Adaptive nonparametric regression with the K-nearest neighbour fused lasso.
Biometrika
; 107(2): 293-310, 2020 Jun.
Article
en En
| MEDLINE
| ID: mdl-32454528
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 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 [Formula see text]-graph rather than a [Formula see text]-nearest-neighbours graph and contrast it with the [Formula see text]-nearest-neighbours fused lasso.
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Bases de datos:
MEDLINE
Idioma:
En
Revista:
Biometrika
Año:
2020
Tipo del documento:
Article
País de afiliación:
Estados Unidos