In:
Biometrika, Oxford University Press (OUP), Vol. 107, No. 2 ( 2020-06-01), p. 293-310
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 $K$-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.
Type of Medium:
Online Resource
ISSN:
0006-3444
,
1464-3510
DOI:
10.1093/biomet/asz071
Language:
English
Publisher:
Oxford University Press (OUP)
Publication Date:
2020
detail.hit.zdb_id:
1119-8
detail.hit.zdb_id:
1470319-1
SSG:
12
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