Adaptive nonparametric regression with the K-nearest neighbour 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 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 [Formula: see text]-nearest-neighbours fused lasso, involves computing the [Formula: see text]-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 [Formula: see text]-nearest-neighbours app

SUBMITTER: Madrid Padilla OH 

PROVIDER: S-EPMC7228543 | biostudies-literature | 2020 Jun

REPOSITORIES: biostudies-literature