Wednesday, 15:15 - 15:40 h, Room: H 1028

 

Rodolphe Jenatton
Proximal methods for hierarchical sparse coding and structured sparsity

Coauthors: Francis Bach, Julien Mairal, Guillaume Obozinski

 

Abstract:
Sparse coding consists in representing signals as sparse linear combinations of atoms selected from a dictionary. We consider an extension of this framework where the atoms are further assumed to be embedded in a tree. This is achieved using a recently introduced tree-structured sparse regularization norm, which has proven useful in several applications. This norm leads to regularized problems that are difficult to optimize, and we propose in this paper efficient algorithms for solving them. More precisely, we show that the proximal operator associated with this norm is computable exactly via a dual approach that can be viewed as the composition of elementary proximal operators. Our procedure has a complexity linear, or close to linear, in the number of atoms, and allows the use of accelerated gradient techniques to solve the tree-structured sparse approximation problem at the same computational cost as traditional ones using the L1-norm. We also discuss extensions of this dual approach for more general settings of structured sparsity. Finally, examples taken from image/video processing and topic modeling illustrate the benefit of our method.

 

Talk 1 of the invited session Wed.3.H 1028
"Structured models in sparse optimization" [...]
Cluster 21
"Sparse optimization & compressed sensing" [...]

 

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