MODEL-SPEC:  Specify model to use for target variables.

Model-spec writes a specification to an existing log file for how the
distribution of targets in a case is defined in terms of the function
computed from the inputs for the case.  How this function of the
inputs is found is specified separately (it might, for instance, be
computed by a neural network).

Models are available for regression with real-valued targets, logistic
regression with binary targets, generalized logistic regression with
targets taking on a finite set of values, and survival analysis with a
hazard function that may depend on various covariates, and on time.

Usage:

     model-spec log-file model-specifications...

or:

     model-spec log-file 


The second form displays the existing specification stored in the log
file, if any.

The first form appends a specification to the log file, which must
not contain any iteratons yet.  If model-spec is invoked more than
once, the last specification is used.  The model is described by
one or more arguments after the log file argument.


Regression for real-valued targets.

Specification:

   real noise-prior [ "acf" corr { corr } ]

A regression model is specified by the argument "real", followed by a
noise prior (see prior.doc).  With this model, the data for each case
consists of the same number of input values as the network has input
units, and the same number of target values as the network has output
units.  The network outputs give the means of independent Gaussian
distributions, with variances determined by the noise hyperparameters.
(Note, however, that if there are implicit case-by-case
hyperparameters, the noise effectively comes from a t-distribution,
rather than a Gaussian.)

The noise prior may be followed by a specification of autocorrelations
for the noise in training cases, consisting of "acf" followed by one
or more autocorrelations, for lags from one on up; autocorrelations at
higher lags are assumed to be zero.  These autocorrelations must be
valid - ie, they must result in a positive definite correlation
matrix.  Note that this option causes the noise to be treated as
autocorrelated only for training cases.  The noise in test cases is
considered to be independent of the noise in the training cases, and
of the noise in other test cases.

If the "acf" option is used, the noise prior must not specify that the
noise variance varies from case to case.  Autocorrelated noise is
currently implemented only for Gaussian process models.


Logistic regression for binary targets.

A logistic regression model for binary data is specified by the
argument "binary".  With this model, the data for each case consists
of the same number of inputs values as the network has input units,
and the same number of binary target values as the network has output
units.  The targets must be specified to be binary using the
int-target option of data-spec.  Each output, o, of the network is
used to derive the probability, p, that the corresponding target will
be '1', via the logistic function, p = 1/(1+exp(-o)).


Generalized logistic regression for class targets ("softmax").

The "class" data model is used to model target values representing
some finite number of "classes".  As with the "real" and "binary"
models, the number of input units must match the number of input
values in each case.  There must be only one target in each case, with
the number of possible values for this target (specified with the
int-target option of data-spec) corresponding to the number of output
units in the network.  The distribution over target values for a case
is found by letting the probability of a particular target value be
proportional to the exponential of the value of the corresponding
output.


Survival data.
 
The data-model arguments to net-spec can also specify that the net is
to be used to model survival data, indicated by a first argument of
"survival".  With a survival model, the inputs to the networks will be
the values of various covariates that may affect survival, plus
perhaps the time.  The net must have a single output, which is used to
construct the log of the hazard function.  The form of the hazard
function is specified by the arguments following "survival", in one of
the following ways:

    const-hazard

       The hazard function is constant through time, though it may depend 
       on the covariates.  Only the covariates are provided as inputs to 
       the network.

    pw-const-hazard  [ "log" ] { time-point }

       The hazard function is piecewise constant, with changes in value
       at the time points listed.  There must be at least two time points, 
       they must be greater than zero, and they must be increasing.  The 
       log of the hazard for times before the first time point is obtained
       from the network output with the first network input set to the first
       time point (or the log of this time, if "log" is specified), and with
       any other inputs set to the covariates.  Similarly, the log of the
       hazard after the last time point is obtained by setting the first
       input to the last time point (or its log).  The log of the hazard at 
       times between two time points is obtained by setting the first input 
       to the average of the two time points (or the average of the logs of
       the two time points if "log" is specified).

The data specification for a survival model must give the number of
covariates as the number of inputs, and must specify that there is a
single target.  Negative values of the target are interpreted as
censored values (with observation stopping at the time given by the
target's absolute value).

Survival models are not implemented for Gaussian proceses.

            Copyright (c) 1995, 1996, 1997 by Radford M. Neal