Abstract
In this paper, we investigate a group sparse optimization problem via ℓp;qregularization in three aspects: Theory, algorithm and application. In the theoretical aspect, by introducing a notion of group restricted eigenvalue condition, we establish an oracle property and a global recovery bound of order O(λ 2 2/2-q ) for any point in a level set of the ℓp;qregularization problem, and by virtue of modern variational analysis techniques, we also provide a local analysis of recovery bound of order O(λ2) for a path of local minima. In the algorithmic aspect, we apply the well-known proximal gradient method to solve the ℓp;qregularization problems, either by analytically solving some specific p;q regularization subproblems, or by using the Newton method to solve general ℓp;qregularization subproblems. In particular, we establish a local linear convergence rate of the proximal gradient method for solving the ℓp;qregularization problem under some mild conditions and by first proving a second-order growth condition. As a consequence, the local linear convergence rate of proximal gradient method for solving the usual ℓl;qregularization problem (0 < q < 1) is obtained. Finally in the aspect of application, we present some numerical results on both the simulated data and the real data in gene transcriptional regulation.
Original language | English |
---|---|
Journal | Journal of Machine Learning Research |
Volume | 18 |
Publication status | Published - 1 Apr 2017 |
Keywords
- Gene regulation network
- Group sparse optimization
- Iterative thresholding algorithm
- Lower-order regularization
- Nonconvex optimization
- Proximal gradient method
- Restricted eigenvalue condition
ASJC Scopus subject areas
- Software
- Control and Systems Engineering
- Statistics and Probability
- Artificial Intelligence