Moreau-Yosida Regularization for Grouped Tree Structure Learning

By Jun Liu, Jieping Ye. 2010

191 citations recorded by the source corpus.

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Citations in the corpus

Regularizing Text Categorization with Clusters of Words (2016, background): “, through sets, trees (Kim and Xing, 2010; Liu and Ye, 2010; Mairal et al., 2010) or graphs (Jenatton et al.”
Hyperspectral Image Classification Based on Structured Sparse Logistic Regression and Three-Dimensional Wavelet Texture Features (2013, methodology): “For sparse group lasso regularization, because there are two regularization terms, λ1 ∑G g=1 |uΩg |2 and λ2|u|1, we can apply the proximal operator on lasso regularization first and then on the group lasso regularization [50]”
Sparse Group Lasso: Consistency and Climate Applications (2012, unknown): “The condition holds in the special case of Gaussian noise; it also holds whenever the noise vector w consists of independent bounded random variables.”
Feature Selection (2016, background): “Recently, Tree-guided Group Lasso is proposed to handle the feature selection for features that can be represented in an index tree (Kim and Xing 2010; Liu and Ye 2010; Jenatton et al. 2010).”
Structured Sparsity in Structured Prediction (2011, methodology): “Proximal-gradient meth-ods are very popular in sparse modeling, both in batch (Liu and Ye, 2010; Bach et al., 2011) and on-line (Duchi and Singer, 2009; Xiao, 2009) settings.”
SLEP: Sparse Learning with Efficient Projections (2011, methodology): “The functions described in the followi ng are based on our work in [38].”
Feature Selection Based on Structured Sparsity: A Comprehensive Study (2017, background): “Thus, overlapping group lasso is proposed in [59].”
Salient Object Detection via Structured Matrix Decomposition (2017, methodology): “Before detailing the structured regularization, we first give the definition of an index tree [74].”
Traffic Sign Recognition via Multi-Modal Tree-Structure Embedded Multi-Task Learning (2017, unknown): “Combining (5) and (16) we obtain the following form: qL(Wt) = argmin W ( 1 2 ‖W −V‖2F + λ̃1‖W‖T ) = arg min W1,...,WD D∑ i=1 ( 1 2 ‖Wi −Vi‖2F + λ̃1‖Wi‖T ) (17) where Wi, Vi denotes the ith row of the matrix W, V respectively.”
Feature Selection for Classification: A Review (2014, background): “Tree-guided group Lasso regularization is proposed for features represented as an index tree [33, 42, 30].”
Lifespan brain age prediction based on multiple EEG oscillatory features and sparse group lasso (2025, unknown): “Sparse solutions are achieved by solving the Moreau-Yosida regularization (Liu and Ye, 2010) as where represents the weight for the j -th group as P (cid:12)(cid:12)(cid:12) (cid:12)(cid:12)(cid:12) and PCC indicating the Pearson correlation coeﬃcient between x i and the other n j feature vectors…”