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.

Bayesian network on a given graph.

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.

Bayesian network on a given graph.

A DAG is a directed graph with no directed paths starting and ending at the same node.

A DAG is a directed graph with no directed paths starting and ending at the same node.

Causal models are crucial for understanding complex systems andidentifying causal relationships among variables. Even though causalmodels are extremely popular, conditional probability calculation offormulas involving interventions pose significant challenges.In case of Causal Bayesian Networks (CBNs), Pearl assumes autonomy of mechanisms that determine interventions to calculate a range ofprobabilities. We show that by making simple yetoften realistic independence assumptions, it is possible to uniquely estimate the probability of an interventional formula (includingthe well-studied notions of probability of sufficiency and necessity). We discuss when these assumptions are appropriate.Importantly, in many cases of interest, when the assumptions are appropriate,these probability estimates can be evaluated usingobservational data, which carries immense significance in scenarioswhere conducting experiments is impractical or unfeasible.

Ensuring safe operation of safety-critical complex systems interacting with their environment poses significant challenges, particularly when the system's world model relies on machine learning algorithms to process the perception input. A comprehensive safety argumentation requires knowledge of how faults or functional insufficiencies propagate through the system and interact with external factors, to manage their safety impact. While statistical analysis approaches can support the safety assessment, associative reasoning alone is neither sufficient for the safety argumentation nor for the identification and investigation of safety measures. A causal understanding of the system and its interaction with the environment is crucial for safeguarding safety-critical complex systems. It allows to transfer and generalize knowledge, such as insights gained from testing, and facilitates the identification of potential improvements. This work explores using causal Bayesian networks to model the system's causalities for safety analysis, and proposes measures to assess causal influences based on Pearl's framework of causal inference. We compare the approach of causal Bayesian networks to the well-established fault tree analysis, outlining advantages and limitations. In particular, we examine importance metrics typically employed in fault tree analysis as foundation to discuss suitable causal metrics. An evaluation is performed on the example of a perception system for automated driving. Overall, this work presents an approach for causal reasoning in safety analysis that enables the integration of data-driven and expert-based knowledge to account for uncertainties arising from complex systems operating in open environments.