Efficient Structure Learning of Markov Networks using L1-Regularization

By Su-In Lee, Varun Ganapathi, Daphne Koller. 2006

208 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Molecular Biology

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Citations in the corpus

Learning generative models for protein fold families (2011, background): “[21] introduced structure learning in MRFs with a pure L1 penalty, i.”
Exploiting compositionality to explore a large space of model structures (2012, background): “There has been much work on structure learning in particular model classes, such as undirected (Lee et al., 2006) and directed (Teyssier and Koller, 2005) graphical models.”
Optimizing Costly Functions with Simple Constraints: A Limited-Memory Projected Quasi-Newton Algorithm (2009, unknown): “In the case of Markov random fields on binary variables (such as Ising models), there is a one-to-one correspondence between parameters and edges in the graph, as in the Gaussian case, and so one can again learn structure by optimizing an `1-penalized log likelihood (Lee et al., 2006).”
Sparse and Locally Constant Gaussian Graphical Models (2009, methodology): “Structure learning through ‘1-regularization has been also proposed for different types of graphical models: Markov random fields (MRFs) by a clique selection heuristic and approximate inference [ 15 ]; Bayesian networks on binary variables by logistic regression [16]; Conditional random fields by p”
Recovering time-varying networks of dependencies in social and biological studies (2009, background): “The specific form of the optimization problem depends on whether the nodal states are assumed to be continuous (13, 16–19) or discrete (20, 21).”
Modeling Discrete Interventional Data using Directed Cyclic Graphical Models (2009, background): “This type of approach to simultaneous parameter and structure learning has previously been explored for undirected graphs (see Lee et al., 2006; Schmidt et al., 2008), but can not be used directly for DAG models (unless we restrict ourselves to a fixed node ordering) because of the acyclicity…”
Finding and Leveraging Structure in Learning Problems (2012, background): “The study of convex approximations to the complexity and goodness of fit metrics has received considerable attention recently [96, 125, 167, 199].”
Recovering Occlusion Boundaries from an Image (2011, background): “fier that can be used for feature selection [53] or learning Markov network structures [39].”
Hierarchical Mixture of Classification Experts Uncovers Interactions between Brain Regions (2009, methodology): “Some incremental approaches [26, 22 ] were proposed for random fields construction.”
Compressed sensing, sparsity, and dimensionality in neuronal information processing and data analysis. (2012, methodology): “Indeed it has been used successfully in learning logistic regression (Lee et al. 2006b) and in various graphical models (Lee et al. 2006a, Wainwright et al. 2007), as well as in point process models of neuronal spike trains (Kelly et al. 2010).”
Structure learning in random fields for heart motion abnormality detection (2008, methodology): “There are three solutions to this: restrict the graph to have low tree width [4, 16]; use approximate inference, such as loopy belief propagation (used in [23]) or brief Gibbs sampling (used in [15]); or change the objective function to pseudo-likelihood [6].”
Convex Structure Learning in Log-Linear Models: Beyond Pairwise Potentials (2010, methodology): “To address this problem, one can use pseudo-likelihood (Wainwright et al., 2006; Höfling and Tibshirani, 2009) or other approximate methods (Lee et al., 2006; Banerjee et al., 2008).”
Estimation of Sparse Binary Pairwise Markov Networks using Pseudo-likelihoods (2009, methodology): “We used an annealing schedule for Lee, Ganapathi, and Koller (2006a) to improve convergence as suggested in their article.”
Learning Graphical Model Structure Using L1-Regularization Paths (2007, background): “In the case of binary Markov networks, one can in principle adopt the same approach, although it is in general NP-hard to estimate the parameters of discrete Markov nets, requiring approximations such as loopy belief propagation ( LGK07 ).”
Coordinate Descent Converges Faster with the Gauss-Southwell Rule Than Random Selection (2015, methodology): “This rule has been used in the context of boosting [Rätsch et al., 2001], graphical models [Della Pietra et al., 1997, Lee et al., 2006, Scheinberg and Rish, 2009], Gaussian processes [Bo and Sminchisescu, 2008], and low-rank tensor approximations [Li et al., 2015].”