For a common approximation model construction problem, the user has only a set of points and corresponding target function values. Using this training data, an approximation model is constructed. However, in some cases, the user can also provide variances of the target function values (output variances) for some points from the sample. GT Approx can handle such kind of information, as output variances are used to construct a approximation model of noisy functions.
This example demonstrates the usage of partly provided output variances with a model example. We compare approximation models constructed with and without the use of output variances for a model function.
Here a one-dimensional model example is considered. The objective function is shown in the picture below.
Note that in this example only highly noisy values of the target function are available.
Now we are ready to construct approximation models with and without the use of output variances. We run GT Approx in both modes: first, only the points and corresponding target function values are used. At the second run, we use points, corresponding target function values and output variances for some of this points. Let’s compare the two resulting approximation models.
The most reliable way to compare different approximation models is to calculate errors of approximation for a separate test data, which consists of target function values in new points. This method is applied.
The picture below illustrates the obtained approximation models.
One can see that Accuracy Evaluation (uncertainty in the approximation model prediction) is more accurate if partly specified output variances are used. It proves that using partly specified output variances is really efficient.