Christina Eilers (MPIA) and I spent a long time today pair-coding her extension to The Cannon in which we marginalize over the true labels of the training data, under the assumption of small, known, Gaussian, label noise. Our job was to vastly speed optimization by getting correct derivatives (gradient) of the objective function (a likelihood function) with respect to parameters, and insertion of this into a proper optimizer. We built tests, did some experimental coding, and then fully succeeded! Eilers's Cannon is slower than other implementations, but more scientifically conservative. We showed by the end of the day that the model becomes a better fit to the data as the label variances are made realistic. Stars really do have simple spectra!
While we were working, Anna Y. Q. Ho and Sven Buder (MPIA) were discovering non-trivial covariances between stellar radial Velocity (or possibly radial velocity mis-estimation) and alpha abundances, with Ho working in LAMOST data and Buder working in GALAH data. Both are using The Cannon. After some investigation, we think the issue is probably related to the collision of alpha-estimating spectral features and ISM and telluric features. We discussed methods for mitigation, which range from censoring data at one end and fully modeling velocity along with the model parameters at the other.
Late in the day, I finished my response to referee and submitted it.