We consider testing and learning problems on causal Bayesian networks as defined by Pearl (Pearl, 2009). Given a causal Bayesian network M on a graph with n discrete variables and bounded in-degree and bounded confounded components'', we show that O(log n) interventions on an unknown causal Bayesian network X on the same graph, and O(n/epsilon 2) samples per intervention, suffice to efficiently distinguish whether X M or whether there exists some intervention under which X and M are farther than epsilon in total variation distance. We also obtain sample/time/intervention efficient algorithms for: (i) testing the identity of two unknown causal Bayesian networks on the same graph; and (ii) learning a causal Bayesian network on a given graph. Although our algorithms are non-adaptive, we show that adaptivity does not help in general: Omega(log n) interventions are necessary for testing the identity of two unknown causal Bayesian networks on the same graph, even adaptively. Our algorithms are enabled by a new subadditivity inequality for the squared Hellinger distance between two causal Bayesian networks.
Judea Pearl was the first to propose a definition of actual causation using causal models. A number of authors have suggested that an adequate account of actual causation must appeal not only to causal structure, but also to considerations of normality. In earlier work, we provided a definition of actual causation using extended causal models, which include information about both causal structure and normality. Extended causal models are potentially very complex. In this paper, we show how it is possible to achieve a compact representation of extended causal models.
Consider a policymaker who wants to decide which intervention to perform in order to change a currently undesirable situation. The policymaker has at her disposal a team of experts, each with their own understanding of the causal dependencies between different factors contributing to the outcome. The policymaker has varying degrees of confidence in the experts’ opinions. She wants to combine their opinions in order to decide on the most effective intervention. We formally define the notion of an effective intervention, and then consider how experts’ causal judgments can be combined in order to determine the most effective intervention. We define a notion of two causal models being compatible , and show how compatible causal models can be combined. We then use it as the basis for combining experts causal judgments. We illustrate our approach on a number of real-life examples.
Structural causal models are a popular tool to describe causal relations in systems in many fields such as economy, the social sciences, and biology. In this work, we show that these models are not flexible enough in general to give a complete causal representation of equilibrium states in dynamical systems that do not have a unique stable equilibrium independent of initial conditions. We prove that our proposed generalized structural causal models do capture the essential causal semantics that characterize these systems. We illustrate the power and flexibility of this extension on a dynamical system corresponding to a basic enzymatic reaction. We motivate our approach further by showing that it also efficiently describes the effects of interventions on functional laws such as the ideal gas law.
This paper describes a Bayesian method for combining an arbitrary mixture of observational and experimental data in order to learn causal Bayesian networks. Observational data are passively observed. Experimental data, such as that produced by randomized controlled trials, result from the experimenter manipulating one or more variables (typically randomly) and observing the states of other variables. The paper presents a Bayesian method for learning the causal structure and parameters of the underlying causal process that is generating the data, given that (1) the data contains a mixture of observational and experimental case records, and (2) the causal process is modeled as a causal Bayesian network. This learning method was applied using as input various mixtures of experimental and observational data that were generated from the ALARM causal Bayesian network. In these experiments, the absolute and relative quantities of experimental and observational data were varied systematically. For each of these training datasets, the learning method was applied to predict the causal structure and to estimate the causal parameters that exist among randomly selected pairs of nodes in ALARM that are not confounded. The paper reports how these structure predictions and parameter estimates compare with the true causal structures and parameters as given by the ALARM network.