Group lasso with overlap and graph lasso

By Laurent Jacob, Guillaume Obozinski, Jean-Philippe Vert. 2009

1,011 citations recorded by the source corpus.

Subfields: Molecular Biology, Statistics and Probability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Molecular Biology

In Statistics and Probability

Citations in the corpus

Regularizing Text Categorization with Clusters of Words (2016, background): “Note that the groups can be overlapping (Jacob et al., 2009; Schmidt and Murphy, 2010; Jenatton et al., 2011; Yuan et al., 2011) even though it makes the optimization harder.”
Optimization with Sparsity-Inducing Penalties (2011, background): “Reducing parsimony to finding the model of lowest cardinality turns out to be limiting, and structured parsimony [15, 62, 64, 66] has emerged as a natural extension, with applications to computer vision [32, 62, 70], text processing [68], bioinformatics [64, 73] or audio processing [80].”
Online Learning for Matrix Factorization and Sparse Coding (2009, methodology): “onvergence results in these cases. Note also that convex smooth approximation of sparse regularizers (Bradley and Bagnell, 2009), or structured sparsity-inducing regularizers (Jenatton et al., 2009a; Jacob et al., 2009) could be used as well even though we have not tested them. 5.2 Using Diﬀerent Co”
Learning with Submodular Functions: A Convex Optimization Perspective (2011, background): “Most of the work based on convex optimization and the design of dedicated sparsity-inducing norms has focused mainly on the specific allowed set of sparsity patterns [213, 111, 107, 113]: if w ∈ Rp denotes the predictor we aim to estimate, and Supp(w) denotes its support, then these norms are design”
STANDARDIZATION AND THE GROUP LASSO PENALTY (2012, background): “Many works explicitly do not orthonormalize (Puig et al. [2009], Foygel and Drton [2010], Jacob et al.”
Feature Selection for Classification: A Review (2014, background): “Algorithms investigating overlapping groups are proposed as [27, 30, 33, 42].”
Flexible Clustered Multi-Task Learning by Learning Representative Tasks (2016, methodology): “According to [27], [54], the value of q is typically chosen from f2;1g.”
Sparse Signal Processing for Grant-Free Massive Connectivity: A Future Paradigm for Random Access Protocols in the Internet of Things (2018, methodology): “Further, the group-sparsity in the MMV model (13) can also be utilized in LASSO [27], in which the (cid:96) 1 /(cid:96) 2 penalty, i.e., the sum of (cid:96) 2 norm penalty, is used to promote the desired sparsity pattern.”
Proximal Methods for Sparse Hierarchical Dictionary Learning (2010, background): “Moreover, it can be easily extended with the same tools to other types of structures corresponding to other norms (Jenatton et al., 2009; Jacob et al., 2009).”
Group sparse optimization by alternating direction method (2013, neutral): “min y −b y + (Ax) y + β 2 ‖z −A y‖(2)2, (18)”
A Sparse-Group Lasso (2013, background): “” Jacob, Obozinski, and Vert (2009) gave a very nice ﬁx for this issue by slightly reformulating the problem, but this more general framework is beyond the scope of our article.”
Weakly decomposable regularization penalties and structured sparsity (2012, methodology): “…paper, we are primarily interested in extensions of the `1-penalty to general structured sparsity penalties such as the group Lasso introduced by Yuan & Lin (2006) and further structured versions given by Zhao et al. (2009), Jacob et al. (2009), Jenatton et al. (2011) and Micchelli et al. 2010.”
Making the Most of Bag of Words: Sentence Regularization with Alternating Direction Method of Multipliers (2014, background): “There has been much work on optimization with overlapping group lasso penalty (Jacob et al., 2009; Jenatton et al., 2011; Chen et al., 2011; Qin & Goldfarb, 2012; Yuan et al., 2013).”
Learning with structured sparsity (2009, methodology): “It is also worth pointing out that independent of this paper, two recent work (Jacob et al., 2009; Jenatton et al., 2009) considered structured sparsity in the convex relaxation setting, and extended group Lasso to more complicated sparse regularization conditions.”
Sparse multi-task reinforcement learning (2014, neutral): “Future work will be focused on providing a better understanding and a relaxation of the theoretical assumptions and on studying alternative multi-task regularization formulations such as in [31] and [13].”
Stochastic Dual Coordinate Ascent with Alternating Direction Method of Multipliers (2014, methodology): “between groups, the proximal operation can not be straightforwardly computed (Jacob et al., 2009).”