Matrix analysis
A new approach to the maximum flow problem
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
A fast parametric maximum flow algorithm and applications
SIAM Journal on Computing
About strongly polynomial time algorithms for quadratic optimization over submodular constraints
Mathematical Programming: Series A and B
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Convergence of a block coordinate descent method for nondifferentiable minimization
Journal of Optimization Theory and Applications
Kernel Methods for Pattern Analysis
Kernel Methods for Pattern Analysis
Convex Optimization
An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Smooth minimization of non-smooth functions
Mathematical Programming: Series A and B
Topographic Independent Component Analysis
Neural Computation
Efficient projections onto the l1-ball for learning in high dimensions
Proceedings of the 25th international conference on Machine learning
The Group-Lasso for generalized linear models: uniqueness of solutions and efficient algorithms
Proceedings of the 25th international conference on Machine learning
Convex multi-task feature learning
Machine Learning
Robust Face Recognition via Sparse Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Learning with structured sparsity
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Group lasso with overlap and graph lasso
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
On Total Variation Minimization and Surface Evolution Using Parametric Maximum Flows
International Journal of Computer Vision
Sparse reconstruction by separable approximation
IEEE Transactions on Signal Processing
Exploiting structure in wavelet-based Bayesian compressive sensing
IEEE Transactions on Signal Processing
On the reconstruction of block-sparse signals with an optimal number of measurements
IEEE Transactions on Signal Processing
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
IEEE Transactions on Information Theory
Joint covariate selection and joint subspace selection for multiple classification problems
Statistics and Computing
Online Learning for Matrix Factorization and Sparse Coding
The Journal of Machine Learning Research
Model-based compressive sensing
IEEE Transactions on Information Theory
A Unified Primal-Dual Algorithm Framework Based on Bregman Iteration
Journal of Scientific Computing
Proximal Methods for Hierarchical Sparse Coding
The Journal of Machine Learning Research
Foundations and Trends® in Machine Learning
The minimum description length principle in coding and modeling
IEEE Transactions on Information Theory
Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries
IEEE Transactions on Image Processing
Structured Variable Selection with Sparsity-Inducing Norms
The Journal of Machine Learning Research
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Optimization with Sparsity-Inducing Penalties
Foundations and Trends® in Machine Learning
Structured sparsity via alternating direction methods
The Journal of Machine Learning Research
Learning invariant feature hierarchies
ECCV'12 Proceedings of the 12th international conference on Computer Vision - Volume Part I
Robust principal component analysis via capped norms
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
Supervised feature selection in graphs with path coding penalties and network flows
The Journal of Machine Learning Research
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We consider a class of learning problems regularized by a structured sparsity-inducing norm defined as the sum of l2- or l∞-norms over groups of variables. Whereas much effort has been put in developing fast optimization techniques when the groups are disjoint or embedded in a hierarchy, we address here the case of general overlapping groups. To this end, we present two different strategies: On the one hand, we show that the proximal operator associated with a sum of l∞-norms can be computed exactly in polynomial time by solving a quadratic min-cost flow problem, allowing the use of accelerated proximal gradient methods. On the other hand, we use proximal splitting techniques, and address an equivalent formulation with non-overlapping groups, but in higher dimension and with additional constraints. We propose efficient and scalable algorithms exploiting these two strategies, which are significantly faster than alternative approaches. We illustrate these methods with several problems such as CUR matrix factorization, multi-task learning of tree-structured dictionaries, background subtraction in video sequences, image denoising with wavelets, and topographic dictionary learning of natural image patches.