Proximal Methods for Sparse Hierarchical Dictionary Learning

By Rodolphe Jenatton, Julien Mairal, Guillaume Obozinski, Francis R. Bach. 2010

398 citations recorded by the source corpus.

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Citations in the corpus

Sparse Partially Linear Additive Models (2014, methodology): “The hierarchical group lasso can be solved efficiently by proximal gradient descent (Beck and Teboulle 2009) as described by Jenatton et al. (2010).”
Regularizing Text Categorization with Clusters of Words (2016, background): “…on how the similarity between features is encoded, e. g., through sets, trees (Kim and Xing, 2010; Liu and Ye, 2010; Mairal et al., 2010) or graphs (Jenatton et al., 2010), the penalization term varies but in any case, we take into account the structure between features, hence the “structured…”
Optimization with Sparsity-Inducing Penalties (2011, methodology): “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].”
Learning with Submodular Functions: A Convex Optimization Perspective (2011, background): “urns out to be limiting, and structured parsimony has emerged as a fruitful practical extension, with applications to image processing, text processing, bioinformatics or audio processing (see, e.g., [213, 111, 103, 107, 119, 113, 142, 131], a review in [11, 12] and Chapter 6 for various examples). ”
Nonparametric sparsity and regularization (2012, methodology): “Indeed, structured sparsity model induced by more complex index sets have been considered, see for example [35], but the penalties are still induced by operators which are orthogonal projections.”
Sparse Additive Generative Models of Text (2011, unknown): “Sparse dictionary learning provides an alternative approach to modeling document content with sparse bases (Jenatton et al., 2010).”
Hierarchical Sparse Modeling: A Choice of Two Group Lasso Formulations (2015, background): “…interactions (Yuan, Joseph and Zou, 2009, Zhao, Rocha and Yu, 2009, Radchenko and James, 2010, Schmidt and Murphy, 2010, Choi, Li and Zhu, 2010, Jenatton et al., 2010, Bien, Taylor and Tibshirani, 2013, Lim and Hastie, 2015, She, Wang and Jiang, 2017, Haris, Witten and Simon, 2016), covariance…”
A Field Guide to Forward-Backward Splitting with a FASTA Implementation (2014, background): “Problems of the form (1) arise frequently in the many areas including machine learning, dictionary learning [1], online learning for streaming data [2], sparse coding [3, 4], spectral clustering [5], sparse covariance estimation [6], approximate nearest neighbor search and vector quantization [7], a”
Exact Recovery of Sparsely Used Overcomplete Dictionaries (2013, methodology): “Other works consider more sophisticated methods from an optimization viewpoint while still alternating between dictionary and coeﬃcient updates [23, 17].”
Collaborative Sparse Regression for Hyperspectral Unmixing (2014, background): “Other works [35], [36] consider tree-organization models of the output to exploit”
Structured Variable Selection with Sparsity-Inducing Norms (2009, background): “Another way to yield a better level of sparsity, even with many overlaps, would beto consider non-convex alternatives to Ω (see, e.g., Jenatton et al., 2010).”
Convergence Rates of Inexact Proximal-Gradient Methods for Convex Optimization (2011, methodology): “, see [12] for the case of overlapping group `1-regularization).”
Network Flow Algorithms for Structured Sparsity (2010, unknown): “Much effort has recently been devoted to designing sparsity-inducing regularizations capable of encoding higher-order information about allowed patterns of non-zero coefficients [5, 6, 7, 8, 9, 10], with successful applications in bioinformatics [6, 11], topic modeling [12] and computer vision [9, 1”
Sparse Group Lasso: Consistency and Climate Applications (2012, unknown): “We follow the method proposed in [17] which is a sub-gradient based approach to solve the primal SGL problem.”
SeqGL Identifies Context-Dependent Binding Signals in Genome-Wide Regulatory Element Maps (2015, methodology): “We used the SPAMS toolbox for solving the classification problem [48], and λs were chosen by 10-fold cross-validation on the training sets.”
Efficient Methods for Overlapping Group Lasso (2011, background): “Recently, it has been shown in [14] that, the efficient computation of the prox imal operator is key to many sparse learning algorithms.”
Learning Sparsely Used Overcomplete Dictionaries via Alternating Minimization (2013, methodology): “More generally the exact lasso and least-squares steps may be replaced with other optimization methods for computational eﬃciency, e.g. [16].”
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].”