  We report a statistical analysis of Ge K-edge X-ray emission spectra
simulated for amorphous GeO$_2$ at elevated pressures. We find that employing
machine learning approaches we can reliably predict the statistical moments of
the K$\beta''$ and K$\beta_2$ peaks in the spectrum from the Coulomb matrix
descriptor with a training set of $\sim 10^4$ samples.
Spectral-significance-guided dimensionality reduction techniques allow us to
construct an approximate inverse mapping from spectral moments to
pseudo-Coulomb matrices. When applying this to the moments of the ensemble-mean
spectrum, we obtain distances from the active site that match closely to those
of the ensemble mean and which moreover reproduce the pressure-induced
coordination change in amorphous GeO$_2$. With this approach utilizing
emulator-based component analysis, we are able to filter out the artificially
complete structural information available from simulated snapshots, and
quantitatively analyse structural changes that can be inferred from the changes
in the K$\beta$ emission spectrum alone.
