NET-DVAR:  Find the variance of a difference in function values.


    net-dvar log-file range / centre n-pairs [ low ] high [ "hidden" ]

This program evaluates the variance of the difference in the (first)
outputs of networks at pairs of input points (differing in the first
input), over the set of networks in the given range, stored in the
given log file.  The variance of the difference is evaluated for
n-pairs+1 pairs of points, with the points in each pair being
equidistant from `centre'.  If only 'high' is present, the separations
of the pairs form an arithmetic progression from zero to 'high'; if
'low' is present, they form a geometric progression from 'low' to
'high'. The separations of the points and the corresponding values of
the variance are written one per line to standard output.

For networks drawn from a prior distribution, the variance is expected
to increase as some power, p, of the distance between points.  For a
prior over smooth functions, we should have p=2.  For a Brownian
prior, we should have p=1.  Values of p between 1 and 2 correspond to
"fractional Brownian" priors.

If a final argument of "hidden" is given, the program evaluates the
variance of the values of hidden units in the final layer, using all
hidden units in each network.  This is similar to the result using the
output, but gives better statistics.

            Copyright (c) 1995 by Radford M. Neal