Causal Inference Through the Structural Causal Marginal Problem
This work addresses a foundational problem in causal inference for researchers, though it appears incremental as it builds on existing structural causal model frameworks.
The paper tackles the problem of counterfactual inference by merging information from multiple datasets, introducing a causal reformulation of the statistical marginal problem to determine joint structural causal models consistent with marginal ones. The result shows this approach reduces the space of allowed marginal and joint SCMs, highlighting a new mode of falsifiability through additional variables.
We introduce an approach to counterfactual inference based on merging information from multiple datasets. We consider a causal reformulation of the statistical marginal problem: given a collection of marginal structural causal models (SCMs) over distinct but overlapping sets of variables, determine the set of joint SCMs that are counterfactually consistent with the marginal ones. We formalise this approach for categorical SCMs using the response function formulation and show that it reduces the space of allowed marginal and joint SCMs. Our work thus highlights a new mode of falsifiability through additional variables, in contrast to the statistical one via additional data.