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We propose an approach to estimate the effect of multiple simultaneousinterventions in the presence of hidden confounders. To overcome the problem ofhidden confounding, we consider the setting where we have access to not onlythe observational data but also sets of single-variable interventions in whicheach of the treatment variables is intervened on separately. We proveidentifiability under the assumption that the data is generated from anonlinear continuous structural causal model with additive Gaussian noise. Inaddition, we propose a simple parameter estimation method by pooling all thedata from different regimes and jointly maximizing the combined likelihood. Wealso conduct comprehensive experiments to verify the identifiability result aswell as to compare the performance of our approach against a baseline on bothsynthetic and real-world data.

Learning Joint Nonlinear Effects from Single-variable Interventions in the Presence of Hidden Confounders