  Trend filtering is a modern approach to nonparametric regression that is more
adaptive to local smoothness than splines or similar basis procedures. Existing
analyses of trend filtering focus on estimating a function corrupted by
homoskedastic Gaussian noise, but our work extends this technique to general
exponential family distributions. This extension is motivated by the need to
study massive, gridded climate data derived from polar-orbiting satellites. We
present algorithms tailored to large problems, theoretical results for general
exponential family likelihoods, and principled methods for tuning parameter
selection without excess computation.
