Stable Robust Regression under Sparse Outlier and Gaussian Noise

Masahiro Yukawa, Kyohei Suzuki, Isao Yamada

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

7 Citations (Scopus)


We propose an efficient regression method which is highly robust against outliers and stable even in the severely noisy situations. The robustness here comes from the adoption of the minimax concave loss, while the stability comes from separate treatments of the outlier and noise by an introduction of an auxiliary vector modeling the Gaussian noise. We present a necessary and sufficient condition for convexity of the smooth part of the entire cost under a certain assumption, where a general model is used with its potential use for other applications envisioned. We show that the proposed formulation can be solved via reformulation by the forward-backward-based primal-dual method under the convexity condition. The numerical examples show the remarkable robustness of the proposed estimator under highly noisy situations.

Original languageEnglish
Title of host publication30th European Signal Processing Conference, EUSIPCO 2022 - Proceedings
PublisherEuropean Signal Processing Conference, EUSIPCO
Number of pages5
ISBN (Electronic)9789082797091
Publication statusPublished - 2022
Event30th European Signal Processing Conference, EUSIPCO 2022 - Belgrade, Serbia
Duration: 2022 Aug 292022 Sept 2

Publication series

NameEuropean Signal Processing Conference
ISSN (Print)2219-5491


Conference30th European Signal Processing Conference, EUSIPCO 2022


  • Moreau envelope
  • minimax concave loss
  • robust regression
  • weakly convex function

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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