Nonparametric regression on a graph

Arne Kovac, Andrew D A C Smith

Research output: Contribution to journalArticle (Academic Journal)

9 Citations (Scopus)

Abstract

The ‘Signal plus Noise’ model for nonparametric regression can be extended to the case of observations taken at the vertices of a graph. This model includes many familiar regression problems. This article discusses the use of the edges of a graph to measure roughness in penalized regression. Distance between estimate and observation is measured at every vertex in the L2 norm, and roughness is penalized on every edge in the L1 norm. Thus the ideas of total variation penalization can be extended to a graph. The resulting minimization problem presents special computational challenges, so we describe a new and fast algorithm and demonstrate its use with examples.

The examples include image analysis, a simulation applicable to discrete spatial variation, and classification. In our examples, penalized regression improves upon kernel smoothing in terms of identifying local extreme values on planar graphs. In all examples we use fully automatic procedures for setting the smoothing parameters. Supplemental materials are available online.

Translated title of the contributionRegression on a graph
Original languageEnglish
Pages (from-to)432-447
Number of pages16
JournalJournal of Computational and Graphical Statistics
Volume20
Issue number2
DOIs
Publication statusPublished - Jun 2011

Bibliographical note

Publisher: American Statistical Association

Keywords

  • active set algorithm
  • image analysis
  • penalized regression
  • total variation

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