Learning Graphical Model Structure Using L1-Regularization Paths

By Mark W. Schmidt, Alexandru Niculescu-Mizil, Kevin P. Murphy. 2007

238 citations recorded by the source corpus.

How researchers see this paper

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

Citations in the corpus

Weakly-Supervised Disentanglement Without Compromises (2020, background): “In this paper, we consider learning disentangled representations from pairs of observations which differ by a few factors of variation (Bengio, 2017; Schmidt et al., 2007; Bengio et al., 2019) as in Figure 1.”
A Meta-Transfer Objective for Learning to Disentangle Causal Mechanisms (2019, background): “…the ﬁrst one is that the causal graph is sparse (has few edges, as in the consciousness prior (Bengio, 2017) and in some methods to learn Bayes net structure, e.g. (Schmidt et al., 2007)); and the second one is that it changes sparsely due to interventions (which is the focus of this work).”
CAM: Causal Additive Models, high-dimensional order search and penalized regression (2013, methodology): “Our proposed approach for estimation and selection of additive structural equation models is based on the following simple idea which is briefly mentioned and discussed in [35] and [31].”
DAGs with NO TEARS: Continuous Optimization for Structure Learning (2018, background): “There is also a wide literature on approximate algorithms based on order search (Teyssier and Koller, 2005; Schmidt et al., 2007; Scanagatta et al., 2015, 2016), greedy search (Heckerman et al., 1995; Chickering, 2003; Ramsey et al., 2016), and coordinate descent (Fu and Zhou, 2013; Aragam and…”
Learning Directed Acyclic Graphs with Penalized Neighbourhood Regression (2015, methodology): “It follows that for each π ∈ S p , supp( β j ( π )) ⊂ S j ( π ) for each j = 1 , . . . , p . e Recall the objective function deﬁned in (1.3) and the associated estimator (1.5). e The spaces D p [ π ] help give us some intuition into what is going on with the estimator B : Suppose we had oracle knowl”
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).”
On the Convexity of Latent Social Network Inference (2010, methodology): “Recently, grap hic l Lasso methods [25, 21, 6, 19] for static sparse graph estimation and extensions to time evolv ing graphical models [1, 8, 22] have been proposed with lots of success.”
Time-Varying Dynamic Bayesian Networks (2009, methodology): “In our experiments, we demonstrate the advantange of TV-DBNs using synthetic networks.”
Mixed Cumulative Distribution Networks (2010, methodology): “inal independence using [7]. This combined technique allowed the structure to be inferred efﬁciently. We compared this copula MCDN to a Gaussian DAG model (ﬁt using just the DAG learning algorithm of [22] and maximum likelihood). The results are shown in table 1. The number of bi-directed edges give”
Is Independence all you need? On the Generalization of Representations Learned from Correlated Data (2020, background): “Changes in natural environments, which typically correspond to changes of only a few underlying factors of variation, provide a weak supervision signal for representation learning algorithms (Goyal et al., 2019; Földiák, 1991; Schmidt et al., 2007; Bengio et al., 2019).”
Inferring Networks of Diffusion and Influence (2012, methodology): “Our work relates to static sparse graph estimation using graphical Lasso methods [Friedman et al. 2008; Meinshausen and Buehlmann 2006; Schmidt et al. 2007; Wainwright et al. 2006], unsupervised structure network inference using kernel methods [Lippert et al. 2009], mutual information relevance…”
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.”
High-dimensional consistency in score-based and hybrid structure learning (2015, methodology): “Schmidt et al. [2007]) and hill-climbing DAG search restricted to the CPDAG-skeleton (e.”