Global Solutions to Folded Concave Penalized Nonconvex Learning.

To “ Global Solutions to Folded Concave Penalized Nonconvex Learning ”

Strong Oracle Optimality of Folded Concave Penalized Estimation By

Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed...

Folded concave penalized sparse linear regression: sparsity, statistical performance, and algorithmic theory for local solutions

This paper concerns the folded concave penalized sparse linear regression (FCPSLR), a class of popular sparse recovery methods. Although FCPSLR yields desirable recovery performance when solved globally, computing a global solution is NP-complete. Despite some existing statistical performance analyses on local minimizers or on specific FCPSLR-based learning algorithms, it still remains open que...

Strong Oracle Optimality of Folded Concave Penalized Estimation.

Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed...

I-lamm for Sparse Learning: Simultaneous Control of Algorithmic Complexity and Statistical Error∗

We propose a computational framework named iterative local adaptive majorize-minimization (I-LAMM) to simultaneously control algorithmic complexity and statistical error when fitting high dimensional models. I-LAMM is a two-stage algorithmic implementation of the local linear approximation to a family of folded concave penalized quasi-likelihood. The first stage solves a convex program with a c...