MAXIMUM LIKELIHOOD FOR SPARSE DIRECTED ACYCLIC GRAPHS

By DE Saravan, P. E. B. Ühlmann. 2013

Subfields: Probabilistic & Bayesian Methods

How researchers see this paper

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

In Probabilistic & Bayesian Methods

Citations in the corpus

Gradient-Based Neural DAG Learning (2019, background): “Even though the authors do not discuss explicitly identifiability issues, they point out consistency results for their LS score in [34, 1, 19].”
CAM: Causal Additive Models, high-dimensional order search and penalized regression (2013, methodology): “…structural equations cannot (be easily) observed, and maximum likelihood estimation among all (e.g. linear Gaussian) DAG models is computationally challenging and statistical guarantees for high-dimensional cases are only available under rather strong assumptions (van de Geer and Bühlmann, 2013).”
DAGs with NO TEARS: Continuous Optimization for Structure Learning (2018, neutral): “Columns: noise types of SEM.”
Identifiability of Gaussian structural equation models with equal error variances (2012, background): “Penalized maximum likelihood estimation does not need such an assumption [van de Geer and Bühlmann, 2013] but pays a price in terms of computational complexity.”
High-dimensional consistency in score-based and hybrid structure learning (2015, background): “Interestingly, van de Geer and Bühlmann (2013) proved high-dimensional consistency of the global optimum of the 0-penalized likelihood score function without assuming strong faithfulness, but assuming a permutation beta-min condition.”
High-dimensional learning of linear causal networks via inverse covariance estimation (2013, background): “A similar result is implicitly contained under some assumptions in van de Geer and Bühlmann (2013), but we provide a more general statement and additionally quantify a regime where the errors may exhibit a certain degree of heteroscedasticity.”
Learning Directed Acyclic Graphs with Penalized Neighbourhood Regression (2015, methodology): “…the identity, the estimator deﬁned by (1.5) is in fact equivalent to a penalized maximum likelihood estimator for B . e This fact has been exploited by van de Geer and B¨uhlmann (2013), who consider a similar (weighted) least squares estimator under the assumption that there exists an…”
Causal inference in partially linear structural equation models (2016, background): “The estimation of the Markov equivalence class of linear Gaussian SEMs in the low-dimensional case has been addressed in, for example, [5, 22], whereas the high-dimensional scenario (requiring sparsity of the true underlying DAG) is discussed in, for example, [2, 10, 13, 27].”