Robust nonparametric regression by controlling sparsity

Gonzalo Mateos, Georgios B. Giannakis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Nonparametric methods are widely applicable to statistical learning problems, since they rely on a few modeling assumptions. In this context, the fresh look advocated here permeates benefits from variable selection and compressive sampling, to robustify nonparametric regression against outliers. A variational counterpart to least-trimmed squares regression is shown closely related to an ℓ0-(pseudo)norm-regularized estimator, that encourages sparsity in a vector explicitly modeling the outliers. This connection suggests efficient (approximate) solvers based on convex relaxation, which lead naturally to a variational M-type estimator equivalent to Lasso. Outliers are identified by judiciously tuning regularization parameters, which amounts to controlling the sparsity of the outlier vector along the whole robustification path of Lasso solutions. An improved estimator with reduced bias is obtained after replacing the ℓ0-(pseudo)norm with a nonconvex surrogate, as corroborated via simulated tests on robust thin-plate smoothing splines.

Original languageEnglish (US)
Title of host publication2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings
Pages3880-3883
Number of pages4
DOIs
StatePublished - Aug 18 2011
Event36th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Prague, Czech Republic
Duration: May 22 2011May 27 2011

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
ISSN (Print)1520-6149

Other

Other36th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011
Country/TerritoryCzech Republic
CityPrague
Period5/22/115/27/11

Keywords

  • Lasso
  • Robustness
  • nonparametric regression
  • outlier rejection
  • sparsity

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