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Review
. 2019 Jun 4:10:524.
doi: 10.3389/fgene.2019.00524. eCollection 2019.

Review of Causal Discovery Methods Based on Graphical Models

Affiliations
Review

Review of Causal Discovery Methods Based on Graphical Models

Clark Glymour et al. Front Genet. .

Abstract

A fundamental task in various disciplines of science, including biology, is to find underlying causal relations and make use of them. Causal relations can be seen if interventions are properly applied; however, in many cases they are difficult or even impossible to conduct. It is then necessary to discover causal relations by analyzing statistical properties of purely observational data, which is known as causal discovery or causal structure search. This paper aims to give a introduction to and a brief review of the computational methods for causal discovery that were developed in the past three decades, including constraint-based and score-based methods and those based on functional causal models, supplemented by some illustrations and applications.

Keywords: causal discovery; conditional independence; directed graphical causal models; non-Gaussian distribution; non-linear models; statistical independence; structural equation models.

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Figures

Figure 1
Figure 1
Illustration of how the PC algorithm works. (A) Original true causal graph. (B) PC starts with a fully-connected undirected graph. (C) The XY edge is removed because XY. (D) The XW and YW edges are removed because XW |Z and YW |Z. (E) After finding v-structures. (F) After orientation propagation.
Figure 2
Figure 2
IIllustration of how the FCI algorithm is able to determine the existence of latent confunders. (A) Original true causal graph. (B) After edges are removed because of conditional independence relations. (C) The output of FCI, indicating that there is at least one unmeasured confounder of Y and Z.
Figure 3
Figure 3
Illustration of causal asymmetry between two variables with linear relations. The causal relation is XY. From top to bottom: X and E both follow the Gaussian distribution (case 1), uniform distribution (case 2), and Laplace distribution (case 3). The two columns on the left show the scatter plot of X and Y and that of X and the regression residual for regressing Y on X, and the two columns on the right correspond to regressing X on Y.
Figure 4
Figure 4
The “extended expert" model for Sachs's data set). See Sachs et al. (2005) or Ramsey and Bryan (2018b) for the significance of the variables.
Figure 5
Figure 5
The Model for the Sach's Data estimated by the FASK algorithm.

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