Exponential Family Trend Filtering on Lattices

Abstract

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.

rtestim: Time-varying reproduction number estimation with trend filtering

“…To enforce smoothness of , we add a trend filtering penalty to Equation (5) (Kim et al, 2009; Sadhanala et al, 2022; Tibshirani, 2014, 2022). Because ℛ t >0, we explicitly penalize the divided differences (discrete derivatives) of neighbouring values of log(ℛ t ).…”