Operationalising Relative Causal Knowledge: Backbone Identifiability from Private Reports on a Shared Outcome

2026-08-11

AI Summary

In multi-agent settings with shared outcomes, each agent possesses only marginal causal information about a single cause of the common outcome, which is generally insufficient to uniquely identify the underlying causal skeleton required for joint interventions. This work demonstrates that, under standard assumptions, such local causal knowledge alone cannot guarantee unique identifiability of the skeleton. However, by imposing an additive separability condition and allowing agents to exchange their causal response functions, unique identification becomes achievable under certain conditions. Leveraging structural causal models, intervention kernel analysis, and residual summarization techniques, the study elucidates the inherent limitations of purely local information and introduces a novel identification strategy based on communication of response functions, thereby establishing a theoretical foundation for distributed causal discovery.

Abstract

The Relativity of Causal Knowledge (RCK) explains how a network of agents with different structural causal models can exchange causal knowledge through a shared interventionally consistent abstraction, or backbone. We ask the prior identification question that this transport mechanism presupposes: when is that backbone determined by the agents' private causal knowledge? In the basic two-agent common-effect case, two private causes influence one shared outcome and each agent identifies only the single-cause causal marginal relevant to its own perspective. We show that, under standard compatibility, non-degeneracy, and local overlap assumptions, those local causal marginals do not identify a unique backbone. Infinitely many joint intervention kernels can induce exactly the same private reports while disagreeing on joint interventions. We then give a conditional recovery result. Additive separability removes the hidden interaction degree of freedom, but observational residual summaries remain insufficient. Identification becomes possible when agents communicate causally identified response functions. An education value-added example illustrates why this is first a communication problem, and only then a policy-composition problem.

Problem

• causal identifiability
• shared outcome
• private causal knowledge
• backbone
• multi-agent causal inference

Innovation

• causal backbone identifiability
• relative causal knowledge
• private causal reports
• additive separability
• interventional consistency