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 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 2-3 for low-signal-to-noise stars. As we marginalize over the covariance matrix of the spectra, the effective prior on these true spectra is non-Gaussian, non-convex and sparsifying, promoting typically small but occasionally large excursions from the mean. The high-fidelity true 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. Our information-gain metric has the potential to inform models of nucleosynthetic yields and optimize the design of future observations.