Learning the solution sparsity of an ill-posed linear inverse problem with the Variational Garrote

Michael Riis Andersen, Sofie Therese Hansen, Lars Kai Hansen

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

The Variational Garrote is a promising new approach for sparse solutions of ill-posed linear inverse problems (Kappen and Gomez, 2012). We reformulate the prior of the Variational Garrote to follow a simple Binomial law and assign a Beta hyper-prior on the parameter. With the new prior the Variational Garrote, we show, has a wide range of parameter values for which it at the same time provides low test error and high retrieval of the true feature locations. Furthermore, the new form of the prior and associated hyper-prior leads to a simple update rule in a Bayesian variational inference scheme for its hyperparameter. As a second contribution we provide evidence that the new procedure can improve on cross-validation of the parameters and we find that the new formulation of the prior outperforms the original formulation when both are cross-validated to determine hyperparameters.
Original languageEnglish
Title of host publication2013 IEEE International Workshop on Machine Learning for Signal Processing (MLSP)
Number of pages6
PublisherIEEE
Publication date2013
DOIs
Publication statusPublished - 2013
Event2013 IEEE International Workshop on Machine Learning for Signal Processing (MLSP) - Southampton, United Kingdom
Duration: 22 Sep 201325 Sep 2013
http://mlsp2013.conwiz.dk

Workshop

Workshop2013 IEEE International Workshop on Machine Learning for Signal Processing (MLSP)
CountryUnited Kingdom
CitySouthampton
Period22/09/201325/09/2013
Internet address
SeriesMachine Learning for Signal Processing
ISSN1551-2541

Keywords

  • Bioengineering
  • Communication, Networking and Broadcast Technologies
  • Computing and Processing
  • General Topics for Engineers
  • Robotics and Control Systems
  • Signal Processing and Analysis
  • Transportation

Cite this

Andersen, M. R., Hansen, S. T., & Hansen, L. K. (2013). Learning the solution sparsity of an ill-posed linear inverse problem with the Variational Garrote. In 2013 IEEE International Workshop on Machine Learning for Signal Processing (MLSP) IEEE. Machine Learning for Signal Processing https://doi.org/10.1109/MLSP.2013.6661919