Kweku Opoku-Agyemang
Working Paper Class 64
Economic reasoning is usually directional: we ask what an intervention does to an outcome. But economists also routinely face the reverse problem—given an observed outcome, what can be learned about the causal state that produced it? This paper develops a theory of when such causal reversal is possible, what information a forward causal mechanism destroys, and how much additional information is required for reconstruction. For a structural causal mechanism, we associate each latent state with its complete response to interventions on the causal antecedent. This response-function map induces a canonical causal quotient: latent states that generate the same response to every intervention are identified. We show that this quotient is the minimal latent object relevant for structural inversion. Exact inverse recovery has two distinct sources of difficulty: the mechanism may be structurally noninvertible, or the causally relevant latent information may be unavailable. We then characterize how much of this latent ambiguity is revealed by the observed outcome. Under regularity conditions, the information revealed by the outcome equals the reduction in the intrinsic dimension of the unresolved causal state. Finally, we define an inverse-causal rate-distortion function that measures the minimum additional information required to reconstruct the causal antecedent at a given resolution. Its high-resolution behavior is governed by the dimension of the unresolved causal state. The resulting theory provides a unified characterization of causal reversibility, causal information loss, and inverse information requirements, linking structural causal models, information theory, differential geometry, and inverse problems.
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Opoku-Agyemang, Kweku A. (2026). "Causal Information Loss and the Inverse Problem: A Theory of Latent Information, Causal Revelation and Reversibility." Machine Learning X Doing Working Paper Class 64. Machine Learning X Doing.
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