Block-wise minimization-majorization algorithm for huber's criterion: Sparse learning and applications

Esa Ollila, Ammar Mian

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

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Abstract

Huber's criterion can be used for robust joint estimation of regression and scale parameters in the linear model. Huber's [1] motivation for introducing the criterion stemmed from nonconvexity of the joint maximum likelihood objective function as well as non-robustness (unbounded influence function) of the associated ML-estimate of scale. In this paper, we illustrate how the original algorithm proposed by Huber can be set within the block-wise minimization majorization framework. In addition, we propose novel data-adaptive step sizes for both the location and scale, which are further improving the convergence. We then illustrate how Huber's criterion can be used for sparse learning of underdetermined linear model using the iterative hard thresholding approach. We illustrate the usefulness of the algorithms in an image denoising application and simulation studies.

Original languageEnglish
Title of host publicationProceedings of the 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing, MLSP 2020
PublisherIEEE
Number of pages6
ISBN (Electronic)9781728166629
DOIs
Publication statusPublished - Sep 2020
MoE publication typeA4 Article in a conference publication
EventIEEE International Workshop on Machine Learning for Signal Processing - Espoo, Finland
Duration: 21 Sep 202024 Sep 2020
Conference number: 30
https://ieeemlsp.cc

Publication series

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

Workshop

WorkshopIEEE International Workshop on Machine Learning for Signal Processing
Abbreviated titleMLSP
CountryFinland
CityEspoo
Period21/09/202024/09/2020
Internet address

Keywords

  • Huber's criterion
  • Minimization-majorization algorithm
  • Robust regression
  • Sparse learning

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