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 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 -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.
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