High-dimensional learning of linear causal networks via inverse covariance estimation

By Po-Ling Loh, Peter Buhlmann. 2013

216 citations recorded by the source corpus.

We establish a new framework for statistical estimation of directed acyclic graphs (DAGs) when data are generated from a linear, possibly non-Gaussian structural equation model. Our framework consists of two parts: (1) inferring the moralized graph from the support of the inverse covariance matrix; and (2) selecting the best-scoring graph amongst DAGs that are consistent with the moralized graph. We show that when the error variances are known or estimated to close enough precision, the true DAG is the unique minimizer of the score computed using the reweighted squared l2-loss. Our population-level results have implications for the identifiability of linear SEMs when the error covariances are specified up to a constant multiple. On the statistical side, we establish rigorous conditions for high-dimensional consistency of our two-part algorithm, defined in terms of a "gap" between the true DAG and the next best candidate. Finally, we demonstrate that dynamic programming may be used to select the optimal DAG in linear time when the treewidth of the moralized graph is bounded.

Subfields: Probabilistic & Bayesian Methods

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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, background): “Such a weaker gap condition is proposed in [13], Section 5.”
DAGs with NO TEARS: Continuous Optimization for Structure Learning (2018, methodology): “Columns: noise types of SEM.”
Learning Sparse Nonparametric DAGs (2019, background): “Fortunately, it is known that this case is somewhat exceptional: Assuming additive noise, as long as the fj are linear with non-Gaussian errors (Kagan et al., 1973; Shimizu et al., 2006; Loh and Bühlmann, 2014) or the functions fj are nonlinear (Hoyer et al.”
Identifying Best Interventions through Online Importance Sampling (2017, background): “There has been a lot of work [27, 16, 12, 15, 35, 29, 24, 33] on learning casual models from data and/or experiments and using it to estimate causal strength questions of the counterfactual nature.”
Learning Directed Acyclic Graphs with Penalized Neighbourhood Regression (2015, methodology): “There has also been progress using multistage methods that separate the learning procedure into several decoupled steps (Loh and Bühlmann, 2014; Bühlmann et al., 2014).”