I am very excited these days about the data-driven model of stellar spectra that Megan Bedell (Chicago) and I are building. In its current form, all it does is fit multi-epoch spectra of a single star with three sets of parameters, a normalization level (one per epoch) times a wavelength-by-wavelength spectral model (one parameter per model wavelength) shifted by a Doppler Shift (one per epoch). This very straightforward technology appears to be fitting the spectra to something close to the photon noise limit (which blows me away). The places where it doesn't fit appear to be interesting. Some of them are telluric absorption residuals, and some are intrinsic variations in the lines in the stellar spectra that are sensitive to activity and convection.
Today we talked about scaling this all up; right now we can only do a small part of the spectrum at a time (and we have a few hundred thousand spectral pixels!). We also spoke about how to regress the residuals against velocity or activity. The current plan is to investigate the residuals, but of course if we find anything we should add it in to the generative model and re-start.