Adaptive nonparametric regression with the K-nearest neighbour fused lasso

Oscar Hernan Madrid Padilla, James Sharpnack, Yanzhen Chen and Daniela M Witten

Biometrika, 2020, vol. 107, issue 2, 293-310

Abstract: SummaryThe 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.

Keywords: Fused lasso; Local adaptivity; Manifold adaptivity; Nonparametric regression; Total variation (search for similar items in EconPapers)
Date: 2020
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