TY - GEN

T1 - On Grouping Effect of Sparse Stable Outlier-Robust Regression

AU - Suzuki, Kyohei

AU - Yukawa, Masahiro

N1 - Funding Information:
This work was supported by the Grants-in-Aid for Scientific Research (KAKENHI) under Grant Numbers 22J22588 and 22H01492.
Publisher Copyright:
© 2022 IEEE.

PY - 2022

Y1 - 2022

N2 - This paper elucidates the grouping effect of the sparse stable outlier-robust regression (S-SORR) estimator which exploits the minimax concave (MC) penalty and the Tikhonov regularization simultaneously together with the MC loss. The main theoretical result is the following: where μ 1 > 0$ is the regularization parameter, and ai and aj are the unit vectors with their associated coefficients hat xi and hat xj. Remarkably, the bound is independent of possible outliers which may be contained in the observation vector y, whereas the bound for the popular elastic net estimator increases in proportion to the norm of y which is largely affected by outliers. Numerical examples show that S-SORR extracts the group structure correctly under huge outliers.

AB - This paper elucidates the grouping effect of the sparse stable outlier-robust regression (S-SORR) estimator which exploits the minimax concave (MC) penalty and the Tikhonov regularization simultaneously together with the MC loss. The main theoretical result is the following: where μ 1 > 0$ is the regularization parameter, and ai and aj are the unit vectors with their associated coefficients hat xi and hat xj. Remarkably, the bound is independent of possible outliers which may be contained in the observation vector y, whereas the bound for the popular elastic net estimator increases in proportion to the norm of y which is largely affected by outliers. Numerical examples show that S-SORR extracts the group structure correctly under huge outliers.

KW - convex optimization

KW - grouping effect

KW - minimax concave function

KW - sparse modeling

KW - sparse outlier-robust regression

UR - http://www.scopus.com/inward/record.url?scp=85142714707&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85142714707&partnerID=8YFLogxK

U2 - 10.1109/MLSP55214.2022.9943515

DO - 10.1109/MLSP55214.2022.9943515

M3 - Conference contribution

AN - SCOPUS:85142714707

T3 - IEEE International Workshop on Machine Learning for Signal Processing, MLSP

BT - 2022 IEEE 32nd International Workshop on Machine Learning for Signal Processing, MLSP 2022

PB - IEEE Computer Society

T2 - 32nd IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2022

Y2 - 22 August 2022 through 25 August 2022

ER -