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Single World Intervention Graphs (SWIGs): A Unification of the Counterfactual and Graphical Approaches to Causality
"... We present a simple graphical theory unifying causal directed acyclic graphs (DAGs) and potential (aka counterfactual) outcomes via a nodesplitting transformation. We introduce a new graph, the SingleWorld Intervention Graph (SWIG). The SWIG encodes the counterfactual independences associated with ..."
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We present a simple graphical theory unifying causal directed acyclic graphs (DAGs) and potential (aka counterfactual) outcomes via a nodesplitting transformation. We introduce a new graph, the SingleWorld Intervention Graph (SWIG). The SWIG encodes the counterfactual independences associated with a specific hypothetical intervention on the set of treatment variables. The nodes on the SWIG are the corresponding counterfactual random variables. We illustrate the theory with a number of examples. Our graphical theory of SWIGs may be used to infer the counterfactual independence relations implied by the counterfactual models developed in Robins (1986, 1987). Moreover, in the absence of hidden variables, the joint distribution of the counterfactuals is identified; the identifying formula is the extended gcomputation formula introduced in (Robins et al., 2004). Although Robins (1986, 1987) did not use DAGs we translate his algebraic results to facilitate understanding of this prior work. An attractive feature of Robins ’ approach is that it largely avoids making counterfactual independence assumptions that are experimentally untestable. As an important illustration we revisit the critique of Robins ’ gcomputation given in (Pearl, 2009, Ch. 11.3.7); we use SWIGs to show that all of Pearl’s claims are either erroneous or based on misconceptions. We also show that simple extensions of the formalism may be used to accommodate dynamic regimes, and to formulate nonparametric structural equation models in which assumptions relating to the absence of direct effects are formulated at the population level. Finally, we show that our graphical theory also naturally arises in the context of an expanded causal Bayesian network in which we are able to observe the natural state of a Potential outcomes are extensively used within Statistics, Political Science, Economics, and Epidemiology for reasoning about causation. Directed acyclic graphs (DAGs) are another formalism used to represent causal systems also
Advanced Applications of Structural Equation Modeling in Counseling Psychology Research
, 2006
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Interventions and causal inference
 Philosophy of Science
, 2007
"... The literature on causal discovery has focused on interventions that involve randomly assigning values to a single variable. But such a randomized intervention is not the only possibility, nor is it always optimal. In some cases it is impossible or it would be unethical to perform such an interventi ..."
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Cited by 13 (1 self)
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The literature on causal discovery has focused on interventions that involve randomly assigning values to a single variable. But such a randomized intervention is not the only possibility, nor is it always optimal. In some cases it is impossible or it would be unethical to perform such an intervention. We provide an account of “hard ” and “soft” interventions, and discuss what they can contribute to causal discovery. We also describe how the choice of the optimal intervention(s) depends heavily on the particular experimental setup and the assumptions that can be made.
Inferring hidden causes
 In R. Alterman & D. Kirsh (Eds.), Proceedings of the 25th annual meeting of the Cognitive Science Society. Austin, TX: Cognitive Science Society. T. Kushnir et al. ⁄ Cognitive Science 34
, 2003
"... One of the important aspects of human causal reasoning is that from the time we are young children we reason about unobserved causes. How can we learn about unobserved causes from information about observed events? Causal Bayes nets provide a formal account of how causal structure is learned from a ..."
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Cited by 12 (5 self)
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One of the important aspects of human causal reasoning is that from the time we are young children we reason about unobserved causes. How can we learn about unobserved causes from information about observed events? Causal Bayes nets provide a formal account of how causal structure is learned from a combination of associations and interventions. This formalism makes specific predictions about the conditions under which learners postulate hidden causes. In this study adult learners were shown a pattern of associations and interventions on a novel causal system. We found that they were able to infer hidden causes as predicted by the Bayes net formalism, and were able to distinguish between one hidden common cause and two hidden independent causes of the observed events.
Two causal theories of counterfactual conditionals
 Cognitive Science
, 2010
"... Bayes nets are formal representations of causal systems that many psychologists have claimed as plausible mental representations. One purported advantage of Bayes nets is that they may provide a theory of counterfactual conditionals, such as If Calvin had been at the party, Miriam would have left ea ..."
