Vacation is over! I spent the train ride from Auckland to Wellington working on the first paper about The Cannon and also my MCMC tutorial. I also thought a bit more about CMB real-space analysis and foregrounds, which led to a breakthrough of sorts:
I realized that the ideal model for the CMB foregrounds is not to try to model each band with linear (or non-linear) combinations of other bands; the right idea is that there are a (hopefully small) number of latent variables that control the emission in many bands; the emission in any one band is a (possibly very non-linear) function of those latent variables. This model would consist of something like K latent-variable all-sky maps and a set of Gaussian processes (one for each observed band) that control how the latent variables generate the bands. Bonus points: Make the non-linear function (generated by the Gaussian process) also be a smooth function of frequency, which I think just involves a small meta-up. In writing this down, I realized that it is just a generalization of the Gaussian Process Latent Variable Model (GPLVM). Great project for Cosmo Hack Week coming up in a bit more than a week's time.