Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Twice Differentiable Spectral Functions
SIAM Journal on Matrix Analysis and Applications
Convex Optimization
Fast maximum margin matrix factorization for collaborative prediction
ICML '05 Proceedings of the 22nd international conference on Machine learning
Numerical Optimization: Theoretical and Practical Aspects (Universitext)
Numerical Optimization: Theoretical and Practical Aspects (Universitext)
On Model Selection Consistency of Lasso
The Journal of Machine Learning Research
Uncovering shared structures in multiclass classification
Proceedings of the 24th international conference on Machine learning
Consistency of the Group Lasso and Multiple Kernel Learning
The Journal of Machine Learning Research
Consistency of the Group Lasso and Multiple Kernel Learning
The Journal of Machine Learning Research
An accelerated gradient method for trace norm minimization
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Spectral Regularization Algorithms for Learning Large Incomplete Matrices
The Journal of Machine Learning Research
Limitations of matrix completion via trace norm minimization
ACM SIGKDD Explorations Newsletter
International Journal of Sensor Networks
Sparse kernel regression for traffic flow forecasting
ISNN'11 Proceedings of the 8th international conference on Advances in neural networks - Volume Part II
Trace norm regularization and application to tensor based feature extraction
ACCV'10 Proceedings of the 2010 international conference on Computer vision - Volume part II
Optimization with Sparsity-Inducing Penalties
Foundations and Trends® in Machine Learning
Distance metric learning with eigenvalue optimization
The Journal of Machine Learning Research
Restricted strong convexity and weighted matrix completion: optimal bounds with noise
The Journal of Machine Learning Research
Active subspace: Toward scalable low-rank learning
Neural Computation
Kernel regression with sparse metric learning
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
A joint convex penalty for inverse covariance matrix estimation
Computational Statistics & Data Analysis
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Regularization by the sum of singular values, also referred to as the trace norm, is a popular technique for estimating low rank rectangular matrices. In this paper, we extend some of the consistency results of the Lasso to provide necessary and sufficient conditions for rank consistency of trace norm minimization with the square loss. We also provide an adaptive version that is rank consistent even when the necessary condition for the non adaptive version is not fulfilled.