Outlier-robust kernel hierarchical-optimization RLS on a budget with affine constraints

Konstantinos Slavakis, Masahiro Yukawa

Research output: Contribution to journalConference articlepeer-review


This paper introduces a non-parametric learning framework to combat outliers in online, multi-output, and nonlinear regression tasks. A hierarchical-optimization problem underpins the learning task: Search in a reproducing kernel Hilbert space (RKHS) for a function that minimizes a sample average ℓp-norm (1 ≤ p ≤ 2) error loss defined on data contaminated by noise and outliers, under affine constraints defined as the set of minimizers of a quadratic loss on a finite number of faithful data devoid of noise and outliers (side information). To surmount the computational obstacles inflicted by the choice of loss and the potentially infinite dimensional RKHS, approximations of the ℓp-norm loss, as well as a novel twist of the criterion of approximate linear dependency are devised to keep the computational-complexity footprint of the proposed algorithm bounded over time. Numerical tests on datasets showcase the robust behavior of the advocated framework against different types of outliers, under a low computational load, while satisfying at the same time the affine constraints, in contrast to the state-of-the-art methods which are constraint agnostic.

Original languageEnglish
Pages (from-to)5335-5339
Number of pages5
JournalICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Publication statusPublished - 2021
Event2021 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2021 - Virtual, Toronto, Canada
Duration: 2021 Jun 62021 Jun 11


  • Adaptive filtering
  • Kernel
  • Online learning
  • Outliers
  • RLS

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering


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