English

Trend Filtering on Graphs

Machine Learning 2016-06-07 v5 Artificial Intelligence Machine Learning Methodology

Abstract

We introduce a family of adaptive estimators on graphs, based on penalizing the 1\ell_1 norm of discrete graph differences. This generalizes the idea of trend filtering [Kim et al. (2009), Tibshirani (2014)], used for univariate nonparametric regression, to graphs. Analogous to the univariate case, graph trend filtering exhibits a level of local adaptivity unmatched by the usual 2\ell_2-based graph smoothers. It is also defined by a convex minimization problem that is readily solved (e.g., by fast ADMM or Newton algorithms). We demonstrate the merits of graph trend filtering through examples and theory.

Keywords

Cite

@article{arxiv.1410.7690,
  title  = {Trend Filtering on Graphs},
  author = {Yu-Xiang Wang and James Sharpnack and Alex Smola and Ryan J. Tibshirani},
  journal= {arXiv preprint arXiv:1410.7690},
  year   = {2016}
}

Comments

A short version appeared in AISTATS'2015

R2 v1 2026-06-22T06:38:57.765Z