Adaptive Non-Parametric Regression With the $K$-NN Fused Lasso
Abstract
The fused lasso, also known as total-variation denoising, is a locally-adaptive function estimator over a regular grid of design points. In this paper, we extend the fused lasso to settings in which the points do not occur on a regular grid, leading to an approach for non-parametric regression. This approach, which we call the -nearest neighbors (-NN) fused lasso, involves (i) computing the -NN graph of the design points; and (ii) performing the fused lasso over this -NN graph. We show that this procedure has a number of theoretical advantages over competing approaches: specifically, it inherits local adaptivity from its connection to the fused lasso, and it inherits manifold adaptivity from its connection to the -NN approach. We show that excellent results are obtained in a simulation study and on an application to flu data. For completeness, we also study an estimator that makes use of an -graph rather than a -NN graph, and contrast this with the -NN fused lasso.
Keywords
Cite
@article{arxiv.1807.11641,
title = {Adaptive Non-Parametric Regression With the $K$-NN Fused Lasso},
author = {Oscar Hernan Madrid Padilla and James Sharpnack and Yanzhen Chen and Daniela M. Witten},
journal= {arXiv preprint arXiv:1807.11641},
year = {2019}
}