Comments on: Sequences of regressions and their independencies

Drton, Mathias; Fox, Christine; Käufl, Andreas

doi:10.1007/s11749-012-0285-3

Cited by 3 publications

(2 citation statements)

References 8 publications

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“…Again, one can define an 'ordinary model' using conditional independence constraints, which is larger than the marginal model but can be smoothly parameterized using the results in Richardson & Spirtes (2002). However, margins of these models also induce Verma constraints and inequalities, as well as more exotic constraints (see 8.3.1 of Richardson & Spirtes, 2002); an overview is given in Drton et al (2012). Fox et al (2015) characterize these models in a fairly large class of graphs, although the general case remains an open problem.…”

Section: Existing Resultsmentioning

confidence: 99%

Graphs for Margins of Bayesian Networks

Evans¹

2015

Scandinavian J Statistics

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Directed acyclic graph (DAG) models, also called Bayesian networks, impose conditional independence constraints on a multivariate probability distribution, and are widely used in probabilistic reasoning, machine learning and causal inference. If latent variables are included in such a model, then the set of possible marginal distributions over the remaining (observed) variables is generally complex, and not represented by any DAG. Larger classes of mixed graphical models, which use multiple edge types, have been introduced to overcome this; however, these classes do not represent all the models which can arise as margins of DAGs. In this paper we show that this is because ordinary mixed graphs are fundamentally insufficiently rich to capture the variety of marginal models.We introduce a new class of hyper-graphs, called mDAGs, and a latent projection operation to obtain an mDAG from the margin of a DAG. We show that each distinct marginal of a DAG model is represented by at least one mDAG, and provide graphical results towards characterizing when two such marginal models are the same. Finally we show that mDAGs correctly capture the marginal structure of causally-interpreted DAGs under interventions on the observed variables.

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Section: Existing Resultsmentioning

confidence: 99%

Graphs for Margins of Bayesian Networks

Evans¹

2015

Scandinavian J Statistics

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“…, X k equal to zero (cf. [2,11]). Denoting the resulting matrix by L k , we then obtain Σ k = L −1 k DL −T k .…”

Section: Modified Cholesky Decompositions (Mcd)mentioning

confidence: 99%

Estimating the effect of joint interventions from observational data in sparse high-dimensional settings

Nandy¹,

Maathuis²,

Richardson³

2017

Ann. Statist.

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We consider the estimation of joint causal effects from observational data. In particular, we propose new methods to estimate the effect of multiple simultaneous interventions (e.g., multiple gene knockouts), under the assumption that the observational data come from an unknown linear structural equation model with independent errors. We derive asymptotic variances of our estimators when the underlying causal structure is partly known, as well as high-dimensional consistency when the causal structure is fully unknown and the joint distribution is multivariate Gaussian. We also propose a generalization of our methodology to the class of nonparanormal distributions. We evaluate the estimators in simulation studies and also illustrate them on data from the DREAM4 challenge.

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