Learning Gaussian Networks

By Dan Geiger, David E. Heckerman. 1994

We describe scoring metrics for learning Bayesian networks from a combination of user knowledge and statistical data. Previous work has concentrated on metrics for domains containing only discrete variables, under the assumption that data represents a multinomial sample. In this paper, we extend this work, developing scoring metrics for domains containing only continuous variables under the assumption that continuous data is sampled from a multivariate normal distribution. Our work extends traditional statistical approaches for identifying vanishing regression coefficients in that we identify two important assumptions, called event equivalence and parameter modularity, that when combined allow the construction of prior distributions for multivariate normal parameters from a single prior Bayesian network specified by a user.

Subfields: 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 Discovery with Reinforcement Learning (2019, methodology): “…acyclic graphs (DAGs) for the best scoring: While there have been well deﬁned score functions such as the BIC/MDL score [20, 5] and the BGe score [9] for linear-Gaussian models, problem (1) is generally NP-hard to solve [4, 6], largely due to its nonconvex and combinatorial nature; the…”
Constraint-based causal discovery from multiple interventions over overlapping variable sets (2014, methodology): “We use the BGE metric for gaussian distributions (Geiger and Heckerman, 1994) as implemented in the BDAGL package Eaton and Murphy (2007b) to calculate the likelihoods of the DAGs.”
UvA-DARE ( Digital Academic Repository ) Causal Discovery with Continuous Additive Noise Models (2014, unknown): “Heckerman and Geiger (1995) discuss how to choose the prior over parameters accordingly.”
A survey of Bayesian Network structure learning (2021, background): “The most common form of hybrid BN is a Conditional Linear Gaussian BN (CLGBN) which allows discrete variables to be parents of a continuous variable, with a separate Gaussian Linear Model with different weighting coefficients for each set of discrete parent values (Geiger and Heckerman, 1994).”
Nonparametric Convergence Assessment for MCMC Model Selection (2003, background): “See, for instance, the articles by Madigan and Raftery (1994), Madigan and York (1995), Geiger and Heckerman (1994) , and Giudici and Green (1999).”
Regression by dependence minimization and its application to causal inference in additive noise models (2009, methodology): “Introduction Most existing methods for learning causal models from observational data assume that continuous variables are multivariate Gaussian (Spirtes et al., 1993; Geiger & Heckerman, 1994; Bollen, 1989).”
Learning linear cyclic causal models with latent variables (2012, methodology): “As baseline we used the learning procedure by Geiger and Heckerman (1994) for acyclic Bayesian networks with linear Gaussian conditional probability distributions, referred to as GH. Experimental data is incorporated into the calculation of the local scores in GH using the technique described by…”
Constraint-based Causal Discovery for Non-Linear Structural Causal Models with Cycles and Latent Confounders (2018, unknown): “For the acyclic case without latent confounders, numerous constraint-based [25,32] and score-based approaches [6, 14, 17] exist.”
Constraint-based Causal Discovery: Conflict Resolution with Answer Set Programming (2014, methodology): “The marginal likelihoods P (y | C) and P (y | x,C) correspond to local scores in the score-based learning framework and have a closed form for categorical variables using a Dirichlet prior (Cooper and Herskovits, 1992) or for continuous variables with linear relations and Gaussian disturbances using”
Learning Bayesian networks: approaches and issues (2011, methodology): “Work in the score-and-search paradigm was done by Geiger and Heckerman (1994), who assume the data are drawn from a multinomial Gaussian and develop a scoring criteria for the case of networks with all continuous (known as BGe) and a mixture of continuous and discrete nodes (known as BcGe).”
D’ya Like DAGs? A Survey on Structure Learning and Causal Discovery (2021, methodology): “Secondly, ABIC [19] extends the continuous optimization paradigm to discover various types (ancestral, arid, bow-free) of ADMGs which account for unmeasured confounding.”
A Bayesian Approach to Causal Discovery (2006, methodology): “See Geiger et al. (1996) for a discussion of this point. This approximation technique for integration is known as Laplace's method, and we refer to Equation 19 as the Laplace approximation. Kass et al. (1988) have shown that, under certain regularity conditions, the relative error of this approximat”
A Linear Non-Gaussian Acyclic Model for Causal Discovery (2006, methodology): “Furthermore, eﬃcient algorithms for estimating the mixing matrix are available (Hyv¨arinen, 1999).”
Partition MCMC for Inference on Acyclic Digraphs (2015, methodology): “…(2008) since their implementation is not available and moreover they are most likely based on one of the incorrect versions of the BGe score (Geiger and Heckerman 1994; Heckerman and Geiger 1995; Geiger and Heckerman 2002), which has only recently been corrected (Consonni and Rocca 2012;…”