New variants of bundle methods
Mathematical Programming: Series A and B
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Support Vector Machines and the Bayes Rule in Classification
Data Mining and Knowledge Discovery
Choosing Multiple Parameters for Support Vector Machines
Machine Learning
Rademacher and gaussian complexities: risk bounds and structural results
The Journal of Machine Learning Research
Kernel Methods for Pattern Analysis
Kernel Methods for Pattern Analysis
Learning the Kernel Matrix with Semidefinite Programming
The Journal of Machine Learning Research
Learning the Kernel Function via Regularization
The Journal of Machine Learning Research
A statistical framework for genomic data fusion
Bioinformatics
On Learning Vector-Valued Functions
Neural Computation
Multi-kernel regularized classifiers
Journal of Complexity
Learning Coordinate Covariances via Gradients
The Journal of Machine Learning Research
Large Scale Multiple Kernel Learning
The Journal of Machine Learning Research
Estimation of Gradients and Coordinate Covariation in Classification
The Journal of Machine Learning Research
Learnability of Gaussians with Flexible Variances
The Journal of Machine Learning Research
Consistency of the Group Lasso and Multiple Kernel Learning
The Journal of Machine Learning Research
The Journal of Machine Learning Research
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In this paper we study the problem of learning the gradient function with application to variable selection and determining variable covariation. Firstly, we propose a novel unifying framework for coordinate gradient learning from the perspective of multi-task learning. Various variable selection methods can be regarded as special instances of this framework. Secondly, we formulate the dual problems of gradient learning with general loss functions. This enables the direct application of standard optimization toolboxes to the case of gradient learning. For instance, gradient learning with SVM loss can be solved by quadratic programming (QP) routines. Thirdly, we propose a novel gradient learning formulation which can be cast as a learning the kernel matrix problem. Its relation with sparse regularization is highlighted. A semi-infinite linear programming (SILP) approach and an iterative optimization approach are proposed to efficiently solve this problem. Finally, we validate our proposed approaches on both synthetic and real datasets.