Vy Tran (TAMU) showed up and we discussed inference of spectral energy distributions of high-redshift galaxies given only photometry (no spectroscopy). She showed us some nice results, but Fadely and I think we could actually infer spectral properties at wavelength resolution higher than that implied by the broad-band (or medium-band) photometry. So we more-or-less launched a collaboration.
On the way to lunch, Fadely, Foreman-Mackey, and I had an epiphany: Foreman-Mackey has been trying to set the hyperparameters of a Gaussian Process to optimize our ability to search for and find exoplanets. This has been befuddling because it is so frequentist (or not even frequentist you might say). The issue is that what you want to optimize (hyperparameter-wise) depends on the details of how you are going to decide what is an exoplanet (that is, on your threshold choices). We realized on the way to lunch that we probably should be choosing the hyperparameters to maximize the area under the ROC curve. Foreman-Mackey launched on this in the afternoon. Cool if it works; novel definitely.
Maybe you can find this of help (http://arxiv.org/abs/1006.5391). We used sparsity to infer SDSS spectra from photometry for stars using ideas from compressed sensing. My guess is that it can be applied to the full SDSS database if a suitable basis is found for the spectra but never tried...
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