Adaptive nonparametric regression with the K-nearest neighbour fused lasso

• 成果类型: Article
• 署名作者: Padilla, Oscar Hernan Madrid; Sharpnack, James; Chen, Yanzhen; Witten, Daniela M.
• 署名单位: University of California System; University of California Los Angeles; University of California System; University of California Davis; Hong Kong University of Science & Technology; University of Washington; University of Washington Seattle
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asz071
• 发表日期: 2020
• 页码: 293310
• 关键词: minimization; FRAMEWORK; algorithm; path

摘要

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 E -graph rather than a K-nearest-neighbours graph and contrast it with the K-nearest-neighbours fused lasso.