The Group-Lasso for generalized linear models: uniqueness of solutions and efficient algorithms

By Volker Roth, Bernd Fischer. 2008

213 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Optimization with Sparsity-Inducing Penalties (2011, background): “A regularization norm exploiting explicitly this group structure, or `1-group norm, can be shown to improve the prediction performance and/or interpretability of the learned models [61, 83, 106, 116, 141, 156].”
Online Learning for Matrix Factorization and Sparse Coding (2009, neutral): “…ℓ 1 , 2 -sparse decomposition problem, which is a subcase of the group Lasso (Turlach et al., 2005; Yuan and Lin, 2006; Bach, 2008), by deﬁning the cost function which can be computed using a block-coordinate descent approach (Friedman et al., 2007) or an active set method (Roth and Fischer, 2008).”
On the Linear Convergence of a Proximal Gradient Method for a Class of Nonsmooth Convex Minimization Problems (2013, methodology): “We refer readers to [6, 7, 13, 16, 18, 20–22] for further studies on group Lasso type of statistical techniques.”
Group lasso with overlap and graph lasso (2009, methodology): “Note that (Roth & Fischer, 2008) provides a faster algorithm for the group Lasso.”
Super-Resolution With Sparse Mixing Estimators (2010, methodology): “This is also called a “group lasso” optimization [61], [50], [4].”
l p -Norm Multiple Kernel Learning (2011, background): “The above problem has been solved by active set methods in the primal (Roth and Fischer, 2008).”
Heterogeneous multitask learning with joint sparsity constraints (2009, unknown): “We can use simliar regularization in logistic regression and multinomial logistic regression for classification tasks[8, 12 ].”
Multi-Task Feature Learning Via Efficient l2, 1-Norm Minimization (2009, methodology): “We plan to improve the practical performance of the proposed algorithms using the adaptive line search proposed in [11], and apply the proposed algorithms for solving the 2,1-norm regularized problems including the group Lasso [27], the logistic group-lasso [13], and the group-lasso for generalized ”
Structured Variable Selection with Sparsity-Inducing Norms (2009, background): “For more sophisticated uniqueness conditions that we have not explored here, we refer the readers to Osborne et al. (2000, Theorem 1, 4 and 5), Rosset et al. (2004, Theorem 5) or Dossal (2007, Theorem 3) in the Lasso case, and Roth and Fischer (2008) for the group Lasso setting.”
On the Linear Convergence of the Approximate Proximal Splitting Method for Non-smooth Convex Optimization (2014, methodology): “We refer the readers to [2, 15] for further applications of Group LASSO, and to [3, 7, 10, 18, 27, 33, 34] for further studies on Group LASSO type of techniques in statistical problems.”
Gradient boosted feature selection (2014, methodology): “Prior work on handling structured sparsity include group lasso [10, 20] and generalized lasso [19].”
Group Lasso with Overlaps: the Latent Group Lasso approach (2011, methodology): “To be specific, for the experiments presented in section 10, we implemented the block-coordinate descent algorithm of Meier et al. (2008) combined with the working set strategy proposed by Roth and Fischer (2008).”
Network Reconstruction From High-Dimensional Ordinary Differential Equations (2016, methodology): “Tibshirani (2008). Sparse inverse covariance estimation with the graphical lasso. Biostatistics 9(3), 432–441. Gao, E., G. C. DeAngelis, and A. Burkhalter (2010). Parallel input channels to mouse primary visual cortex.”
On Similarity Preserving Feature Selection (2013, methodology): “To address the problem, below we propose an efficient path algorithm by linking our formulation to the group-LAR [30], [47] algorithm, which leads to the SPFS-LAR algorithm for feature selection.”
Optimization for machine learning (2010, methodology): “A regularization norm exploiting explicitly this group structure can be shown to improve the prediction performance and/or interpretability of the learned models (Yuan and Lin, 2006; Roth and Fischer, 2008; Huang and Zhang, 2009; Obozinski et al., 2009; Lounici et al., 2009).”
Network Flow Algorithms for Structured Sparsity (2010, unknown): “While the settings where the penalized groups of variables do not overlap [12] or are embedded in a tree-shaped hierarchy [11] have already been studied, sparsityinducing regularizations of general overlapping groups have, to the best of our knowledge, never been considered within the proximal metho”