DFT-PRED:  Make predictions for test cases using Dirichlet diffusion trees.

Dft-pred prints the log of the predictive joint probability (or
density) for the target values in each test case given.  Target values
and average log probabilities can be displayed as well.

Usage:

    dft-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 Dirichlet diffusion trees to use for
the predictions are taken from the records with the given ranges of
indexes in the given log files.  Generation of new data points from
each of these trees is simulated to produce an approximation to the
predictive distribution.

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
iterations to be selected whose numbers are multiples of "mod", with
the default being "mod" of one.  The "num" form allows the total
number of iterations used to be specified; they are distributed as
evenly as possible within the specified range.  Note that it is
possible that the number of diffusion trees 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:

    t   Display the target values for each case.

    r   Use the raw form of the target values, before transformation.

    p   Display the log of the joint probability (or probability density)
        of the true targets.  Logs are to base e.

    b   Suppress headings and averages - just bare numbers for each case.
        The numbers are printed in exponential format, to high precision.

    a   Display only the average log probability (density), suppressing 
        the results for individual cases.  (Makes sense only if 'p' is
        specified as well, but not 't'.)

The predictive distribution is calculated by a stratified Monte Carlo
method.  For each tree, paths directed to each of the training cases
are simulated in turn, which diverge from the path to this training
case at some random time.  The location and time of this divergence
define a Gaussian distribution.  For real-valued data, the predictive
distribution is approximated by an equal mixture of all these Gaussian
distributions.  For binary data, values from each Gaussian
distribution are chosen at random, and used to define 0/1
probabilities that are mixed to produce the predictive distribution.

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 average log probability figure is accompanied by +- its standard
error (as long as there is more than one test case).

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

            Copyright (c) 1995-2004 by Radford M. Neal