Addendum on the scoring of Gaussian directed acyclic graphical models

By Jack Kuipers, Giusi Moffa, David E. Heckerman. 2014

84 citations recorded by the source corpus.

We provide a correction to the expression for scoring Gaussian directed acyclic graphical models derived in Geiger and Heckerman (2002) [Annals of Statistics, 20, 1414-1440] and discuss how to evaluate the score efficiently.

Subfields: Artificial Intelligence, Statistics and Probability, Probabilistic & Bayesian Methods

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Citations in the corpus

Bayesian Structure Learning with Generative Flow Networks (2022, neutral): “Examples of modular scores include the BDe score (Heckerman et al., 1995) and the BGe score (Geiger and Heckerman, 1994; Kuipers et al., 2014).”
Causal Inference through a Witness Protection Program (2014, methodology): “This is analogous to the binary case, where here we use the corrected BGe score (Kuipers et al., 2014).”
DAGs with NO TEARS: Continuous Optimization for Structure Learning (2018, background): “This can be written as the following combinatorial optimization problem: Popular score functions include BDe(u) (Heckerman et al., 1995), BGe (Kuipers et al., 2014), BIC (Chickering and Heckerman, 1997), and MDL (Bouckaert, 1993).”
Efficient Sampling and Structure Learning of Bayesian Networks (2018, methodology): “For continuous multivariate Gaussian data, the inverse Wishart prior leads to the BGe score (Geiger and Heckerman, 2002; corrected in Kuipers et al., 2014).”
Towards Scalable Bayesian Learning of Causal DAGs (2020, methodology): “With the notation αμ and αw we adhere to the choices in the key references [9, 17].”
Variational Causal Networks: Approximate Bayesian Inference over Causal Structures (2021, methodology): “Calculate the per-sample marginal log-likelihood log p ( D|G ( i ) ) by marginalising θ to obtain the BGe Score [10, 23]. φ ← Update parameters using gradients g .”
Partition MCMC for Inference on Acyclic Digraphs (2015, methodology): “We work with the BGe score (Geiger and Heckerman 1994; Heckerman and Geiger 1995; Geiger and Heckerman 2002), corrected as in Consonni and Rocca (2012) and Kuipers, Moffa, and Heckerman (2014) and sped up following Kuipers, Moffa, and Heckerman (2014).”
Differentiable Causal Discovery Under Latent Interventions (2022, methodology): “…constrained optimization methods for ﬁnding a DAG ( directed acyclic graph ); other approaches include constraint-based (Spirtes et al., 1993; Pearl, 2000; Spirtes et al., 2013) and score-based methods (Bouckaert, 1993; Heckerman et al., 1994; Chickering and Heckerman, 1997; Kuipers et al., 2021).”