spectral representation; purely geometric spectroscopic parallaxes

Today was a low-research day! Research was pretty-much limited to a (great) call with Rix (MPIA) and Eilers (MPIA). We discussed several important successes of Eilers's work on latent-variable models. One is that she finds that she can improve the performance of The Cannon operating on stellar spectra if she reduces the dimensionality of the stellar spectra before she starts! That's crazy; how can you throw away information and do better? I think the answer must have something to do with model wrongness: The model is wrong (as all models are), and it is probably less wrong in the projected space than it was in the original pixel basis. This all relates to data representation issues that I have worried about (but done nothing about) before.

Another important success is that Eilers can run the Gaussian-Process latent-variable model on the dimensionality-reduced space much, much faster than the original data space, and not only does it do better than it did before, it does better than The Cannon. That's great, but it isn't just performance we are looking for: The GPLVM has better model structure, such that we can infer labels without having training data that have nuisance parameter labels. That is, we can make a predictive model for the interesting subspace of the label space. This is tremendously important going in to Gaia DR2, because we want to train a spectroscopic parallax method using only geometric inputs: No stellar models, ever!

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