A Hierarchical Bayesian Framework for Constructing Sparsity-inducing Priors

Abstract : Variable selection techniques have become increasingly popular amongst statisticians due to an increased number of regression and classification applications involving high-dimensional data where we expect some predictors to be unimportant. In this context, Bayesian variable selection techniques involving Markov chain Monte Carlo exploration of the posterior distribution over models can be prohibitively computationally expensive and so there has been attention paid to quasi-Bayesian approaches such as maximum a posteriori (MAP) estimation using priors that induce sparsity in such estimates. We focus on this latter approach, expanding on the hierarchies proposed to date to provide a Bayesian interpretation and generalization of state-of-the-art penalized optimization approaches and providing simultaneously a natural way to include prior information about parameters within this framework. We give examples of how to use this hierarchy to compute MAP estimates for linear and logistic regression as well as sparse precision-matrix estimates in Gaussian graphical models. In addition, an adaptive group lasso method is derived using the framework.
Type de document :
Rapport
[Research Report] arXiv:1009.1914, 2010
Liste complète des métadonnées

https://hal.inria.fr/inria-00518430
Contributeur : Francois Caron <>
Soumis le : vendredi 17 septembre 2010 - 12:05:57
Dernière modification le : jeudi 11 janvier 2018 - 06:22:36

Lien texte intégral

Identifiants

  • HAL Id : inria-00518430, version 1
  • ARXIV : 1009.1914

Collections

INRIA | IMB | LARA

Citation

Anthony Lee, Francois Caron, Arnaud Doucet, Chris Holmes. A Hierarchical Bayesian Framework for Constructing Sparsity-inducing Priors. [Research Report] arXiv:1009.1914, 2010. 〈inria-00518430〉

Partager

Métriques

Consultations de la notice

414