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Trend filtering is a modern approach to nonparametric regression that is moreadaptive to local smoothness than splines or similar basis procedures. Existinganalyses of trend filtering focus on estimating a function corrupted byhomoskedastic Gaussian noise, but our work extends this technique to generalexponential family distributions. This extension is motivated by the need tostudy massive, gridded climate data derived from polar-orbiting satellites. Wepresent algorithms tailored to large problems, theoretical results for generalexponential family likelihoods, and principled methods for tuning parameterselection without excess computation.

Exponential Family Trend Filtering on Lattices