GP-EVAL: Evaluate function drawn from a Gaussian process over a grid. GP-eval displays functions 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. Usage: gp-eval 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.) 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 output consists of a section for each function drawn, with sections separated by blank lines. Each section contains as many lines as there are grid points, with each line giving the input values followed by the output values. When there is 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 final argument is "targets", 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. Similarly, it is the raw function value (or generated target value) that is displayed, without any transformation. 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) 1996, 1997 by Radford M. Neal