension and pseudodimension of feedforward neural networks composed of piecewise polynomial activation functions. We show that if the number of layers is fixed, then the VC dimension and pseudo-dimension grow as W log W, where W is the number of parameters in the network. This result stands in opposition to the case where the number of layers is unbounded, in which case the VC dimension and pseudo-dimension grow as W2. We combine our results with recently established approximation error rates and determine error bounds for the problem of regression estimation by piecewise polynomial networks with unbounded weights.