Conference paper
Learning the solution sparsity of an ill-posed linear inverse problem with the Variational Garrote
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.
| Language: | English |
|---|---|
| Publisher: | IEEE |
| Year: | 2013 |
| Pages: | 1-6 |
| Proceedings: | 2013 IEEE International Workshop on Machine Learning for Signal Processing |
| Series: | Machine Learning for Signal Processing |
| ISBN: | 1479911798 , 1479911801 , 9781479911790 and 9781479911806 |
| ISSN: | 21610363 and 15512541 |
| Types: | Conference paper |
| DOI: | 10.1109/MLSP.2013.6661919 |
| ORCIDs: | Hansen, Sofie Therese and Hansen, Lars Kai |
Bioengineering Communication, Networking and Broadcast Technologies Computing and Processing General Topics for Engineers Robotics and Control Systems Signal Processing and Analysis Transportation
Bayes methods Bayesian variational inference scheme Beta hyper-prior Data models Equations Ill-posed inverse problem Mathematical model Mean square error methods Noise Variational Garrote Vectors binomial distribution hyperparameter ill-posed linear inverse problem inverse problems linear regression parameter cross-validation parameter values simple binomial law solution sparsity learning true feature locations update rule variational Garrote variational techniques
