Multiple kernel learning, conic duality, and the SMO algorithm
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Smooth minimization of non-smooth functions
Mathematical Programming: Series A and B
Learning the Kernel Function via Regularization
The Journal of Machine Learning Research
A DC-programming algorithm for kernel selection
ICML '06 Proceedings of the 23rd international conference on Machine learning
A Framework for Learning Predictive Structures from Multiple Tasks and Unlabeled Data
The Journal of Machine Learning Research
Feature space perspectives for learning the kernel
Machine Learning
Fixed-Point Continuation for $\ell_1$-Minimization: Methodology and Convergence
SIAM Journal on Optimization
Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
SIAM Journal on Imaging Sciences
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
Efficient Online and Batch Learning Using Forward Backward Splitting
The Journal of Machine Learning Research
Optimization with Sparsity-Inducing Penalties
Foundations and Trends® in Machine Learning
Convergence analysis of a proximal Gauss-Newton method
Computational Optimization and Applications
Sparse linear wind farm energy forecast
ICANN'12 Proceedings of the 22nd international conference on Artificial Neural Networks and Machine Learning - Volume Part II
Regularizers for structured sparsity
Advances in Computational Mathematics
Nonparametric sparsity and regularization
The Journal of Machine Learning Research
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Proximal methods have recently been shown to provide effective optimization procedures to solve the variational problems defining the l1 regularization algorithms. The goal of the paper is twofold. First we discuss how proximal methods can be applied to solve a large class of machine learning algorithms which can be seen as extensions of l1 regularization, namely structured sparsity regularization. For all these algorithms, it is possible to derive an optimization procedure which corresponds to an iterative projection algorithm. Second, we discuss the effect of a preconditioning of the optimization procedure achieved by adding a strictly convex functional to the objective function. Structured sparsity algorithms are usually based on minimizing a convex (not strictly convex) objective function and this might lead to undesired unstable behavior. We show that by perturbing the objective function by a small strictly convex term we often reduce substantially the number of required computations without affecting the prediction performance of the obtained solution.