Hyperparameter Estimation in Maximum a Posteriori Regression Using Group Sparsity with an Application to Brain Imaging

Yousra Bekhti (1, 2) , Roland Badeau (1, 2) , Alexandre Gramfort (1, 2)

1 Télécom ParisTech
2 LTCI - Laboratoire Traitement et Communication de l'Information

Setting hyperparameters is a recurrent problem in the statistics literature. Popular strategies are cross-validation or Bayesian inference, yet it remains an active topic of research in order to offer better or faster algorithms. The models considered in this work are sparse regression models with convex or non-convex group-Lasso-like penalties. Starting from a recent work of Pereyra et al. [1], where they give an analytical expression to estimate the regularization parameter, we show that their framework used as such is may be suitable for an analysis prior, but can not work for a synthesis prior. The main contribution of this paper is to overcome this issue. Second, we demonstrate how one can estimate one regularization parameter per group of coefficients to improve both the support and the amplitude bias in the convex group-Lasso problem. This approach is compared with an alternative method that uses a single parameter but a non-convex penalty. Results are presented on simulations and on a brain source localization problem using magneto/electroencephalography.

Domaines: Traitement du signal et de l'image [eess.SP]

Yousra Bekhti, Roland Badeau, Alexandre Gramfort. Hyperparameter Estimation in Maximum a Posteriori Regression Using Group Sparsity with an Application to Brain Imaging. 25th European Signal Processing Conference (EUSIPCO) , Aug 2017, Kos, Greece. pp.256-260. ⟨hal-01531238⟩