Adaptive nonparametric regression with the K-nearest neighbour fused lasso. (29th January 2020)

• Record Type: Journal Article
• Authors: Madrid Padilla, Oscar Hernan; Sharpnack, James; Chen, Yanzhen; Witten, Daniela M
• Is Part Of: Biometrika. Volume 107:Number 2(2020:Jun.)
• Page Start: 293
• Page End: 310
• Publication Date: 2020-01-29
• Subjects: Fused lasso -- Local adaptivity -- Manifold adaptivity -- Nonparametric regression -- Total variation; Biometry -- Periodicals; 570.1519505
• DOI: 10.1093/biomet/asz071
• Languages: English
• ISSNs: 0006-3444

Abstract

Summary: The fused lasso, also known as total-variation denoising, is a locally adaptive function estimator over a regular grid of design points. In this article, we extend the fused lasso to settings in which the points do not occur on a regular grid, leading to a method for nonparametric regression. This approach, which we call the $K$ -nearest-neighbours fused lasso, involves computing the $K$ -nearest-neighbours graph of the design points and then performing the fused lasso over this graph. We show that this procedure has a number of theoretical advantages over competing methods: specifically, it inherits local adaptivity from its connection to the fused lasso, and it inherits manifold adaptivity from its connection to the $K$ -nearest-neighbours approach. In a simulation study and an application to flu data, we show that excellent results are obtained. For completeness, we also study an estimator that makes use of an $\epsilon$ -graph rather than a $K$ -nearest-neighbours graph and contrast it with the $K$ -nearest-neighbours fused lasso.