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.

arXiv comment53 pages; 6 figures; 3 tables

References in corpus (12)

• Public Perception of Climate Change and the New Climate Dice
• Generalized SURE for Exponential Families: Applications to Regularization
• Adaptive piecewise polynomial estimation via trend filtering
• Properties and refinements of the fused lasso
• Fast and Flexible ADMM Algorithms for Trend Filtering
• Modular proximal optimization for multidimensional total-variation regularization
• Extensions of smoothing via taut strings
• Optimal rates for total variation denoising
• Nonparametric regression in exponential families
• New Risk Bounds for 2D Total Variation Denoising
• Optimal Dynamic Regret in Exp-Concave Online Learning
• Logistic regression with total variation regularization