English

Fused $\ell_{1}$ Trend Filtering on Graphs

Statistics Theory 2024-01-11 v1 Statistics Theory

Abstract

This paper is dedicated to the fused trend filtering on a general graph, which is a combination of fused estimator and 1-st order trend filtering on a graph. There are two cases of fusion regularisers studied in this work: anisotropic total variation (i.e. fused lasso) and nearly-isotonic restriction. For the trend filtering part we consider general trend filtering on a given graph and Kronecker trend filter for the case of lattice data. We show how these estimators are related to each other and propose a computationally feasible numerical solution with a linear complexity per iteration with respect to the amount of edges in the graph.

Keywords

Cite

@article{arxiv.2401.05250,
  title  = {Fused $\ell_{1}$ Trend Filtering on Graphs},
  author = {Vladimir Pastukhov},
  journal= {arXiv preprint arXiv:2401.05250},
  year   = {2024}
}
R2 v1 2026-06-28T14:13:20.652Z