This script provides a minimal working example for the approximation of empirical measures/designs with kernels based on MMD minimisation. It is accompanying the talk "Nicht nur Glückssache" by Guido Grützner, held on DAV/DGVFM Herbsttagung, November 16th 2021.
The script generates a large sample and then selects a small design from the large sample based on the Maximum Mean Discrepancy given by a Kernel. The optimisation/search is done by Trial&Error, i.e. uniform subsampling without replacement.
The kernel function fun_kernel contains two examples of possible kernels.
- The exponential kernel discussed in the talk
- A matern kernel of the ν =1/2 p=0 variety in the terminology of wikipedia
Set/Unset appropriate comments in fun_kernel to select the kernel you want.
Can be found in the original presentation (in German) or the English translation.