Open Access
2024 Exponential family trend filtering on lattices
Veeranjaneyulu Sadhanala, Robert Bassett, James Sharpnack, Daniel J. McDonald
Author Affiliations +
Electron. J. Statist. 18(1): 1749-1814 (2024). DOI: 10.1214/24-EJS2241


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.

Funding Statement

DJM was partially supported by the National Sciences and Engineering Research Council of Canada (NSERC) grant RGPIN-2021-02618.


The authors would like to thank the anonymous referees, an Associate Editor and the Editor for their constructive comments that improved the quality of this paper.


Download Citation

Veeranjaneyulu Sadhanala. Robert Bassett. James Sharpnack. Daniel J. McDonald. "Exponential family trend filtering on lattices." Electron. J. Statist. 18 (1) 1749 - 1814, 2024.


Received: 1 July 2023; Published: 2024
First available in Project Euclid: 19 April 2024

arXiv: 2209.09175
Digital Object Identifier: 10.1214/24-EJS2241

Primary: 62G08
Secondary: 62G20

Keywords: Denoising , Kronecker , local adaptivity , nonparametric , Total variation

Vol.18 • No. 1 • 2024
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