Balson: Bayesian least squares optimization with nonnegative L1-Norm constraint

Jiyang Xie, Zhanyu Ma*, Guoqiang Zhang, Jing Hao Xue, Jen-Tzung Chien, Zhiqing Lin, Jun Guo

*Corresponding author for this work

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

1 Scopus citations

Abstract

A Bayesian approach termed the BAyesian Least Squares Optimization with Nonnegative L 1 -norm constraint (BALSON) is proposed. The error distribution of data fitting is described by Gaussian likelihood. The parameter distribution is assumed to be a Dirichlet distribution. With the Bayes rule, searching for the optimal parameters is equivalent to finding the mode of the posterior distribution. In order to explicitly characterize the nonnegative L 1 -norm constraint of the parameters, we further approximate the true posterior distribution by a Dirichlet distribution. We estimate the moments of the approximated Dirichlet posterior distribution by sampling methods. Four sampling methods have been introduced and implemented. With the estimated posterior distributions, the original parameters can be effectively reconstructed in polynomial fitting problems, and the BALSON framework is found to perform better than conventional methods.

Original languageEnglish
Title of host publication2018 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2018 - Proceedings
EditorsNelly Pustelnik, Zheng-Hua Tan, Zhanyu Ma, Jan Larsen
PublisherIEEE Computer Society
ISBN (Electronic)9781538654774
DOIs
StatePublished - 31 Oct 2018
Event28th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2018 - Aalborg, Denmark
Duration: 17 Sep 201820 Sep 2018

Publication series

NameIEEE International Workshop on Machine Learning for Signal Processing, MLSP
Volume2018-September
ISSN (Print)2161-0363
ISSN (Electronic)2161-0371

Conference

Conference28th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2018
CountryDenmark
CityAalborg
Period17/09/1820/09/18

Keywords

  • Bayesian learning
  • Dirichlet distribution
  • L -norm constraint
  • Least squares optimization
  • Sampling method

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  • Cite this

    Xie, J., Ma, Z., Zhang, G., Xue, J. H., Chien, J-T., Lin, Z., & Guo, J. (2018). Balson: Bayesian least squares optimization with nonnegative L1-Norm constraint. In N. Pustelnik, Z-H. Tan, Z. Ma, & J. Larsen (Eds.), 2018 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2018 - Proceedings [8517036] (IEEE International Workshop on Machine Learning for Signal Processing, MLSP; Vol. 2018-September). IEEE Computer Society. https://doi.org/10.1109/MLSP.2018.8517036