GP-EVAL: Evaluate function drawn from a Gaussian process. GP-eval displays function values drawn at random from the Gaussian processes defined by values for hyperparameters stored at various iterations in a log file. If no training data is specified, the functions are drawn from the prior defined by the hyperparameters; if there is training data, the functions are drawn from the conditional process given this training data, or from the conditional process given particular values for the function at the training points and/or values for the noise variance at each training point, if these are stored in the log file. The points at which to evaluate the function are either taken from a file, or are generated on a grid. Note that although gp-eval is related to gp-pred, it differs in that it does NOT average over iterations, and it generates functions at random, rather than computing summaries such as the mean. The gp-dgen program is also related, and in some respects is more general. Usage: gp-eval [ -l ] [ -t ] log-file range [ [-]N ] data-file [ "targets" ] or: gp-eval [ -l ] [ -t ] log-file range [ [-]N ] { / low high grid-size } [ "targets" ] N functions (default 1) are generated based on each iteration in the named log-file, within the specified range. The range has the usual form, of "[low][:[high]][%mod]", with 'high' defaulting to 'low' if the colon is absent, and to the end of the file if the colon is present. The random number seed used for the i'th function generated for iteration t is 100*t+i, if no "-" precedes the value N, or just i, if a "-" does precede N. (The latter option may be useful to see how the function generated by one seed varies with varying hyperparameter values, though the effects are sensitive to the method used, based on a Cholesky decomposition.) For the first form, points at which to evaluate the functions are read from the given file specification (which can have any of the forms described in numin.doc), in the same way (and with the same transformations) as training data is read. In the second form each group of the remaining arguments describes the grid along one input dimension, with 'low' and 'high' being the range of the grid along that dimension, and grid-size + 1 being the number of grid points spread across that range. The number of such argument groups must be the same as the number of input dimensions, and currently cannot be more than two. The Gaussian process model in the log file must have only one output value. The output consists of a section for each function drawn, with sections separated by blank lines. Each section contains as many lines as are in the data file, or as there are grid points. If the inputs are from a grid, each line contains the input values followed by the output values. If the inputs come from a file, eachh line contains only the output values. When a grid is used for more than one input variable, a blank line is output between groups of points where all but the last variable are the same. There must be only one output value. If the -l option is not incldued, and latent values for training cases are present, the functions are drawn from the conditional distribution given these latent values. If thee are no latent values, or if the -l option is included, the functions are drawn from the conditional distribution given the target values. Note, however, that this is possible only for regression models (ie, for "real" models). If the -t option is included, or the final argument is "targets" (this for backward compatibility), then rather than writing the function values themselves, the program instead generates target values from these outputs, as defined by the data model. This option is currently allowed only for real targets values. The noise for these target values will not be autocorrelated, though if the data model so specifies, the generation of these values will be affected by autocorrelation in the noise for the training cases (if any). If the covariance does not include a jitter part, and there is no noise added (ie, "targets" is not specified for a regression model), then gp-eval will add a small amount (1e-6) to the diagonal of the covariance to try to prevent numerical problems. Round off error may still make the covariance matrix appear to not be positive definite, however, in which case a message about not being able to find the Cholesky decomposition will appear. Note that the grid gives the actual values for the inputs. Any transformations that may have been specified with "data-spec" are ignored. (However, values from a data file are transformed as specified by data-spec.) Similarly, it is the raw function value (or generated target value) that is displayed, without any transformation (regardless of where the input values come from). NOTE: The output produced with two inputs can be plotted as a surface using "gnuplot". Save the output of gp-eval in a file (eg, "plt"), and then use the following gnuplot commands: set parametric set data style lines set hidden3d splot "plt" The viewpoint can be changed with the "set view" and "replot" commands. Copyright (c) 1995-2004 by Radford M. Neal