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Cited by 11 (1 self)
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Bayes nets are formal representations of causal systems that many psychologists have claimed as plausible mental representations. One purported advantage of Bayes nets is that they may provide a theory of counterfactual conditionals, such as If Calvin had been at the party, Miriam would have left early. This article compares two proposed Bayesnet theories as models of people’s understanding of counterfactuals. Experiments 13 show that neither theory makes correct predictions about backtracking counterfactuals (in which the event of the ifclause occurs after the event of the thenclause), and Experiment 4 shows the same is true of forward counterfactuals. An amended version of one of the approaches, however, can provide a more accurate account of these data. Counterfactuals, Forward and Backward / 3 1.
Of starships and Klingons: Bayesian logic for 23rd century
 Proc. UAI05
, 2005
"... Intelligent systems in an open world must reason about many interacting entities related to each other in diverse ways and having uncertain features and relationships. Traditional probabilistic languages lack the expressive power to handle relational domains. Classical firstorder logic is sufficien ..."
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Intelligent systems in an open world must reason about many interacting entities related to each other in diverse ways and having uncertain features and relationships. Traditional probabilistic languages lack the expressive power to handle relational domains. Classical firstorder logic is sufficiently expressive, but lacks a coherent plausible reasoning capability. Recent years have seen the emergence of a variety of approaches to integrating firstorder logic, probability, and machine learning. This paper presents Multientity Bayesian networks (MEBN), a formal system that integrates First Order Logic (FOL) with Bayesian probability theory. MEBN extends ordinary
Causality and graphical models in time series
 Richardson (Eds.), Highly Structured Stochastic Systems
, 2003
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Modeling causal learning using Bayesian generic priors on generative and preventive powers
 In R. Sun & N. Miyake (Eds.), Proceedings of the Twentyeighth Annual Conference of the Cognitive Science Society
, 2006
"... We present a Bayesian model of causal learning that incorporates generic priors on distributions of weights representing potential powers to either produce or prevent an effect. These generic priors favor necessary and sufficient causes. Across three experiments, the model explains the systematic pa ..."
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Cited by 9 (4 self)
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We present a Bayesian model of causal learning that incorporates generic priors on distributions of weights representing potential powers to either produce or prevent an effect. These generic priors favor necessary and sufficient causes. Across three experiments, the model explains the systematic pattern of human judgments observed for questions regarding support for a causal link, for both generative and preventive causes.
Causal Reasoning through Intervention
"... Causal knowledge enables us to predict future events, to choose the right actions to achieve our goals, and to envision what would have happened if things had been different. Thus, it allows us to reason about observations, interventions and counterfactual possibilities. ..."
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Cited by 9 (0 self)
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Causal knowledge enables us to predict future events, to choose the right actions to achieve our goals, and to envision what would have happened if things had been different. Thus, it allows us to reason about observations, interventions and counterfactual possibilities.
Using DomainGeneral Principles to Explain Children’s Causal Reasoning Abilities
, 2006
"... A connectionist model of causal attribution is presented, emphasizing the use of domaingeneral principles of processing and learning previously employed in models of semantic cognition. The model categorizes objects dependent upon their observed “causal properties ” and is capable of making several ..."
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Cited by 8 (2 self)
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A connectionist model of causal attribution is presented, emphasizing the use of domaingeneral principles of processing and learning previously employed in models of semantic cognition. The model categorizes objects dependent upon their observed “causal properties ” and is capable of making several types of inferences that fouryearold children have been shown to be capable of. The model gives rise to approximate conformity to normative models of causal inference and gives approximate estimates of the probability that an object presented in an ambiguous situation actually possesses a particular causal power, based on background knowledge and recent observations. It accounts for data from three sets of experimental studies of the causal inferencing abilities of young children. The model provides a base for further efforts to delineate the intuitive mechanisms of causal inference employed by children and adults, without appealing to inherent principles or mechanisms specialized for causal as opposed to other forms of reasoning.