On the weekend, Bernhard Schölkopf (Tübingen) showed up in Heidelberg to hang out and talk shop. What an honor and pleasure! We spent time im Garten discussing various things, but he was particularly insightful in the projects we have been doing with Christina Eilers (MPIA) on extending The Cannon to situations where stellar labels (even in the training set) are either noisy or missing. As we described the training and test steps, we drew graphical models and then looked at the inconsistencies of those graphical models—or not really inconsistencies, but limitations. We realized that we couldn't keep the model interpretable (which is a core idea underlying The Cannon) without putting stronger priors on both the label space (the properties of stars) and the coefficient space (the control parameters of the spectral expectation). If we put on these priors, the model ought to get regularized into a sensible place. I think I know how to do this!
He also pointed out that a probabilistic version of The Cannon would look a lot like the GPLVM (Gaussian Process latent-variable model). That means that there might be out-of-the-box code that could conceivably help us. I am slightly suspicious,
because my idea of the priors or regularization in the label domain is so specific, astrophysical, and informative. But it is worth thinking about this.