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

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: Pustelnik, N and Ma, Z and Tan, ZH and Larsen, J, (eds.) 2018 IEEE 28th International Workshop on Machine Learning for Signal Processing (MLSP). IEEE Green open access

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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.

Type: Proceedings paper
Title: Balson: Bayesian least squares optimization with nonnegative L1-Norm constraint
Event: IEEE 28th International Workshop on Machine Learning for Signal Processing (MLSP), 17-20 September 2018, Aalborg, Denmark
Location: Aalborg, DENMARK
Dates: 17 September 2018 - 20 September 2018
ISBN-13: 978-1-5386-5477-4
Open access status: An open access version is available from UCL Discovery
DOI: 10.1109/MLSP.2018.8517036
Publisher version: https://doi.org/10.1109/MLSP.2018.8517036
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Bayes methods , Optimization , Monte Carlo methods , Sampling methods , Linear programming , Laplace equations , Data models, Bayesian learning , least squares optimization , L1-norm constraint , Dirichlet distribution , sampling method
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: http://discovery.ucl.ac.uk/id/eprint/10067418
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