Gamma Test Distribution
+=======================+

These programs implement the Gamma Test and Meta Back-Prop and are based on
work by Adalbjorn Stefansson, Nenad Koncar and Professor Antonia Jones
(copyright 1997). Please send all comments or bug reports to
"Nick.Green@cs.cf.ac.uk" or "S.Margetts@cs.cf.ac.uk"

The files in these distributions are listed below (note that only the relevant
files are included in each distribution):
	gamma		UNIX (SUN4) version
	gamma32.exe	PC Win95 version
	gammados.exe	PC DOS version
	gamma.src	An example script file explaining the various options

	mbp		UNIX (SUN4) Meta Back-Prop
	mbp32.exe	PC Win95 version
	mbpdos.exe	PC DOS version
	net		UNIX (SUN4) network interpreter
	net32.exe	PC Win95 version
	netdos.exe	PC DOS version

	hen100.asc	Sample test data used by "gamma.src" and "mbp.src"
	README.TXT	This file
	
Please note that the DOS versions (eg "gammados.exe") are limited to 640K,
and so may have problems with large input files.  If at all possible,
please use the Win95 versions.

All programs work from the command line.  This means that to run them from
Win95, you must first open a DOS window.  Running any program without a
script file will display the version number, copyright message and a
summary of all the options and their default values.  As an example, the
following command line will run the example script for the Gamma Test:

	"gamma32 gamma.src"

 Gamma Test
+==========+

The Gamma test is designed to give a data derived estimate of the Mean
Squared Error of ANY smooth data model from input (vector) to output
(scalar). This is that part of the variance in the output value which
cannot be accounted for by a smooth model from input to output. Given
sufficient data points the estimate returned by the Gamma test can be used
for example to determine the best performance one can hope to get from a
neural network (which is not overtrained) without undergoing numerous
attempts at training.

Let the data is represented by a set of input-output pairs, say (X, y),
where (X) could be a vector of several inputs.  The Gamma Test measures the
MSE of the noise (R) of the input-output mapping, by assuming that "y =
f(X) + R", where (f) is some unknown smooth function of (X)

As a rule of thumb, low Gamma values (the intercept of the regression plot)
are "good", as they indicate that the data has a low level of noise.
Negative Gamma values are better, and can be taken to indicate very small
levels of noise. The slope of the regression plot gives some guide to the
complexity of (f), the input-output mapping.

The software can also be used to find the set of inputs which best describe
the output - a process sometimes called feature selection.  This is done by
searching through the space of possible input "masks" or "embeddings".  The
software implements several methods for finding the best embedding; see the
example script file "gamma.src" for examples and descriptions.  This file
also lists the various options and gives explanations of their usage.

 Meta Back-Prop
+==============+

This program implements a neural-network training scheme which uses the
information from the Gamma test to guide both the training process and the 
architecture of the neural network. It works in much the same manner as
the Gamma Test program, except the output is a trained neural network.

The neural network is comprised of a number of "hills" (so called because
they are intended to form a hill-shaped lump in the input-output mapping).
The number of hills chosen is guided by the slope of the regression line as
calculated by the Gamma test.  Each hill is a collection of hidden nodes
and a single output node, where each layer has a bias neuron attached.

Most of the options are similar to those used by the Gamma test. All are
described in more detail in the file "mbp.src".

The program outputs the trained network to a file (specified in the script
file).  This network file can then be tested or used by using the network
interpreter program "net".  This program also works from the command line,
taking inputs from the standard input and writing the result to the
standard output.  Example:

	"net test.net"
	
This will load the network described by "test.net" and wait for inputs.
Note that the network description includes the mask it was trained with;
any inputs not selected by the mask still must be entered on the command
line.  The input/output redirection symbols "<" and ">" can be useful if
using the network interpreter to test many points.