Trace Norm Regularization: Reformulations, Algorithms, and Multi-Task Learning
By Ting Kei Pong, Paul Tseng, Shuiwang Ji, Jieping Ye. 2010
239 citations recorded by the source corpus.
Subfields: Artificial Intelligence, Computational Mechanics, Optimization & Training
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Citations in the corpus
- An Overview of Multi-task Learning (2018, methodology): “Based on the analysis in optimization, regularizing with the trace norm, which is defined as ‖W‖S(1) = ∑min(m,d) i=1 μi (W), can make a matrix low-rank and hence trace-norm regularization is widely used in MTL with [26] as a representative work.”
- A Survey on Multi-Task Learning (2017, methodology): “Specifically, an objective function with the trace norm regularization is proposed in [49] as”
- Multi-Task Learning and Algorithmic Stability (2015, methodology): “The trace norm is widely used in multi-task learning as a regularizer (Argyriou, Evgeniou, and Pontil 2006; Zhang and Yeung 2010a; Pong et al. 2010; Chen, Liu, and Ye 2010; Chen, Zhou, and Ye 2011; Chen, Liu, and Ye 2012) since the trace norm regularization can learn a low-rank matrix which matches…”
- Learning to Multitask (2018, methodology): “As its special case, the trace norm is widely used in multitask learning [26] as a regularizer to capture the low-rank structure in W .”
- Low-Rank Matrix Recovery via Efficient Schatten p-Norm Minimization (2012, background): “2009), multitask learning (Abernethy et al. 2006; Pong et al. 2010; Argyriou, Evgeniou, and Pontil 2008), image/video completion (Liu et al.”
- Learning Sparse Task Relations in Multi-Task Learning (2017, methodology): “which is the multi-task model with a given Ω, the MTL-TNR method (Pong et al. 2010) which is the multi-task model with trace norm regularization, the MTL-STNR method (Argyriou, Evgeniou, and Pontil 2006) which is the multi-task model with the squared trace norm regularization, the MTL-CNR method (Ja”
- Fast and Accurate Matrix Completion via Truncated Nuclear Norm Regularization (2013, background): “ESTIMATING missing values from very limited information of an unknown matrix has attracted considerable interest recently [1], [2], [3], [4], [5], [6], [7].”
- Local Rademacher Complexity-based Learning Guarantees for Multi-Task Learning (2016, background): “It should be mentioned that similar data-dependent MT-LRC bounds can be easily obtained by a similar deduction process.”
- Tensor Completion for Estimating Missing Values in Visual Data (2009, background): “[ Although its ranks unfolded along three modes are 164 , 198 , 165] , they can decrease to [35 , 42 , 36] if removing small singular values less than 0 .”
- Linearized augmented Lagrangian and alternating direction methods for nuclear norm minimization (2012, methodology): “For example, it is shown in [1, 2, 36, 38] that certain multi-task learning problems with least squares loss functions can be exactly captured by (1.2).”
- Hankel Matrix Rank Minimization with Applications to System Identification and Realization (2013, methodology): “This method has also been used in [45,51] for nuclear norm related problems.”
- Robust multi-task feature learning (2012, background): “On the contrary, algorithms under implicit structure sharing do not explicitly impose all tasks to share certain parameters, but they implicitly capture some common structures; for example, the algorithms in [29, 24] constrain all tasks to share a common low rank subspace and the algorithms in [27, ”
- An accelerated proximal gradient algorithm for nuclear norm regularized linear least squares problems (2009, background): “It also appears in multi-class classification and multi-task learning; see [37] and the references therein.”