Smooth minimization of non-smooth functions
Mathematical Programming: Series A and B
Fast maximum margin matrix factorization for collaborative prediction
ICML '05 Proceedings of the 22nd international conference on Machine learning
Uncovering shared structures in multiclass classification
Proceedings of the 24th international conference on Machine learning
Classifying matrices with a spectral regularization
Proceedings of the 24th international conference on Machine learning
Consistency of Trace Norm Minimization
The Journal of Machine Learning Research
Improving maximum margin matrix factorization
Machine Learning
Convex multi-task feature learning
Machine Learning
A New Approach to Collaborative Filtering: Operator Estimation with Spectral Regularization
The Journal of Machine Learning Research
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
Joint covariate selection and joint subspace selection for multiple classification problems
Statistics and Computing
Mathematical Programming: Series A and B
An efficient algorithm for a class of fused lasso problems
Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining
Learning incoherent sparse and low-rank patterns from multiple tasks
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Spectral Regularization Algorithms for Learning Large Incomplete Matrices
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Fast optimization for mixture prior models
ECCV'10 Proceedings of the 11th European conference on computer vision conference on Computer vision: Part III
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Limitations of matrix completion via trace norm minimization
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The minimum-rank gram matrix completion via modified fixed point continuation method
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Integrating low-rank and group-sparse structures for robust multi-task learning
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Anomaly localization for network data streams with graph joint sparse PCA
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Linear discriminant dimensionality reduction
ECML PKDD'11 Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part I
Trace norm regularization and application to tensor based feature extraction
ACCV'10 Proceedings of the 2010 international conference on Computer vision - Volume part II
Towards feature selection in network
Proceedings of the 20th ACM international conference on Information and knowledge management
Composite splitting algorithms for convex optimization
Computer Vision and Image Understanding
Transactional Database Transformation and Its Application in Prioritizing Human Disease Genes
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Trace Norm Regularization: Reformulations, Algorithms, and Multi-Task Learning
SIAM Journal on Optimization
Learning Incoherent Sparse and Low-Rank Patterns from Multiple Tasks
ACM Transactions on Knowledge Discovery from Data (TKDD)
A novel framework based on trace norm minimization for audio event detection
ICONIP'11 Proceedings of the 18th international conference on Neural Information Processing - Volume Part II
Exact matrix completion via convex optimization
Communications of the ACM
Optimal exact least squares rank minimization
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Web-scale multi-task feature selection for behavioral targeting
Proceedings of the 21st ACM international conference on Information and knowledge management
Max-margin embedding for multi-label learning
Pattern Recognition Letters
Exploiting social relations for sentiment analysis in microblogging
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Computing real solutions of polynomial systems via low-rank moment matrix completion
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Efficient gradient descent algorithm for sparse models with application in learning-to-rank
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Global analytic solution of fully-observed variational Bayesian matrix factorization
The Journal of Machine Learning Research
Lead-lag analysis via sparse co-projection in correlated text streams
Proceedings of the 22nd ACM international conference on Conference on information & knowledge management
Shifted subspaces tracking on sparse outlier for motion segmentation
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Social spammer detection in microblogging
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Social trust prediction using rank-k matrix recovery
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Audio classification with low-rank matrix representation features
ACM Transactions on Intelligent Systems and Technology (TIST) - Special Section on Intelligent Mobile Knowledge Discovery and Management Systems and Special Issue on Social Web Mining
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We consider the minimization of a smooth loss function regularized by the trace norm of the matrix variable. Such formulation finds applications in many machine learning tasks including multi-task learning, matrix classification, and matrix completion. The standard semidefinite programming formulation for this problem is computationally expensive. In addition, due to the non-smooth nature of the trace norm, the optimal first-order black-box method for solving such class of problems converges as O(1/√k), where k is the iteration counter. In this paper, we exploit the special structure of the trace norm, based on which we propose an extended gradient algorithm that converges as O(1/k). We further propose an accelerated gradient algorithm, which achieves the optimal convergence rate of O(1/k2) for smooth problems. Experiments on multi-task learning problems demonstrate the efficiency of the proposed algorithms.