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تسجيل مستخدم جديدAdaptive Non-Parametric Regression With the $K$-NN Fused Lasso
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نشر من قبل
Oscar Hernan Madrid Padilla
تاريخ النشر
2018
مجال البحث
الاحصاء الرياضي
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English
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The fused lasso, also known as total-variation denoising, is a locally-adaptive function estimator over a regular grid of design points. In this paper, we extend the fused lasso to settings in which the points do not occur on a regular grid, leading to an approach for non-parametric regression. This approach, which we call the $K$-nearest neighbors ($K$-NN) fused lasso, involves (i) computing the $K$-NN graph of the design points; and (ii) performing the fused lasso over this $K$-NN graph. We show that this procedure has a number of theoretical advantages over competing approaches: specifically, it inherits local adaptivity from its connection to the fused lasso, and it inherits manifold adaptivity from its connection to the $K$-NN approach. We show that excellent results are obtained in a simulation study and on an application to flu data. For completeness, we also study an estimator that makes use of an $epsilon$-graph rather than a $K$-NN graph, and contrast this with the $K$-NN fused lasso.
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