Convex Structure Learning in Log-Linear Models: Beyond Pairwise Potentials

By Mark W. Schmidt, Kevin P. Murphy. 2010

69 citations recorded by the source corpus.

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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, methodology): “3 have notably proven to be useful in the context of hierarchical variable selection [9, 121, 157],”
Learning with Submodular Functions: A Convex Optimization Perspective (2011, methodology): “The corresponding penalty was first used in [213]; one of it simplest instance in the context of regression is the sparse group Lasso [194, 71]; it has found numerous applications, for instance, wavelet-based denoising [213, 15, 103, 114], hierarchical dictionary learning for both topic modelling an”
Convergence Rates of Inexact Proximal-Gradient Methods for Convex Optimization (2011, methodology): “However, despite the many recent works showing impressive empirical performance of (accelerated) proximal-gradient methods that use an approximate proximity operator [7, 13, 9, 10, 14, 15], up until recently there was no theoretical analysis on how the error in the calculation of the proximity opera”
Structured Variable Selection with Sparsity-Inducing Norms (2009, background): “Prior works with nested groups (Zhao et al., 2009; Bach, 2008a; Kim and Xing, 2010; Jenatton et al., 2010a; Schmidt and Murphy, 2010) have also used a similar DAG structure, with the slight difference that in these works, the corresponding hierarchy of variables is built from the prior knowledge abo”
Structured Sparsity in Structured Prediction (2011, background): “Schmidt and Murphy (2010) used to generative models, while our approach emphasizes discriminative learning.”
Structure Regularization for Structured Prediction (2014, background): “recent studies on structured sparsity in structured prediction scenarios [11, 8], via adopting mixed norm regularization [10], Group Lasso [22], and posterior regularization [5].”
Structured sparsity through convex optimization (2011, background): “…learning for both topic modelling and image restoration (Jenatton et al., 2011b), log-linear models for the selection of potential orders (Schmidt and Murphy, 2010), bioinformatics, to exploit the tree structure of gene networks for multi-task regression (Kim and Xing, 2010), and…”
Optimization for machine learning (2010, methodology): “This class of algorithms takes advantage of sparsity from a computational point of view (Lee et al., 2007; Szafranski et al., 2007; Bach, 2008a; Roth and Fischer, 2008; Obozinski et al., 2009; Jenatton et al., 2009; Schmidt and Murphy, 2010), since the subproblems that need to be solved are typicall”
Global Quantitative Modeling of Chromatin Factor Interactions (2014, methodology): “Moreover, we constrained the model structure to be hierarchical: a triplet interaction involving i, j, k will only be non-zero when all three pair-wise interactions i-j, j-k and i-k are non-zero, using algorithms described in [18].”
Spatial Pattern Templates for Recognition of Objects with Regular Structure (2013, methodology): “by block-wise regularization for sparsity [12] (16 segments) and subsequently also for higher-order potentials with a hierarchical constraint [13] (30 segments).”