SSSpaNG! Stellar Spectra as Sparse, data-driven, Non-Gaussian processes
  Upcoming million-star spectroscopic surveys have the potential to
revolutionize our view of the formation and chemical evolution of the Milky
Way. Realizing this potential requires automated approaches to optimize
estimates of stellar properties, such as chemical element abundances, from the
spectra. The volume and quality of the observations strongly motivate that
these approaches should be data-driven. With this in mind, we introduce
SSSpaNG: a data-driven non-Gaussian Process model of stellar spectra. We
demonstrate the capabilities of SSSpaNG using a sample of APOGEE red clump
stars, whose model parameters we infer via Gibbs sampling. Pooling information
between stars to infer their covariance, we permit clear identification of the
correlations between spectral pixels. Harnessing these correlations, we infer
the true spectrum of each star, inpainting missing regions and denoising by a
factor of at least 2 for stars with signal-to-noise of ~20. As we marginalize
over the covariance matrix of the spectra, the effective prior on these true
spectra is non-Gaussian and sparsifying, favouring typically small but
occasionally large excursions from the mean. The high-fidelity inferred spectra
produced will enable improved elemental abundance measurements for individual
stars. Our model also allows us to quantify the information gained by observing
portions of a star's spectrum, and thereby define the most mutually informative
spectral regions. Using 25 windows centred on elemental absorption lines, we
demonstrate that the iron-peak and alpha-process elements are particularly
mutually informative for these spectra, and that the majority of information
about a target window is contained in the 10-or-so most informative windows.
Such mutual-information estimates have the potential to inform models of
nucleosynthetic yields and the design of future observations.
