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July  2021, 8(3): 203-231. doi: 10.3934/jdg.2021008

Causal discovery in machine learning: Theories and applications

1. 

LIAAD - INESC TEC, Rua Dr. Roberto Frias, Porto, 4200 - 465, Portugal, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre 1021/1055, Porto, 4169-007, Portugal

2. 

LIAAD - INESC TEC, Rua Dr. Roberto Frias, Porto, 4200 - 465, Portugal

* Corresponding author: Ana Rita Nogueira

Received  October 2019 Revised  March 2020 Published  July 2021 Early access  March 2021

Fund Project: The first author is supported by Fundação para a Ciência e Tecnologia (FCT) (Portugal) PhD grant SFRH/BD/146197/2019

Determining the cause of a particular event has been a case of study for several researchers over the years. Finding out why an event happens (its cause) means that, for example, if we remove the cause from the equation, we can stop the effect from happening or if we replicate it, we can create the subsequent effect. Causality can be seen as a mean of predicting the future, based on information about past events, and with that, prevent or alter future outcomes. This temporal notion of past and future is often one of the critical points in discovering the causes of a given event. The purpose of this survey is to present a cross-sectional view of causal discovery domain, with an emphasis in the machine learning/data mining area.

Citation: Ana Rita Nogueira, João Gama, Carlos Abreu Ferreira. Causal discovery in machine learning: Theories and applications. Journal of Dynamics & Games, 2021, 8 (3) : 203-231. doi: 10.3934/jdg.2021008
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[12]

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[16]

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[17]

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[21]

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[22]

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48]">Figure 1.  Overview of the evolution of the term "causality" and the main contributors [48]
Figure 2.  Example of a DAG
Figure 3.  Example of a v-structure
100]">Figure 4.  Example of a Causal Neural Network with one hidden layer [100]
56] and comparison with a normal Decision Tree">Figure 5.  Example of a Causal Decision Tree [56] and comparison with a normal Decision Tree
38]">Figure 6.  GeNie [38]
21]">Figure 7.  Tetrad [21]
Table 1.  Survey studies overview
Survey Title Reference Causal Bayesian Networks Non-bayesian methods Causal discovery over Time Causal discovery in statistics Tools/Frameworks for causal discovery Evaluation Metrics Possible Applications
Reference Assumptions Constraint-Based BN Score-Bases BN
Review of CausalDiscovery Methods Based on Graphical Models [30]
A Review on Algorithms for Constraint-based Causal Discovery [104]
A review of causal inference for biomedical informatics [50]
Causal discovery and inference: concepts and recent methodological advances [89]
A Survey of Learning Causality with Data:Problems and Methods [34]
Causality and Statistical Learning [27]
Machine learning for causal inference in Biostatistics [79]
Causal Interpretabilityfor Machine Learning - Problems, Methods and Evaluation [65]
*metrics to measure how explainable an algorithm is
Survey Title Reference Causal Bayesian Networks Non-bayesian methods Causal discovery over Time Causal discovery in statistics Tools/Frameworks for causal discovery Evaluation Metrics Possible Applications
Reference Assumptions Constraint-Based BN Score-Bases BN
Review of CausalDiscovery Methods Based on Graphical Models [30]
A Review on Algorithms for Constraint-based Causal Discovery [104]
A review of causal inference for biomedical informatics [50]
Causal discovery and inference: concepts and recent methodological advances [89]
A Survey of Learning Causality with Data:Problems and Methods [34]
Causality and Statistical Learning [27]
Machine learning for causal inference in Biostatistics [79]
Causal Interpretabilityfor Machine Learning - Problems, Methods and Evaluation [65]
*metrics to measure how explainable an algorithm is
Table 2.  Example of a partial contingency table (in where $ c_k = \{A = a1, B = b1\} $)
$ c_k=\{A,B\} $ $ C=c_1 $ $ C=c_2 $ Total
$ D=d_1 $ $ n_{11k} $ $ n_{12k} $ $ n_{1.k} $
$ D=d_2 $ $ n_{21k} $ $ n_{22k} $ $ n_{2.k} $
Total $ n_{.1k} $ $ n_{.2k} $ $ n_{..k} $
$ c_k=\{A,B\} $ $ C=c_1 $ $ C=c_2 $ Total
$ D=d_1 $ $ n_{11k} $ $ n_{12k} $ $ n_{1.k} $
$ D=d_2 $ $ n_{21k} $ $ n_{22k} $ $ n_{2.k} $
Total $ n_{.1k} $ $ n_{.2k} $ $ n_{..k} $
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