Trend filtering in exponential families

Trend filtering is a modern approach to nonparametric regression that is more adaptive to local smoothness than splines or basis procedures while being computationally simpler. Current theoretical and empirical analysis of trend filtering focuses on estimating a function corrupted by 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 inference algorithms tailored to large problems, theoretical results for general loss functions, and principled methods for tuning parameter selection without excess computation.