NET-PRED:  Make predictions for test cases using neural network model.

Net-pred prints guesses at the target values for a set of test cases.
Guesses are as defined by a network or set of networks.  If the true
targets are known, performance of the guesses can also be evaluated.
Inputs can be printed as well.  

If Annealed Importance Sampling was used, the marginal likelihood of
the model will be displayed. 


    net-pred options { log-file range } [ / test-inputs [ test-targets ] ]

The final optional arguments give the source of inputs and targets for
the cases to look at; they default to the test data specification in
the first log file given.  The networks to use in making guesses are
taken from the records with the given ranges of indexes in the given
log files.  The outputs of all these networks are combined to give a
single guess for each case.

An index range can have one of the forms "[low][:[high]][%mod]" or
"[low][:[high]]+num", or one of these forms preceded by "@".  When "@"
is present, "low" and "high" are given in terms of cpu time, otherwise
they are iteration numbers.  When just "low" is given, only that index
is used.  If the colon is included, but "high" is not, the range
extends to the highest index in the log file.  The "mod" form allows
networks to be selected whose iteration numbers are multiples of
"mod", with the default being "mod" of one.  The "num" form allows the
total number of networks used to be specified; they are distributed as
evenly as possible within the specified range.  Note that it is
possible that the number of networks used in the end may not equal
this number, if records with some indexes are missing.

The 'options' argument consists of one or more of the following letters:

    i   Display the input values for each case
    t   Display the target values for each case
    r   Use the raw form of the target values, before transformation

    p   Display the log probability of the true targets

    m   Display the guess based on the mode, and whether it is in error
    n   Display the guess based on the mean, and its squared error
    d   Display the guess based on the median, and its absolute error
    D   Display the guess based on the mean of the median for each iteration.
        This is mostly useful to get an accurate median for one network.

    q   Display the 10% and 90% quantiles of the predictive distributions
        for the targets.  Note that these distributions include the noise.
    Q   Display the 1% and 99% quantiles of the predictive distributions.

    b   Suppress headings and averages - just bare numbers for each case.
        The numbers are printed in exponential format, to high precision.
    B   Bare numbers, but with blank lines whenever first input changes

    a   Display only average log probabilities and errors, suppressing 
        the results for individual cases (makes sense only in combination 
        with one or more of 'p', 'm', 'n', and 'd', and not with 'i' or 't')

    0-9 If any of these characters are used, output connections from 
        hidden layers other than those named are suppressed.  Input-output
        connections and output biases are also suppressed.  This option
        is useful in seeing the components of an additive network model.
        (But note that if the identity of a component can change during a 
        run, this option will be meaningful only when the predictions are 
        based on a single iteration.)

Some of these options are illegal for some data models.  The illegal
combinations are marked with an 'X' in the following table:

        binary  class  real-valued  survival  no-model

    r     X       X
    p                                            X
    m                      X           X         X
    d/D   X       X    
    q/Q   X       X    

Furthermore, the 'a' option is incompatible with 'b', 'i', 't', or
'q', and the 't', 'p', and 'a' options may be used only if the true
targets are given.  The errors for individual cases are also displayed
only if the true targets are known. The 'n' option for class models
displays the mean probabilities for each class, and computes a single
figure for squared error that is the sum of the squares of the
differences between these probabilities and the indicator variables
that are one for the right class and zero for the wrong classes. 

The median and quantiles for the 'd', 'q', and 'Q' options are
calculated by Monte Carlo, using a sample consisting of 101 points
from each network's target distribution.  These computations are not
allowed if the data is weighted, as produced with Annealed Importance
Sampling.  These Monte Carlo estimates are found using a random number
stream initialized by setting the seed to one at the start of the
program.  Accuracy can be increased by repeating the same
log-file/range combination several times, effectively increasing the
sample size use.

The mean median found using 'D' is calculated exactly, without Monte
Carlo.  This option is mostly useful for survival models, when a
single iteration specified, since it then produces an accurate value
for the median prediction with that one network (more accurate than
would be obtained using 'd').  No error value is produced to go with
the mean median.

Each average performance figure is accompanied by +- its standard
error (as long as there is more than one test case).  If Annealed
Importance Sampling was done, the estimated marginal likelihood is
also accompanied by an estimated standard error, as long as the
"adjusted sample size" (defined in mc-ais.doc) is at least two.  Note
that the actual error might be much larger than the estimated standard
error if the AIS runs have missed an important part of the

For survival data, if the survival time in a test case is censored,
the censoring time (coded as negative) is used as the time of death
for the purpose of computing squared or absolute error.  This is not
very meaningful.

If only inputs and targets are to be displayed (no predictions), one
may give just a single log file with no range.  Otherwise, at least
one network must be specified.

            Copyright (c) 1995, 1998, 1999, 2001 by Radford M. Neal