Sparse Stable Outlier-Robust Regression with Minimax Concave Function

Kyohei Suzuki, Masahiro Yukawa

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

2 Citations (Scopus)

Abstract

We propose a novel formulation for stable sparse recovery from measurements contaminated by outliers and severe noise. The proposed formulation evaluates noise and outliers with a quadratic function and the minimax concave function, respectively, to reflect their statistical properties (Gaussianity and sparsity). This makes a significant difference from the conventional robust methods, which typically evaluate noise and outliers with a single loss function, leading to stability of the estimate. While the proposed formulation involves a nonconvex penalty to reduce estimation biases of sparse estimates, overall convexity of the whole cost is guaranteed under a certain condition by adding the Tikhonov regularization term. The problem is solved via a reformulation by the forward-backward primal-dual splitting algorithm, for which convergence conditions are derived. The remarkable outlier-robustness of the proposed method is demonstrated by simulations under highly noisy environments.

Original languageEnglish
Title of host publication2022 IEEE 32nd International Workshop on Machine Learning for Signal Processing, MLSP 2022
PublisherIEEE Computer Society
ISBN (Electronic)9781665485470
DOIs
Publication statusPublished - 2022
Event32nd IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2022 - Xi'an, China
Duration: 2022 Aug 222022 Aug 25

Publication series

NameIEEE International Workshop on Machine Learning for Signal Processing, MLSP
Volume2022-August
ISSN (Print)2161-0363
ISSN (Electronic)2161-0371

Conference

Conference32nd IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2022
Country/TerritoryChina
CityXi'an
Period22/8/2222/8/25

Keywords

  • convex optimization
  • mini- max concave function
  • robust regression
  • robust sparse recovery
  • sparse modeling

ASJC Scopus subject areas

  • Human-Computer Interaction
  • Signal Processing

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