*Empirical Learning curves*
We have compared the performance of neural networks trained
with two Bayesian methods, (i) the Evidence Framework of
MacKay (1992)
and (ii) a Markov Chain Monte Carlo method due to
R. Neal (1996) on a task of
classifying segmented outdoor images.
In order to quantify how much the performance of a
neural network is affected by the amount of training data,
we have we conducted experiments reducing the number
of data points in the training sets.

A neural network with an hidden layer with 30 units
has been trained with both the Bayesian techniques.

*Plot of the learning curves for the EF and MCMC methods *

obtained
by reducing the number of data points in the training sets.

The figure shows the plots of the misclassification as a function
of the number of
training data.

For both the methods each point of the plot
corresponds to a different training set.
We used 2 training sets with 2916 data, 4 with 1458,
8 with 729 and 10 training sets with each of
365, 182, 91, and 46 data points.

Our results suggest that on this task using large amounts of training
data the evidence framework and Markov Chain Monte Carlo
performance is similar, but that the MCMC method
seems superior on smaller-sized training sets.

A paired 2-sided t-test finds that the
differences between EF and MCMC
are statistically significant at the p < 0.05 level
for training set sizes 1458, 729, 182, 91 and 46.

The results presented in this web page have been published
in the paper ** Using Bayesian Neural Networks to
Classify segmented Images**
which is available as
compressed postscript
.

**Contact names**

*Francesco Vivarelli*

*Dr. Christopher K. I. Williams*

*Dr. W. Andrew Wright*

*This page is maintained by
Francesco Vivarelli*
(`vivarelf@aston.ac.uk`)

Last modified: Thu Jun 26 19:56:20 BST