Based on things I have been learning about linear regression this year, I suggested this morning to Lily Zhao (Yale) that she replace our generative model for stellar spectral variability with a discriminative model, which tries to predict the radial-velocity offset of a star from changes in the stellar spectral shape. It's not a trivial model, since the number of parameters (features) is immense (more than 200,000) and the number of training-set examples is small (45-ish). But by the afternoon she did it and it works. Indeed, it looks like it works better than the generative models we have, even when tested by cross-validation.
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