THE MLP-MC-2 METHOD

   Regression and classification with multilayer perceptron networks 
       trained by Bayesian methods using Markov chain Monte Carlo
               with Automatic Relevance Determination (ARD)
                      and direct linear connections

                      Radford M. Neal, 28 July 1997

This method is similar to mlp-mc-1, and like it is based on Radford
Neal's flexible Bayesian modeling software.  The release used is that
of 1997-07-22.  The main difference from mlp-mc-1 is that the time
allowed is specified in terms of iterations, not compute time.  The
number of network applications (and hence compute time, approximately)
is the same as for mlp-bgd-1, mlp-bgd-2, and mlp-bgd-3.  The Markov
chain method used is also somewhat different from mlp-mc-1, primarily
in that "partial gradients" are used (somewhat analogous to online
training for gradient descent).  Unlike mlp-mc-1, versions of the
method are defined for binary and multi-class classification tasks.
The method does not work for tasks with more than one target.

This method produces predictions for all loss functions (S, A, and L
for regression, Z, Q, and L for classification), except that Q loss
isn't handled for binary targets, just because it turns out to be
inconvenient given the way the programs work.

The standard DELVE encoding is used for all inputs and targets, except
that categorical targets must be encoded in the 0-up format (ordering
is arbitrary) or 0/1 with an arbitrary value being passive for a
binary target.

The method is run using the shell files "runr", "runb", and "runc",
for regression, binary classification, and multi-way classification
respectively. The runr and runb shell files take the number of inputs
and the instance number as arguments.  The runc shell file takes the
number of categories, the number of inputs, and the instance number as
arguments.  When applied to instance N, the shell files apply the
method to the training data in the DELVE train.N file and make
predictions for the cases in test.N.  For regression tasks, the
predictions are stored in cguess.S.N, cguess.A.N, and clptarg.L.N.
For binary classification tasks, predictions are stored in cguess.N
and lptarg.N.  For multi-way classification tasks, predictions are
stored in cguess.N and prob.N.