scholarly journals Enumeration of labelled chain graphs and labelled essential directed acyclic graphs

2003 ◽  
Vol 270 (1-3) ◽  
pp. 267-278 ◽  
Author(s):  
Bertran Steinsky
Keyword(s):  
Directed Acyclic Graphs ◽  
Acyclic Graphs ◽  
Chain Graphs

scholarly journals An Order-Independent Algorithm for Learning Chain Graphs

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.

scholarly journals Chain graph reduction into Power Chain Graphs

2021 ◽  
Author(s):  
Víthor Rosa Franco ◽  
Guilherme Wang Barros ◽  
Marie Wiberg ◽  
Jacob Arie Laros
Keyword(s):  
Correlation Matrix ◽  
Graphical Model ◽  
Structure Learning ◽  
Directed Acyclic Graphs ◽  
Original Graph ◽  
Stable Algorithm ◽  
Acyclic Graphs ◽  
Learning Procedure ◽  
Correlational Data ◽  
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.

scholarly journals Information Theoretic Causal Effect Quantification

Entropy ◽  
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.

scholarly journals Directed acyclic graphs: An under-utilized tool for child maltreatment research

2019 ◽  
Vol 91 ◽  
pp. 78-87 ◽  
Author(s):  
Anna E. Austin ◽  
Tania A. Desrosiers ◽  
Meghan E. Shanahan
Keyword(s):  
Child Maltreatment ◽  
Directed Acyclic Graphs ◽  
Acyclic Graphs

scholarly journals On directed analogues of expander and hyperfinite graph sequences

2021 ◽  
pp. 1-14
Author(s):  
Endre Csóka ◽  
Łukasz Grabowski
Keyword(s):  
Directed Acyclic Graphs ◽  
Acyclic Graphs ◽  
Probabilistic Construction

Abstract We introduce and study analogues of expander and hyperfinite graph sequences in the context of directed acyclic graphs, which we call ‘extender’ and ‘hypershallow’ graph sequences, respectively. Our main result is a probabilistic construction of non-hypershallow graph sequences.

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