Parameterizations and Fitting of Bi‐directed Graph Models to Categorical Data

Lupparelli, Monia; Marchetti, Giovanni M.; Bergsma, Wicher

doi:10.1111/j.1467-9469.2008.00638.x

Cited by 29 publications

(39 citation statements)

References 33 publications

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“…For instance, it remains an open question whether it is possible to develop a similar graphical criterion that is complete in a stricter sense than the one used in this paper. It also remains an open question whether our faithfulness result in Appendix A for regular Gaussian probability distributions can be extended to discrete probability distributions with the help of the parameterizations in [12]. Another line of action is the application of our graphical criterion in bioinformatics.…”

Section: Discussionmentioning

confidence: 94%

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Reading dependencies from covariance graphs

Peòa

2013

International Journal of Approximate Reasoning

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The covariance graph (aka bi-directed graph) of a probability distribution p is the undirected graph G where two nodes are adjacent iff their corresponding random variables are marginally dependent in p. (It is worth mentioning that our definition of covariance graph is somewhat non-standard. The standard definition states that the lack of an edge between two nodes of G implies that their corresponding random variables are marginally independent in p. This difference in the definition is important in this paper.) In this paper, we present a graphical criterion for reading dependencies from G, under the assumption that p satisfies the graphoid properties as well as weak transitivity and composition. We prove that the graphical criterion is sound and complete in certain sense. We argue that our assumptions are not too restrictive. For instance, all the regular Gaussian probability distributions satisfy them.

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Section: Discussionmentioning

confidence: 94%

“…Since then, they have received considerable attention. See, for instance, [1,4,[6][7][8]10,12,13,18,25,[30][31][32][33][34]. The works [1,10] are particularly important for the interpretation of covariance graphs in terms of independencies.…”

Section: Introductionmentioning

confidence: 98%

Reading dependencies from covariance graphs

Peòa

2013

International Journal of Approximate Reasoning

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“…Graphical models of marginal independence were originally introduced by Cox and Wermuth (1993) for the analysis of multivariate Gaussian distributions, and subsequently extended to the discrete case by Drton and Richarson (2008a), Lupparelli (2006) and Lupparelli et al (2009).…”

Section: Introductionmentioning

confidence: 99%

Conjugate and conditional conjugate Bayesian analysis of discrete graphical models of marginal independence

Ntzoufras

Tarantola

2013

Computational Statistics & Data Analysis

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractWe propose a conjugate and conditional conjugate Bayesian analysis of models of marginal independence with a bi-directed graph representation. We work with Markov equivalent directed acyclic graphs (DAGs) obtained using the same vertex set with the addition of some latent vertices when required. The DAG equivalent model is characterised by a minimal set of marginal and conditional probability parameters. This allows us to use compatible prior distributions based on products of Dirichlet distributions. For models with DAG representation on the same vertex set, the posterior distribution and the marginal likelihood is analytically available, while for the remaining ones a data augmentation scheme introducing additional latent variables is required. For the latter, we estimate the marginal likelihood using Chib's (1995) estimator. Additional implementation details including identifiability of such models is discussed. For all models, we also provide methodology for the computation of the posterior distributions of the marginal log-linear parameters based on a simple transformation of the simulated values of the probability parameters. We illustrate our method using a popular 4-way dataset.

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“…It is illustrated on the basis of bi-directed graphs, which are essentially undirected graphs with edges represented by bi-directed arrows instead of full lines [18].…”

Section: Average Distancementioning

confidence: 99%

Fast methods for designing circulant network topology with high connectivity and survivability

2016

J Cloud Comp

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This paper proposes two fast methods to design network topologies with high connectivity and survivability based on circulant graph theory. The first method, namely, the Combination Method (CM), investigates the average distances of circulant graphs with different combinations of chordal jumps, and tries to locate the optimal one among them. For this purpose, empirical formulas are proposed to describe the fluctuation features of average distances on curved surfaces. Furthermore, an enhanced Local Search Method (LSM) is proposed to find the local minimum points in troughs of the surfaces. The second method, namely, the Spider Web Method (SWM), is based on a bionic concept deriving from observation of the spider web, which is a classical example of network connectivity and survivability in natural world. The relation between CM and SWM in certain situations is also discussed. Finally, the connectivity and survivability of the topologies designed by CM and SWM are verified via simulated experiments involving vertex destruction.

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Parameterizations and Fitting of Bi‐directed Graph Models to Categorical Data

Cited by 29 publications

References 33 publications

Reading dependencies from covariance graphs

Reading dependencies from covariance graphs

Conjugate and conditional conjugate Bayesian analysis of discrete graphical models of marginal independence

Fast methods for designing circulant network topology with high connectivity and survivability

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