Efficient Structure Learning of Markov Networks using L1-Regularization

By Bernhard Schölkopf, John C. Platt, Thomas Hofmann. 2007

152 citations recorded by the source corpus.

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Citations in the corpus

Learning generative models for protein fold families (2011, background): “While approximations to the partition function based on Loopy Belief Propagation [15] have been proposed as an alternative, such approximations can lead to inconsistent estimates.”
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.”
Coordinate Descent Converges Faster with the Gauss-Southwell Rule Than Random Selection (2015, methodology): “This rule has been used in the context of boosting [R¨atsch 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].”
Hierarchical Mixture of Classification Experts Uncovers Interactions between Brain Regions (2009, methodology): “The structural learning method proposed in this paper offers an entirely new way to assess the interactions between brain regions based on the exchange of information between ROIs so that the accuracy of decoding experimental conditions from the data is improved.”
Structure learning in random fields for heart motion abnormality detection (2008, unknown): “[19] (G ,U ,N) Inductive logic program Markov net [26] (G ,U ,Y) L1MB Gaussian [37] (G ,U ,Y) L1MB Binary [23] (G ,U ,Y) L1RF + LBP Binary [16] (G ,U ,Y) MER + jtree Bnry, Thin [28] (G ,U ,N) Exhaustive search -”
Modeling Discrete Interventional Data using Directed Cyclic Graphical Models (2009, methodology): “Our work is also closely related to work on path diagrams and structural equation models (SEMs) (Wright, 1921), models of functional dependence that have long been used in genetics, econometrics, and the social sciences (see Pearl (2000)).”
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 (cid:96) 1 -penalized log likelihood (Lee et al., 2006).”
Sparse and Locally Constant Gaussian Graphical Models (2009, methodology): “Some methods assume a one-dimensional spatial neighborhood (e.g. silhouettes) and that variables far apart are only weakly correlated [8], interaction between a priori known groups of variables as in [9], or block structures as in [10] in the context of Bayesian networks.”
Convex Structure Learning in Log-Linear Models: Beyond Pairwise Potentials (2010, methodology): “, 2006; Ho ing and Tibshirani, 2009) or other approximate methods (Lee et al., 2006; Banerjee et al., 2008).”
Empirical Risk Minimization of Graphical Model Parameters Given Approximate Inference, Decoding, and Model Structure (2011, background): “• to select also a graphical model topology (along with parameters) that gets good results despite loopy BP inference, still using back-propagation but on a modified objective (Lee et al., 2006); • to re-incorporate a Bayesian prior (the need for which was pointed out by Minka (2000)—the present pap”
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.”
Finding and Leveraging Structure in Learning Problems (2012, methodology): “[Lee et al., 2007] introduced structure learning in MRFs with a pure L1 penalty, i.e. q = 1, but do not go further to explore the cases when q = {2,∞}.”
Multi-Task Learning of Gaussian Graphical Models (2010, background): “…learning has been applied to very diverse problems, such as linear regression (Liu et al., 2009), classification (Jebara, 2004), compressive sensing (Qi et al., 2008), reinforcement learning (Wilson et al., 2007) and structure learning of Bayesian networks (Niculescu-Mizil & Caruana, 2007).”