Joint support recovery under high-dimensional scaling: Benefits and perils of ℓ 1,∞ -regularization

By Sahand N. Negahban, Martin J. Wainwright. 2008

84 citations recorded by the source corpus.

Subfields: Statistics and Probability, Statistical Learning Theory

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Citations in the corpus

An Overview of Multi-Task Learning in Deep Neural Networks (2017, background): “[Negahban and Wainwright, 2008] show that if features do not overlap by much, (cid:96) 1 /(cid:96) q regularization might actually be worse than element-wise (cid:96) 1 regularization.”
Multi-Stage Multi-Task Feature Learning (2012, neutral): “…et al., 2010; Negahban and Wainwright, 2011) and a common set of shared features (Argyriou et al., 2008; Gong et al., 2012; Kim and Xing, 2009; Kolar et al., 2011; Lounici et al., 2009; Liu et al., 2009; Negahban and Wainwright, 2008; Obozinski et al., 2006; Yang et al., 2009; Zhang et al., 2010).”
Distributed multi-task classification: a decentralized online learning approach (2017, methodology): “Representative MTL methods to boost the generalization performance on batch data include: common parameter sharing [9], low-rank subspace projection [1,24] and trace norm regularization [27].”
Robust Dynamic Trajectory Regression on Road Networks: A Multi-task Learning Framework (2014, background): “Moreover, as mentioned in [17], the ∞,1 norm intuitively contributes to favorable recovery of the non-zero elements in non-zero columns.”
SLEP: Sparse Learning with Efficient Projections (2011, background): “l1/lq-Norm Regularization Recent studies in areas such as machine learning and statist ics have also witnessed growing interests in extending the l1-regularization to thel1/lq-regularization [2, 3, 6, 10, 28, 29, 30, 31, 33, 40, 43, 49, 50, 53, 72, 73].”
On Learning Discrete Graphical Models using Group-Sparse Regularization (2011, methodology): “regression [32, 8, 22, 18, 24, 25, 2] show that under such group-sparse settings, group-sparse regularization outperforms the use of l1 penalization.”
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, ”
On the Effectiveness of Richardson Extrapolation in Machine Learning (2020, unknown): “This form includes traditional regularizers such as the `1-norm, the `∞-norm, grouped `1-`∞-norms (Negahban and Wainwright, 2008), or more general sparsityinducing norms (Bach, 2010).”
A Dirty Model for Multi-task Learning (2010, methodology): “The corresponding “clean” models would either just use blo cksparse regularizations [8, 10] or just elementwise sparsit y egularizations [14, 18], so that either method would perform better in certain suited regimes.”