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Upcoming million-star spectroscopic surveys have the potential torevolutionize our view of the formation and chemical evolution of the MilkyWay. Realizing this potential requires automated approaches to optimizeestimates of stellar properties, such as chemical element abundances, from thespectra. The volume and quality of the observations strongly motivate thatthese approaches should be data-driven. With this in mind, we introduceSSSpaNG: a data-driven non-Gaussian Process model of stellar spectra. Wedemonstrate the capabilities of SSSpaNG using a sample of APOGEE red clumpstars, whose model parameters we infer via Gibbs sampling. Pooling informationbetween stars to infer their covariance, we permit clear identification of thecorrelations between spectral pixels. Harnessing these correlations, we inferthe true spectrum of each star, inpainting missing regions and denoising by afactor of at least 2 for stars with signal-to-noise of ~20. As we marginalizeover the covariance matrix of the spectra, the effective prior on these truespectra is non-Gaussian and sparsifying, favouring typically small butoccasionally large excursions from the mean. The high-fidelity inferred spectraproduced will enable improved elemental abundance measurements for individualstars. Our model also allows us to quantify the information gained by observingportions of a star's spectrum, and thereby define the most mutually informativespectral regions. Using 25 windows centred on elemental absorption lines, wedemonstrate that the iron-peak and alpha-process elements are particularlymutually informative for these spectra, and that the majority of informationabout a target window is contained in the 10-or-so most informative windows.Such mutual-information estimates have the potential to inform models ofnucleosynthetic yields and the design of future observations.

SSSpaNG! Stellar Spectra as Sparse, data-driven, Non-Gaussian processes