Distributed Cartesian Power Graph Segmentation for Graphon Estimation
Abstract
We study an extention of total variation denoising over images to over Cartesian power graphs and its applications to estimating nonparametric network models. The power graph fused lasso (PGFL) segments a matrix by exploiting a known graphical structure, $G$, over the rows and columns. Our main results shows that for any connected graph, under subGaussian noise, the PGFL achieves the same meansquare error rate as 2D total variation denoising for signals of bounded variation. We study the use of the PGFL for denoising an observed network $H$, where we learn the graph $G$ as the $K$nearest neighborhood graph of an estimated metric over the vertices. We provide theoretical and empirical results for estimating graphons, a nonparametric exchangeable network model, and compare to the state of the art graphon estimation methods.
 Publication:

arXiv eprints
 Pub Date:
 May 2018
 arXiv:
 arXiv:1805.09978
 Bibcode:
 2018arXiv180509978W
 Keywords:

 Statistics  Machine Learning;
 Computer Science  Machine Learning;
 Statistics  Methodology;
 62H99