Chain graph reduction into Power Chain Graphs

Reduction of graphs is a class of procedures used to decrease the dimensionality of a given graph in which the properties of the reduced graph are to be induced from the properties of the larger original graph. This paper introduces both a new method for reducing chain graphs to simpler directed acyclic graphs (DAGs), that we call power chain graphs (PCG), as well as a procedure for structure learning of this new type of graph from correlational data of a Gaussian Graphical model (GGM). A definition for PCGs is given, directly followed by the reduction method. The structure learning procedure is a two-step approach: first, the correlation matrix is used to cluster the variables; and then, the averaged correlation matrix is used to discover the DAGs using the PC-stable algorithm. The results of simulations are provided to illustrate the theoretical proposal, which demonstrate initial evidence for the validity of our procedure to recover the structure of power chain graphs. The paper ends with a discussion regarding suggestions for future studies as well as some practical implications.

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Structure learning of sparse directed acyclic graphs incorporating the scale-free property

Computational Statistics ◽

10.1007/s00180-018-0841-8 ◽

2018 ◽

Vol 34 (2) ◽

pp. 713-742

Author(s):

Xiao Guo ◽

Hai Zhang ◽

Yao Wang ◽

Yong Liang

Keyword(s):

Structure Learning ◽

Directed Acyclic Graphs ◽

Scale Free ◽

Acyclic Graphs

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An Order-Independent Algorithm for Learning Chain Graphs

The International FLAIRS Conference Proceedings ◽

10.32473/flairs.v34i1.128365 ◽

2021 ◽

Vol 34 (1) ◽

Author(s):

Mohammad Ali Javidian ◽

Marco Valtorta ◽

Pooyan Jamshidi

Keyword(s):

Directed Acyclic Graphs ◽

High Dimensional ◽

P Values ◽

Order Dependence ◽

Error Measures ◽

Acyclic Graphs ◽

Simulation Results ◽

Improved Performance ◽

Low Dimensional ◽

Chain Graphs

LWF chain graphs combine directed acyclic graphs and undirected graphs. We propose a PC-like algorithm, called PC4LWF, that finds the structure of chain graphs under the faithfulness assumption to resolve the problem of scalability of the proposed algorithm by Studeny (1997). We prove that PC4LWF is order dependent, in the sense that the output can depend on the order in which the variables are given. This order dependence can be very pronounced in high-dimensional settings. We propose two modifications of the PC4LWF algorithm that remove part or all of this order dependence. Simulation results with different sample sizes, network sizes, and p-values demonstrate the competitive performance of the PC4LWF algorithms in comparison with the LCD algorithm proposed by Ma et al. (2008) in low-dimensional settings and improved performance (with regard to error measures) in high-dimensional settings.

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Enumeration of labelled chain graphs and labelled essential directed acyclic graphs

Discrete Mathematics ◽

10.1016/s0012-365x(02)00838-5 ◽

2003 ◽

Vol 270 (1-3) ◽

pp. 267-278 ◽

Cited By ~ 10

Author(s):

Bertran Steinsky

Keyword(s):

Directed Acyclic Graphs ◽

Acyclic Graphs ◽

Chain Graphs

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Information Theoretic Causal Effect Quantification

Entropy ◽

10.3390/e21100975 ◽

2019 ◽

Vol 21 (10) ◽

pp. 975

Author(s):

Aleksander Wieczorek ◽

Volker Roth

Keyword(s):

Information Theory ◽

Time Series ◽

Causal Effect ◽

Directed Acyclic Graphs ◽

Second Step ◽

Information Theoretic ◽

Acyclic Graphs ◽

Outcome Framework ◽

Directed Information ◽

Chain Graphs

Modelling causal relationships has become popular across various disciplines. Most common frameworks for causality are the Pearlian causal directed acyclic graphs (DAGs) and the Neyman-Rubin potential outcome framework. In this paper, we propose an information theoretic framework for causal effect quantification. To this end, we formulate a two step causal deduction procedure in the Pearl and Rubin frameworks and introduce its equivalent which uses information theoretic terms only. The first step of the procedure consists of ensuring no confounding or finding an adjustment set with directed information. In the second step, the causal effect is quantified. We subsequently unify previous definitions of directed information present in the literature and clarify the confusion surrounding them. We also motivate using chain graphs for directed information in time series and extend our approach to chain graphs. The proposed approach serves as a translation between causality modelling and information theory.

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STRUCTURE-LEARNING OF CAUSAL BAYESIAN NETWORKS BASED ON ADJACENT NODES

International Journal of Artificial Intelligence Tools ◽

10.1142/s021821301350005x ◽

2013 ◽

Vol 22 (02) ◽

pp. 1350005 ◽

Cited By ~ 2

Author(s):

XIA LIU ◽

YOULONG YANG ◽

MINGMIN ZHU

Keyword(s):

Bayesian Networks ◽

Latent Variables ◽

Conditional Independence ◽

Structure Learning ◽

Original Graph ◽

Independence Tests ◽

Acyclic Graphs ◽

Causal Bayesian Networks ◽

Unobserved Variables ◽

Direct Acyclic Graphs

Due to the infeasibility of randomized controlled experiments, the existence of unobserved variables and the fact that equivalent direct acyclic graphs obtained generally can not be distinguished, it is difficult to learn the true causal relations of original graph. This paper presents an algorithm called BSPC based on adjacent nodes to learn the structure of Causal Bayesian Networks with unobserved variables by using observational data. It does not have to adjust the structure as the existing algorithms FCI and MBCS*, while it can guarantee to obtain the true adjacent nodes. More important is that algorithm BSPC reduces computational complexity and improves reliability of conditional independence tests. Theoretical results show that the new algorithm is correct. In addition, the advantages of BSPC in terms of the number of conditional independence tests and the number of orientation errors are illustrated with simulation experiments from which we can see that it is more suitable in order to learn the structure of Causal Bayesian Networks with latent variables. Moreover a better latent structure representation is returned.

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